Bikash Sahoo
email: bikashsahoo@nitrkl.ac.in

Saeid Abbasbandy
email: abbasbandy@yahoo.com

Sébastien Poncet
email: sebastien.poncet@univ-amu.fr

A brief note on the computation of the Bödewadt flow with Navier slip boundary conditions

Keywords: Rotating flow, Partial slip, Finite difference method, Keller-box method MSC codes here, 76U05, 76A05, 34B15

In this short communication, numerical solutions are obtained for the steady Bödewadt flow of a viscous fluid subject to partial slip boundary conditions. The resulting system of nonlinear and fully coupled similarity equations are integrated accurately by a finite difference scheme and by the Keller-box method. It is observed that slip has a prominent effect on the velocity field, reducing drastically the axial velocity and the pressure. Moreover, the torque required to maintain the disk at rest decreases for increasing values of slip.

Introduction

The steady laminar flow of a viscous incompressible fluid near a rotating disk, originally solved by von Kármán [START_REF] Th | Über laminare und turbulente Reibung[END_REF], is one of the few problems in fluid dynamics for which the Navier-Stokes equations admit an exact solution. The twin problem arising when the fluid rotates with a uniform angular velocity at a large distance from a stationary disk, is known as the Bödewadt flow. This problem, for a viscous incompressible fluid, also admits an exact solution for the Navier-Stokes equations, subject to the conventional no-slip boundary conditions, as shown theoretically by Bödewadt [START_REF] Bödewadt | Die Drehströmung über festem Grunde[END_REF]. The flow is characterized by the radial pressure gradient being balanced by the centrifugal forces. Fluid flows towards the axis of rotation and swepts upwards. The boundary layer, which develops on the disk, produces a secondary flow of stagnation type in the von Kármán case and of wake type in the Bödewadt problem. Batchelor [START_REF] Batchelor | Note on the class of solutions of the Navier-Stokes equations representing staedy non-rotationally symmetric flow[END_REF] suggested that for large Reynolds numbers, the rotor-stator flow consists of boundary layers on each disk separated by a core of fluid rotating as a solid body. It can be seen as the connection of a Von Kármán flow along the rotor with a Bödewadt flow along the stator. Nowadays, this type of flow still receives a constant attention by the introduction of more complex and combined phenomena: heat transfer, non-Newtonian fluid [START_REF] Sahoo | Steady Bödewadt flow of a non-Newtonian Reiner-Rivlin fluid[END_REF][START_REF] Sahoo | Steady revolving flow and heat transfer of a non-Newtonian Reiner-Rivlin fluid[END_REF], magnetic field or partial slip.

All the studies mentioned above admit no-slip condition on the walls, which is more a hypothesis than a condition deduced from any principle. Evidence of the fluid slip on a solid surface has been reported by Matthews and Hill [START_REF] Matthews | Newtonian flow with nonlinear Navier boundary condition[END_REF]. For example, if one considers a zero-thickness disk admitting a stress-free condition on its surface and rotating around its axis, it does not modify the motion of the surrounding fluid, which would remain at rest. It confirms an intuitive result that the boundary condition on the disk plays a key role on the fluid motion. Slip condition has also some industrial relevance when the fluid is composed of emulsions, suspensions, foams or polymer solutions. In other situations where the wall surface is rough, the no-slip boundary condition also becomes impractical to apply exactly. The proper boundary condition is then well described by the general Navier's condition [START_REF] Navier | Sur les lois du mouvement des fluides[END_REF], where the amount of relative slip is proportional to the local shear stress through the slip length(es). If the characteristic scale of roughness is small compared to the boundary layer thickness, the no-slip condition may be well approximated by a partial slip condition [START_REF] Navier | Sur les lois du mouvement des fluides[END_REF]. Miklavčič and Wang [START_REF] Miklavčič | The flow due to a rough rotating disk[END_REF] have considered the von Kármán swirling flow of a viscous fluid with slip boundary condition. More recently, Sherwood [START_REF] Sherwood | Resistance coefficients for Stokes flow around a disk with a Navier slip condition[END_REF] solved the flow due to a zero-thickness disk rotating around its axis by the use of Hankel transforms. The combined effects of slip and non-Newtonian cross-viscous parameter on the rotating flows past free rotating disks have been thoroughly studied by Sahoo [START_REF] Sahoo | Effects of partial slip, viscous dissipation, Joule heating on Von Kármán flow and heat transfer of an electrically conducting non-Newtonian fluid[END_REF] and Sahoo and Poncet [START_REF] Sahoo | Effects of slip on steady Bödewadt flow of a non-Newtonian fluid[END_REF].

A literature survey shows that no particular attention has been paid to the effects of slip on the Bödewadt flow of a viscous fluid. The present work is devoted to study the effects of slip on the steady Bödewadt flow of a viscous fluid. A second order finite difference method and an effective Keller box method are used to solve the fully coupled and highly nonlinear differential equations. The present paper is a step forward in the computation of the rotor-stator flow with partial slip effects to establish reference solutions for numerical benchmarks.

Formulation of the problem

One considers a viscous fluid occupying the space z > 0 over an infinite stationary disk, which coincides with z = 0. The motion is due to the rotation of the fluid like a rigid body with constant rotation rate Ω at a large distance from the disk. One shall assume that the principal directions of the roughness are the radial and azimuthal, i.e. a concentrically grooved disk [START_REF] Miklavčič | The flow due to a rough rotating disk[END_REF], but the results could also apply to the case of a randomly rough disk. The flow is described in the cylindrical polar coordinates (r, φ, z) with the rotational symmetry, ∂ ∂φ ≡ 0. Let V = (u, v, w) be the fluid velocity vector. Considering the usual boundary layer approximations and using the similarity transform [START_REF] Th | Über laminare und turbulente Reibung[END_REF]:

u = rΩF (ζ), v = rΩG(ζ), w = √ ΩνH(ζ), z = √ ν Ω ζ, p -p ∞ = -ρνΩP
(1) the equations of continuity and motion take the form [START_REF] Bödewadt | Die Drehströmung über festem Grunde[END_REF][START_REF] Owen | Flow and heat transfer in rotating disk systems[END_REF]:

dH dζ + 2F = 0, (2)
d 2 F dζ 2 -H dF dζ -F 2 + G 2 = 1, (3)
d 2 G dζ 2 -H dG dζ -2F G = 0, ( 4
)
dP dζ -H dH dζ + d 2 H dζ 2 = 0 (5)
The no-slip boundary conditions in terms of similarity variables become,

ζ = 0 : F = 0, G = 0, H = 0, ζ → ∞ : F → 0, G → 1, P → 0. (6)
A generalization of the Navier's partial slip condition [START_REF] Navier | Sur les lois du mouvement des fluides[END_REF][START_REF] Miklavčič | The flow due to a rough rotating disk[END_REF] gives, in the radial and azimuthal directions:

u| z=0 = λ 1 τ rz | z=0 (7) v| z=0 = λ 2 τ φz | z=0 (8)
where λ 1 , λ 2 are the slip coefficients, and τ rz , τ φz are the physical components of the stress tensor. One defines the dimensionless slip coefficients as:

λ = λ 1 √ Ω ν µ, η = λ 2 √ Ω ν µ. (9)
With the help of the transformations (1), the corresponding partial slip boundary conditions ( 7)-( 8) become:

F (0) = λF ′ (0), G(0) = ηG ′ (0), H(0) = 0, (10) F (∞) → 0, G(∞) → 1, P (∞) → 0.

Finite difference solution

The finite difference method (FDM) has been used to solve the system of coupled nonlinear Eqs. ( 2)-( 5) subject to the slip boundary conditions [START_REF] Sherwood | Resistance coefficients for Stokes flow around a disk with a Navier slip condition[END_REF]. The semi-infinite domain [0, ∞) is replaced by a finite domain [0, ζ ∞ ), with ζ ∞ sufficiently large so that the numerical solution closely approximates the terminal boundary conditions. One approximates the functions and their derivatives by their finite difference counterparts to solve a sequence of linear systems.

1. One solves:

F ′′ -H (k) F ′ = (F (k) ) 2 -(G (k) ) 2 + 1 ( 11
)
using the derivative boundary conditions [START_REF] Sherwood | Resistance coefficients for Stokes flow around a disk with a Navier slip condition[END_REF] and denotes the solution of (11) as F (k+1) . To obtain convergence, one defines F (k+1) by the following smoothing formula:

F (k+1) = α 1 F (k+1) + (1 -α 1 ) F (k) , 0 ≤ α 1 ≤ 1 (12)
2. The same procedure is successively used for the G and H components and then for the pressure P :

G ′′ -H (k) G ′ = 2F (k+1) G (k) (13)
G (k+1) = α 2 G(k+1) + (1 -α 2 ) G(k) , 0 ≤ α 2 ≤ 1 (14) H ′ = -2F (k+1) (15) H (k+1) = α 3 H(k+1) + (1 -α 3 ) H(k) , 0 ≤ α 3 ≤ 1 (16) P ′ -2F ′ = -2H (k+1) F (k+1) (17) P (k+1) = α 4 P (k+1) + (1 -α 4 ) P (k) , 0 ≤ α 4 ≤ 1 (18)
3. The iterations start with suitable initial guesses F (0) , G (0) and H (0) , borrowed from the work by Sahoo and Poncet [START_REF] Sahoo | Effects of slip on steady Bödewadt flow of a non-Newtonian fluid[END_REF].

If (F (k+1) , F (k) ), (G (k+1) , G (k) ), (H (k+1) , H (k)
) and (P (k+1) , P (k) ) are close enough to each other, one stops, otherwise one sets k = k + 1 and goes back to step 1.

In order to solve the above system of equations by finite difference method, we introduce a grid in 0 ≤ ζ ≤ ζ ∞ by dividing it into n equal parts with a mesh size h equal to 0.01. It has been verified that this value guarantees a grid independent solution. One approximates the derivatives by:

F ′ (ζ i ) = F i+1 -F i-1 2h , F ′′ (ζ i ) = F i+1 -2F i + F i-1 h 2 , i = 1, 2, . . . n -1 (19)
In order to obtain a diagonally dominant linear algebraic system for Eqs. [START_REF] Sahoo | Effects of partial slip, viscous dissipation, Joule heating on Von Kármán flow and heat transfer of an electrically conducting non-Newtonian fluid[END_REF] and (13), F ′ and G ′ are discretized by backward difference approximations as H (k+1) i > 0 for Bödewadt flow. One obtains:

[1 + hH (k) i ]F i-1 + [-2 -hH (k) i ]F i + F i+1 = h 2 [(F (k) ) 2 -(G (k) ) 2 + 1] (20) [1 + hH (k) i ]G i-1 + [-2 -hH (k) i ]G i + G i+1 = 2h 2 F (k+1) i G k i (21)
Finally, Eqs. ( 15) and ( 17) are discretized by central difference approximations. The above algebraic system is solved by a generalized Gauss-Seidel method instead of a successive over relaxation method. The convergence of the generalized Gauss-Seidel method for the above diagonally dominant system is reached after 15 iterations to achieve an accuracy of O(10 -6 ). The FORTRAN 90 code was compiled and run using the NIT Rourkela server composed of Dual Intel Xeon (8 Gb RAM, 4 Gbps Lan card).

Solution by Keller-box method

The nonlinear Eqs. ( 3)-( 4), by considering [START_REF] Bödewadt | Die Drehströmung über festem Grunde[END_REF], are reduced to:

d 3 H dζ 3 -H d 2 H dζ 2 + 1 2 ( dH dζ ) 2 -2G 2 + 2 = 0, ( 22
)
d 2 G dζ 2 -H dG dζ + G dH dζ = 0, (23)
and boundary conditions [START_REF] Sherwood | Resistance coefficients for Stokes flow around a disk with a Navier slip condition[END_REF] are converted to:

H ′ (0) = λH ′′ (0), G(0) = ηG ′ (0), H(0) = 0, H ′ (∞) → 0, G(∞) → 1. ( 24
)
New dependent variables S(ζ), Q(ζ) and T (ζ) are introduced such that the Eqs. ( 22)-( 23) can be written as:

dH dζ = S(ζ), (25)
dS dζ = Q(ζ), (26)
dG dζ = T (ζ), (27)
dQ dζ -HQ + 1 2 S 2 -2G 2 + 2 = 0, (28)
dT dζ -HT + SG = 0. ( 29
)
The boundary conditions (24) become:

S(0) = λQ(0), G(0) = ηT (0), H(0) = 0, S(∞) → 0, G(∞) → 1. ( 30
)
One considers the segment [ζ j-1 , ζ j ], with the midpoint ζ j-1/2 :

ζ 0 = 0, ζ j = ζ j-1 + h, ζ J = ζ ∞ , (31)
where h = 0.01 is the ∆ζ-spacing and j = 1, 2, • • • , J is a sequence number that indicates the coordinate location. The finite difference approximations of Eq. ( 25)-( 29) are written at the midpoint ζ j-1/2 , as:

H j -H j-1 - 1 2 h(S j + S j+1 ) = 0, (32)
S j -S j-1 - 1 2 h(Q j + Q j+1 ) = 0, (33)
G j -G j-1 - 1 2 h(T j + T j+1 ) = 0, (34)
Q j -Q j-1 - 1 4 h(H j + H j-1 )(Q j + Q j-1 ) + 1 8 h(S j + S j-1 ) 2 - 1 2 h(G j + G j-1 ) 2 + 2h = 0, (35)
T j -T j-1 - 1 4 h(H j + H j-1 )(T j + T j-1 ) + 1 4 h(S j + S j-1 )(G j + G j-1 ).
The Eqs.( 32)-( 36) are imposed for j = 1, 2, • • • , J for sufficiently large ζ ∞ . The boundary conditions (30) are converted to:

S 0 = λQ 0 , G 0 = ηT 0 , H 0 = 0, S J = 0, G J = 1. ( 37
)
One can linearize the nonlinear system (32)-( 36) by the Newton's method, and the linearized system, which has a block-tridiagonal structure, can then be solved by the block elimination method. The MATHEMATICA code for the Keller-box method was run on a 64-bit Windows machine with Intel Core i7 and 3.4 GHz processor.

Results and discussions

To validate the two numerical approaches, the values of F , G and H for the no-slip case (λ = η = 0) are compared to those reported by Owen and Rogers [START_REF] Owen | Flow and heat transfer in rotating disk systems[END_REF] in Table 1. An excellent agreement is thus obtained with relative differences of the extrema far less than 0.01%.

In order to have an insight of the effects of slip on the Bödewadt flow, results are shown for the uniform roughness (λ = η) using the finite difference method only. More comparisons between the two approaches are provided at the end of this section. It is noteworthy that, for other combinations of λ and η (not shown here), the behavior remains the same. Figs. 1a to 1c show the effects of slip on the velocity field. Fig. 1a shows the variation of the radial velocity component F with the slip parameter λ. The effect of slip on F is prominent near the disk. Clearly, the maximum value of the radial inflow decreases with an increase in slip and its location moves towards the disk. The radial velocity gets positive away from the disk and approaches the asymptotic value at a shorter distance from the disk for larger λ. Multiple cross-overs are observed for the radial velocity profiles. Fig. 1b shows the azimuthal velocity G(ζ). Its value increases with ζ, reaches its maximum, then decreases and reaches its asymptotic value G = 1. One can observe that G increases with an increase in slip, near the disk and decreases away from the disk, as expected. The oscillations occurring in the boundary layer when the fluid rotates near a stationary disk can be explained in the following manner. The radial inflow, induced by a low tangential velocity in the vicinity of the stationary disk, tends to conserve the angular momentum and thus tends to increase the tangential velocity with decreasing radius. For an overshoot, radial advection of the angular momentum near the disk must be strong enough to do more than balancing the dissipation of angular momentum caused by the wall shear. This inward radial advection of surplus angular momentum is possible as long as the distribution of circulation in the outer flow increases with increasing radius. A local overshoot in the tangential velocity increases the centrifugal force locally which then tends to induce a radial outflow. This radial outflow convects an angular momentum defect to force an undershoot in the tangential velocity, and the above process is repeated to yield oscillatory approach to infinity. The variation of the axial velocity component H with λ can be seen in Fig. 1c. It is observed that H decreases significantly with an increase in slip. The axial profiles become flatter with an increase in λ. The axial velocity at infinity, H ∞ is strongly reduced compared to the no-slip case λ = 0, for which H ∞ = 1.349421. It is interesting to find that slip dominates oscillations in the velocity profiles.

The prominent effect of slip on the pressure distribution can be observed in Fig. 1d. It is evident that in absence of slip, for λ(= η) = 0, the dimensionless pressure P has a dominating effect near the stationary disk. This induces a radial inward flow near the disk surface. Pressure decreases with an increase in slip near the disk and consequently, the strength of the radial inflow decreases, as shown in Fig. 1a. In presence of slip, the pressure profiles attain their asymptotic value P = 0 closer to the disk surface.

The tangential τ φ and radial τ r shear stresses and the dimensionless moment coefficient C m are defined as:

τ φ = τ φ ρr √ νΩ 3 = G ′ (0), τ r = τ r ρr √ νΩ 3 = F ′ (0), C m = -πG ′ (0) √ R (38)
where R = R 2 Ω ν is the Reynolds number based on the radius and the tip velocity. Throughout the computation, the value of R has been fixed as R = 1. This definition of C m is an extension of the finite disk problem, which supposes that the disk radius is large enough. In the following, these three quantities, denoted with * , are normalized by their value obtained for λ = 0, such that

C * m (λ) = C m (λ)/C m (λ = 0) for example.
Figure 2 depicts the effects of slip on the normalized surface shear stress in the radial direction τ * r and compares the finite difference and Keller box methods. It is noticeable that τ r remains negative throughout the range of the slip parameter with τ r (λ = 0) = -0.941971. The present results show that the magnitude of τ * r decreases with an increase in λ. It is also reduced by a factor 4 between λ = 0 and λ = 1. The tangential shear stress τ * φ and the moment coefficient C * m in their dimensionless form are strictly equal. Figure 2 shows that they both decrease with an increase in slip. τ φ remains always positive for the entire range of slip parameter with τ φ (λ = 0) = 0.772886. On the contrary, C m exhibits negative values with C m (λ = 0) = -2.428092. It may be attributed to the flow problem. The Von Kármán flow considered by Sahoo [START_REF] Sahoo | Effects of partial slip, viscous dissipation, Joule heating on Von Kármán flow and heat transfer of an electrically conducting non-Newtonian fluid[END_REF] is precisely the inverse problem, which explains the different signs for C m . It is important to note that the linear nature of the τ * r , τ * φ and C * m profiles for the current viscous flow is contrary to corresponding profiles for non-Newtonian flows [START_REF] Sahoo | Effects of partial slip, viscous dissipation, Joule heating on Von Kármán flow and heat transfer of an electrically conducting non-Newtonian fluid[END_REF][START_REF] Sahoo | Effects of slip on steady Bödewadt flow of a non-Newtonian fluid[END_REF]. This may be due to the presence of extra nonlinear terms in the expressions for τ r , τ φ and C m , associated with the non-Newtonian cross-viscous parameter [START_REF] Sahoo | Effects of partial slip, viscous dissipation, Joule heating on Von Kármán flow and heat transfer of an electrically conducting non-Newtonian fluid[END_REF][START_REF] Sahoo | Effects of slip on steady Bödewadt flow of a non-Newtonian fluid[END_REF]. For these three quantities, there is an excellent agreement between the finite difference and the Keller-box methods.

To compare the efficiency of the aforementioned two numerical schemes, Table 2 shows the CPU time (in seconds) for different values of the slip parameter and a given mesh distribution (ζ ∞ = 14 and h = 0.01). Though the FDM is more effective than the KBM in some sense, the CPU time for the FDM is significantly much higher as compared to the Keller-box method. It should be taken with certain caution as the methods have been run using different machines with different configurations. However, the calculations remain quite fast and for both schemes, the CPU time increases with an increase in λ.

Conclusions

In this brief note, an effective second order finite difference method and the Keller box method are adopted to solve the system of coupled, highly nonlinear differential equations, arising due to the Bödewadt flow of a viscous fluid, subject to partial slip boundary conditions. It is found that slip decreases the radial inflow near the disk. With an increase in slip, the azimuthal velocity G increases near the disk and decreases away from the disk. It is also observed that slip dominates the oscillations in the velocity profiles. One of the significant findings of the present study is that the moment coefficient C m , which is a measure of the torque required to maintain the disk at rest, decreases with an increase in slip.

Figure 1 :

 1 Figure 1: Variation with λ(= η) of (a) F, (b) G, (c) H and (d) P. Results obtained using the FDM.

Figure 2 :

 2 Figure 2: Variations of τ * r , τ * φ (= C * m ) with λ(= η). Comparisons between the FDM (lines) and the Keller box method (symbols).

Table 1 :

 1 Variations of F , G and H for λ(= η) = 0.

			F			G			H
	ζ	FDM	Keller-Box	Owen & Rogers [4]	FDM	Keller-Box	Owen & Rogers [4]	FDM	Keller-Box	Owen & Rogers [4]
	0.0	0.000000	0.000000	0.0000	0.000000	0.000000	0.0000	0.000000	0.000000	0.0000
	0.5	-0.348651	-0.348651	-0.3487	0.383430	0.383427	0.3834	0.194374	0.194365	0.1944
	1.0	-0.478766	-0.478769	-0.4788	0.735429	0.735425	0.7354	0.624103	0.624090	0.6241
	1.5	-0.449634	-0.449639	-0.4496	1.013401	1.013399	1.0134	1.098743	1.098730	1.0987
	2.0	-0.328745	-0.328751	-0.3287	1.192367	1.192368	1.1924	1.492876	1.492870	1.4929
	2.5	-0.176207	-0.176210	-0.1762	1.272136	1.272140	1.2721	1.745870	1.745870	1.7459
	3.0	-0.036086	-0.036088	-0.0361	1.271405	1.271411	1.2714	1.849641	1.849640	1.8496
	3.5	0.066311	0.066310	0.0663	1.218219	1.218225	1.2182	1.830807	1.830810	1.8308
	9.5	-0.010216	-0.010217	-0.0102	1.011849	1.011850	1.0118	1.361698	1.361690	1.3617
	10.0	-0.003282	-0.003283	-0.0033	1.012120	1.012121	1.0121	1.368330	1.368320	1.3683
	10.5	0.001820	0.001819	0.0018	1.009906	1.009907	1.0099	1.368882	1.368880	1.3689
	11.0	0.004738	0.004738	0.0047	1.006537	1.006537	1.0065	1.365423	1.365420	1.3654
	11.5	0.005681	0.005681	0.0057	1.003090	1.003090	1.0031	1.360067	1.360060	1.3601
	12.0	0.005170	0.005171	0.0052	1.000271	1.000272	1.0003	1.354546	1.354540	1.3545
	12.5	0.003827	0.003827	0.0038	0.998411	0.998411	0.9984	1.350003	1.350000	1.3500
	20.0	0.000102	0.000102	-	0.999893	0.999893	-	1.349325	1.349320	-
	25.0	0.000009	0.000009	-	1.000014	1.000013	-	1.349457	1.349450	-
	25.5	0.000011	0.000011	-	1.000007	1.000007	-	1.349447	1.349440	-
	26.0	0.000010	0.000010	-	1.000001	1.000001	-	1.349437	1.349430	-
	26.5	0.000008	0.000008	-	0.999997	0.999997	-	1.349428	1.349420	-
	28.0	0.000000	0.000000	0.0000	1.000000	1.000000	1.0000	1.349421	1.349410	1.3494

Table 2 :

 2 Tabulation of CPU time (in seconds) for different values of λ(= η) for 15 iterations.

	λ(= η)	FDM	Keller-box method
	0	820.2	21.5
	1	852.6	21.7
	2	906.6	25.6
	3	931.8	25.7


Eric Verdeil
email: eric.verdeil@normalesup.org

The energy of revolts in Arab cities. The case of Jordan and Tunisia

Keywords: electricity, urban metabolism, urban protest, neoliberalism, basic infrastructure

Energy has become a new urban public issue in Arab cities and, hence, the trigger of new claims, mobilizations, and even revolts or riots. This article proposes another approach of energy politics. In my view, a set of transformations in energy circuits are directly involved in the 'urbanization' of energy issues. By such a phrase, I mean different processes that reframe and rescale energy issues, usually national and international ones, at the level of the city. Energy reliability and affordability are new claims in the political arena in many Arab cities. Based on earlier research in Tunisia and Jordan, the article examines how policies of electrification in Arab cities have created a new metabolism associated with new power relations, specifically enhancing State legitimacy through symbolical and economical means. But the neoliberal turn in electricity policies, coupled with fossil fuel prices pressures, is undoing this pact. Claims for affordable prices and effective power supply have been fostered in the context of the current uprisings. Grid-embedded resistance practices by ordinary people (customers or workers), which are analyzed in this article, put new light on the vulnerability of urban electricity circuits.

Energy issues are among the usual geopolitical concerns associated with Middle East politics, the oil supply being at the core of the economy of many Arab countries. But the emphasis on the regional and international dimensions of such a problem hides the fact that energy has become a new urban public issue in Arab cities and, hence, this article contends, the trigger of new claims, mobilizations, and even revolts or riots. Some authors have already linked the Arab Spring movements to the transformations in oil politics [START_REF] Achcar | The People Want: A Radical Exploration of the Arab Uprising[END_REF][START_REF] Mitchell | Carbon democracy : political power in the age of oil[END_REF]. The peak oil and the subsequent decrease of income from oil would have been a major driver of the Arab revolts because of the resulting destabilisation of the social contract between States and their constituencies, where these States were funding cheap public services and public employment thanks to oil rent. Whatever one can think about this explanation, it can be stated that it makes no room for the spatiality of these movements, and specifically their urban dimension which several studies and this thematic issue are beginning to delve into [START_REF] Allegra | Rethinking Cities in Contentious Times: The Mobilisation of Urban Dissent in the « Arab Spring[END_REF]Verdeil 2011a) In this article, the aim is to explore another approach of energy politics. In my view, a set of transformations in energy circuits are directly involved in the 'urbanization' of energy issues. By such a phrase, I mean different processes that reframe and rescale energy issues, usually national and international ones, at the level of the city. I am not implying that urban or metropolitan authorities are now becoming key actors in managing energy. Such emerging trends are being observed in several world cities but this is affecting Global Southern cities very marginally [START_REF] Bulkeley | Cities and Low Carbon Transitions 1 re éd[END_REF][START_REF] Hodson | World cities and climate change : producing urban ecological security[END_REF][START_REF] Rutherford | Urban Energy Transitions: Places, Processes and Politics of Sociotechnical Change[END_REF]. The well recognized lack of autonomy and of financial means of urban and metropolitan governance in Arab Cities [START_REF] Signoles | Réformes de l'Etat et transformation de l'action publique[END_REF]United Cities and Local Governements 2008) makes the existence of such urban or metropolitan energy policies very unlikely. Nevertheless, Arab cities rely increasingly, like elsewhere, upon complex energy infrastructures and experiment a growing demand for energy, stirred by State policies of electrification, increasing demographics and new middle class habits specifically found in urban areas. Such an 'interaction between urban change and the transformation of [the energy system] can be labeled as an urban energy transition' (Rutherford & Coutard 2013, p.3). At the same time, the energy stress caused by rising hydrocarbons prices and peak oil threats has placed claims for energy reliability and affordability in the political arena in many Arab cities. The urbanization of energy issues is then both material and political. Such claims have gained momentum with other political mobilizations and have fueled the current Arab revolts.

In order to deepen the hypothesis of an 'urbanization' of energy issues, this article attempts to understand energy transitions as political processes embedded in the materiality of energy circuits. It highlighs the intersection of such circuits with the urban, conceived of as a site of metabolic relationships where political struggle for the use of energy takes place. To fit with the requested size of the article, I present an overview on findings from on-going research in Jordan and Tunisia in recent years. Further details about field methodology and empirical findings are to found in the following references (Verdeil 2011b;Verdeil 2013a;Bennasr & Verdeil forthcoming).

Energy transition and urban metabolism: the case of electricity

Far being technical and managerial processes, energy transitions are widely recognized as political and contested processes [START_REF] Rutherford | Urban Energy Transitions: Places, Processes and Politics of Sociotechnical Change[END_REF][START_REF] Bulkeley | Governing urban low carbon transitions[END_REF][START_REF] Hodson | World cities and climate change : producing urban ecological security[END_REF]. By examining successively the transition from biomass to coal and then from coal to oil, Timothy Mitchell's book on Carbon Democracy has provided a inspiring account that links this political dimension to the particular materiality of energy circuits [START_REF] Mitchell | Carbon democracy : political power in the age of oil[END_REF]). This linkage is fruitful for the purpose of this article. He defines his approach as to 'follow closely a set of connections that were engineered over the course of a century between carbon fuels and certain kinds of democratic and undemocratic politics ' (p.252). He states that 'exploring the properties of oil, the networks along which it flowed, and the connections established between the flows of energy, finance and other objects provides a way to understand how the relations between these various elements and forces were constructed. The relations connected energy and politics, materials and ideas, humans and nonhumans, calculations and the objects of calculation, representations and forms of violence, the present and the future' (p.253).

The mapping of these circuits allows for identifying the spatial and physical components of the networks as well as understanding the political and contested nature of the connections through which rests the continued circulation of energy at different points of the networks. A fundamental point of Mitchell's analysis is the unraveling of the vulnerability associated to these connections. This vulnerability is to be understood as socially constructed and inherently political. Mitchell offers rich insights about the political struggles over the control of the strategic nodes of the energy circuits. Oil geopolitics has rest, for a century, on fragile, risky, shifting and vulnerable alliances of transnational firms, the British and US governments, and the local elites during the twentieth century.

Mitchell shows that the vulnerability must not only be conceived at the level of national or geopolitical alliances, but also thought in relationship with the very nature of different forms of energy and the material organization of the networks through which it flows. The successful fights by the worker unions in coal mining and transportation to impose democratic and social rights in Western Europe from the end of the 19 th century until the 1940's owed much to the spatial concentration of the production and transportation of coal. Indeed, the material nature of coal (a very heavy ore), whose transportation was dependent upon human work in the mines, transportation on canals, or railways from the mines to the places of consumption, gave power to the workers in these sectors to block these flows until their claims were accepted.

That example highlights the power of the energy workers and hence, the relevance of social struggles in addition to geopolitics in understanding the political vulnerability of energy circuits. But the customers also have their say in these struggles for energy, as shown by the politics of electricity meters in Nicaragua [START_REF] Cupples | Shifting Networks of Power in Nicaragua: Relational Materialisms in the Consumption of Privatized Electricity[END_REF]. The privatization of power distribution there has prompted customers' mobilizations against price hikes. Specifically, as will be underlined in this article, demonstrations and political campaigning as well as meter tampering are different illustrations of the power of end-users in disrupting energy circuits. Examining the political struggles that shape energy circuits thus implies taking into consideration not only the traditional big players (governments, transnational companies and national utilities) but also the sector's workers and their unions, as well as the customers, their practices of consumption and their representations of energy as a right.

Examining the materiality of energy circuits and the particularly vulnerable connections nodes in them allows for identifying sites for politics, where the governance of energy system might be challenged. But despite Mitchell's interest in the material properties of energy, place and the urban have almost no role in his framework.

I am here conceiving of the urban as constituted of a set of metabolic relationships hybridizing nature and society. Following Swyngedouw, 'we wish to see the city as a metabolic circulatory process that materializes as an implosion of socio-natural and socio-technical relations organized through socially articulated networks and conduits whose origin, movement, and position is articulated through complex political, social, economic, and cultural relations. These relations are invariably infused with myriad configurations of power that saturate material practices, symbolic ordering, and imaginary (or imagined) visions.' [START_REF] Swyngedouw | Circulations and metabolisms:(hybrid) natures and (cyborg) cities[END_REF]. Rethinking the energy flows into and throughout the cities as urban metabolism [START_REF] Heynen | the nature of cities[END_REF]) allows to unravel their political nature and hence, to reconnect them with social movements in the city [START_REF] Swyngedouw | Every Revolution Has Its Square[END_REF]. The circuits of energy are a good illustration of such 'socially articulated networks and conduits' through which natural phenomena like oil, water force, or wind speed, etc. are transformed and hybridized into new material and symbolical forms -all along with other 'natural' products like water, concrete, iron, asphalt, etc. and social forces -human work, money -to produce urban landscapes.

At this stage, it must be stated that the empirical study cannot keep on speaking about energy, as an abstraction. In order to analyse the intersection of energy flows and the urban, it's necessary to specify which form of energy it will deal with, since only unraveling the material properties enable to address the concrete assemblage of power which are at stake. It is common to imagine the modern city as the city of oil, with its reliance on car, its networks of highways and clover-leaf interchanges, or on another register, the high-rise headquarters of petroleum companies [START_REF] Hein | Global Landscapes of Oil[END_REF]. Such a view is of course particularly relevant for Arab cities, which sometimes were literally born out of the oil fields [START_REF] Fuccaro | Introduction: Histories of Oil and Urban Modernity in the Middle East. Comparative Studies of South Asia[END_REF]. Nevertheless, in this article, I choose to insist more on the link between electricity and city. Historians have well documented how electricity has shaped the modern city, with its illuminated high-rise buildings served by electrically powered lifts and cooled thanks to electrically produced conditioned air, tramways and subways for transportation, luminous advertisings and general stores or the spreading of electrical devices at home [START_REF] Platt | The Electric City: Energy and the Growth of the Chicago Area, 1880-1930[END_REF]. Thus, the rise of the 'electric city' is par excellence an energy transition which is associated with a considerable change in the urban landscape as well as in the way of life and the configurations of power relations. Paying attention to electricity allows us to finely analyse energy flows and socio-political changes not only at the scale of the city but also at the level of the building and even the home.

In the next section, I will expose a few trends showcasing how the recent but almost complete electrification of Arab cities has transformed both the everyday practices of the urbanites and their urban imagination while it has reinforced the symbolical reordering of the social hierarchy in the city. But those metabolic changes, in turn, open new vulnerabilities. The following section deals with the energy stress encountered by urbanites in recent years, in the form of electricity shortages and price hikes, thus making challenging the political assemblages and triggering claims against the regimes in Egypt, Jordan and Tunisia. The last section highlights the specific intersections of electricity circuits and marginalized urban sites, and unravels various tactics of resistance to energy policies threatening people's way of life. The combination of both represents a major factor of unrest in Arab cities nowadays.

The transition to electricity in Arab cities and the affirmation of State

In the cities of the Arab world, electrification began in the 1920's-1930's and was boosted after the independences, in a trend that accelerated in the 1970' to deliver its fruits in the 1990's with universalization of electricity in Arab cities. This was the result of significant the State-led efforts, since electricity symbolized the promises of development. It also deeply transformed the material practices and way of life of urbanites.

According to the International Energy Agency, in 2009 the electrification level in North African cities was 99.6% and 98.6% in the Middle Eastern ones. Indicators for the electrified population at the urban level are not provided by international data bases but since almost everywhere the urban population exceeds the half and even in many cases, 70% of the total population, national level data show that apart from specific cases like Yemen or post-war Iraq, most countries have almost reached total urban electrification. Since historical records for electrification are sparse, a few examples better suggest the recent changes that have happened. In Jordan, national and urban electrification levels amounted to 71.5% and 78% in 1979, in Tunisia in 1975 respectively 34.2% and 68.21 . In every case, they have now reached 97-100% at the national level, the cities being fully connected. In this respect, Arab cities are distinct from Sub-Saharan African cities or other poor countries like India [START_REF] Heuraux | L'électricité au coeur des défis africains[END_REF]. Their trajectories make them look like more industrialized countries even though their level of industrialization is low.

The universalization of electricity in cities cannot be understood apart from the strong involvement of states in that sector. The of Tunisia and Jordan showcase the tight intertwining of electrification and state-building, where the quest for legitimacy was a struggle of independence against the former metropolis, and also destined to counter internal contestation.

In Tunisia, STEG (Société tunisienne d'électricité et de gaz) was created in 1962 as a public company in charge of the production and distribution of electricity and the distribution of gas. It replaced a set of French private companies that operated fragmented, inefficient, and socially exclusive electricity grids in Tunisian biggest cities during the Protectorate. STEG was in charge of expanding the network into the cities and into the countryside. After the launching of a national strategy aiming at rehabilitating informal settlements in the 1980's, STEG -with other public infrastructure companies -became an arm of the State devoted to the social regulation of these neighborhoods, with the double objective to calm down social and political protests by the unions and the left, and then by the islamist movements, and therefore to legitimise president Ben Ali, who took power in 1987 [START_REF] Chabbi | La réhabilitation des quartiers populaires en Tunisie: de l'intégration à la régulation sociale[END_REF]. This policy proved successful with connection rates nearing 100% in the end of the 2000's.

The Jordanian case features similar State commitment towards cities electrification. Private initiatives have also been at the origin of the electricity network in Amman2 and, in association with the municipality, in Irbid, the second largest city. During the 1960's the State nationalized the generation sector, and parts of the distribution one (except in Amman), and built a national network, which it then extended toward the countryside. Meanwhile, and specifically after the Black September event in 1970, the Palestinian camps and the informal settlements in major cities were upgraded and progressively connected to the electricity grid (Ababsa 2013 sur Amman). During this period ranging from the 1970's and the 1990's, Amman and Irbid experienced a very strong demographic increase, partly due to waves of migrations from the Arabic Gulf, but the State managed to follow the pace with infrastructural achievements, specifically in the electricity sector as statistical records quoted above illustrate. Concerns for security and search for political legitimacy have prompted the Jordanian government to devise a policy that presents many parallels with the Tunisian case, except that the nationalization carried out under the auspices of the Jordan Electricity Authority allowed the existing private distribution companies to remain operating. This universalization of access to electricity has a direct impact on daily practices, as shown by the generalization of electrical appliances. Fridges and TV's are to be found in 95 and 96% of households in Jordan in 2010 and in 90 and 95% in urban Tunisian households in 2004. Such uses probably have impacts on the social roles within the household but lack of research prevents from drawing conclusions. A spectacular and recent new practice is the spreading of air conditioning, estimated at 15% of households in Tunisia, but 30% in big cities, which indicates changing perceptions of the body [START_REF] Shove | Transnational Transitions: The Diffusion and Integration of Mechanical Cooling[END_REF]). Electricity has reconfigured the standards of living and the social relationships, from the level of the body to the whole city (street lighting, work places, etc.).

The new material practices and uses of electricity are strongly articulated with a symbolical (re)ordering, through which social hierarchies are reaffirmed. The development of shopping malls, heavily illuminated and cooled thanks to electricity, has become the symbol of a new era of consumption fetishizing imported commodities. Such places, that are mainly found in upscale districts, attract people of various origins, many of can only desire the products, but not consume them (Pages-El Karoui 2012; Schwedler 2010). In the light and in the coolness, social hierarchies are reasserted. Conversely, in many informal areas, the struggle for regularization is also a fight for light, not only in the home, but also for street lighting, which places a neighborhood in the night map and promises security for the people. Remaining in the dark nowadays means remaining outside the city (Verdeil 2013b).

The electrification of Arab cities since the independence period has fostered a new metabolism through which the urban has been radically transformed, both materially, symbolically and politically. The wired city is materially reshaped, the way of life remade through the wide use of domestic and office appliances, while the light and other electrical devices have transformed its perception. A specificity of Arab cities regarding electricity probably resides in the way this flow of energy has helped building the legitimacy and the political power of the State, the main supplier of this service, in exchange of providing electrical service at cheap rates. These facts are clearly in line with Marvin and Graham's observation about new independent countries, that "The expansion of infrastructure networks began to be seen as the material representation of modernization and the assertion of an embryonic national identity in the form of airports, four-lane highways and power stations that would sweep away the divisions of colonialism and the barriers of traditionalism" (Graham & Marvin 2001) p.84). Yet, this new imagination of the luminous city and its entanglement with state-building went along with the symbolical and material reassertion of social hierarchies in the city, as shown by unequal lighting of impoverished areas. This social pact has come under threat in recent years.

Neoliberalization of the Electricity Sector, Changing Role of the State, and Urban Revolts

From the 1990's and in the 2000's, the electricity sector has been increasingly transformed by neoliberal policies, while pressures on hydrocarbon fuel supply (both geological and geopolitical) changed the economic terms of electricity generation. Neoliberal policies regarding the electricity sector have been promoted by international funding agencies, like the World Bank, and the local ruling class, as part of a more global package of Structural Adjustment Policies. Such policies involved the unbundling of state-utilities, their privatization and the commodification of electricity, i.e. the removal of subsidies on tariff [START_REF] Harvey | A brief history of neoliberalism[END_REF][START_REF] Graham | Splintering urbanism : networked infrastructures, technological mobilities and the urban condition[END_REF]. Aside from the usual concern for 'waste of public funds', the claim for removing subsidies found another justification in the new context of fuel supply. Whereas new energy-consuming practices prompted a surge in electricity demand, the hydrocarbon market has experienced a strong increase in prices since 2003, because of rising international demand and low rising or even stagnation of hydrocarbon production [START_REF] Mason | Renewable Energy in the Middle East[END_REF]. The geopolitical struggle in the Middle East, with the consequences of the Iraq war, also added to those pressures [START_REF] Mitchell | Carbon democracy : political power in the age of oil[END_REF]. The implementation of these policies has threatened the new ways of life as well as the symbolical inclusion in the urban modernity electrification had spurred. Therefore, these policies have been met with discontent and increasing contestation, while the State was marred with allegations of corruption -touching among other the electricity sector. The social pacts between the state and the people were then weakened, while the electrified way of life and the aspiration to it were threatened, prompting concerns for continued affordable access to electricity. The ongoing revolts and revolutions in Jordan and Tunisia offer insights in this electricity anger.

During the 1990's, under the pressure of international money lenders and with the implementation of the Structural Adjustment Policy, the Tunisian government authorized a first Independent Power Producer to operate a new power plant that went to the grid in 2000 and now generates about 25% of Tunisian electricity. Meanwhile, STEG's strategy became defined through 'contractualisation' with the State, which led to the adoption of market-oriented management tools aiming at increasing its efficiency, containing the growth of its manpower and targeting the end of tariff subsidies [START_REF] Ben Letaïef | L' État et les entreprises publiques en Tunisie, l'Harmattan[END_REF]. This policy was justified by the increasing energy dependency of Tunisia, whose own hydrocarbon resource do not meet the domestic demand anymore.

These changes and specifically the rise in tariff implemented in the late 2000's, has changed the image of STEG in the population. While it embodied national pride and modernity, STEG became associated with opaque billing practices and unfair advantages for its employees who receive free electricity. A specific claim dealt with the television tax that is paid through the electricity bill3 . Moreover, corruption benefiting relatives of the former President have marred several projects contracted by STEG. If these claims were not at the heart of the claims that led to the Tunisian Revolution, they nevertheless played their role in the people's discontent and are nurturing its course since January 2011, along with other claims more generally related to public services and essential goods (Bennasr & Verdeil forthcoming).

The Jordanian case features similar changes. Pressures toward privatization proved even stronger than in Tunisia and led in the end of the 1990's to a reshuffling of the electricity sector which was unbundled. In 2007, the State sold the majority of its participation in the generation and distribution sectors, and authorized foreign firms to operate new power plants needed to accommodate the sharp rise in power demand. Meanwhile, Jordan structural dependency upon oil and gas imports has been heightened by regional geopolitics: the invasion of Iraq, which ended the cheap supply from this country in 2003 (Mason et al. 2009); and the Egyptian revolution which resulted, for complex reasons, in a disruption in natural gas delivery from this country. Both factors have led to considerable increases in the cost of electricity, and hence, in the burden of public subsidies needed to compensate the electricity tariff (Verdeil 2013a).

The successive Jordanian governments have been striving, since 2008, to review the tariff in order to cut the rising public debt. Three rises have been implemented but they remained lower than expected, because of major demonstrations and strong lobbying by powerful groups like merchants, industrialists and hospitals unions. Combined with the demonstrations against the rise of the price in other basic goods, as well as with denunciations of corruption4 , and in the context of the Arab revolts in several countries, including neighboring Syria, such a movement has shaken the successive governments and even the regime, since calls for a constitutional monarchy have been voiced [START_REF] Moore | Middle East Research and Information Project[END_REF].

Uncontrolled movements on the oil market as well as the breaches of the social pact between the State and the population, about a service that is at the heart of the city's way of life, have opened up new vulnerabilities in the financial and political circuits of electricity. The increasing power cuts affecting Tunisian and Jordanian cities recently offer a material illustration of it, while street protests about tariff also illustrate the high sensitivity of urban population to energy -and specifically electricity -in the context of the Arab Spring5 . A mostly urban concern is becoming a public issue contested in the public space. In the last section of the article, the unraveling of the practices of resistance to the reforms of the sector helps understand the disruptive potential of mobilizations related to urban electricity circuits.

The vulnerability of urban electricity circuits

Indeed, the dissatisfaction revolving around electricity and the way it became a part of the protests highlight the technical-political vulnerability of urban electricity circuits and illustrate the people's agency in resisting to the above mentioned change of the State's role. Here, I want to shed light on a specific segment of the electricity network: the end of lines, where utilities employees and of customers assert their power.

The end of lines is the location of connections between the utility networks, the customers and the utilities workers. In these areas, the electric power is transformed from high/middle into low voltage. The stations are physically located within the neighbourhoods and though entering them can be dangerous, they are easier to access than other parts of the networks. Similarly, after the transformers, the power flows through low voltage lines, which skilled people can relatively easily hook-up [START_REF] Zaki | L'électrification temporaire des bidonvilles casablancais : aspects et limites d'une transformation « par le bas » de l'action publique[END_REF]. The connection also materialises through the electricity meter, which itself can be targeted and tampered with in various ways. In case of conflicts between the utility and the customers about the tariff, the schedule of delivery, the conditions of connection, all these points of the network can be seized and bypassed in ways that highlight the power of customers and end-line users who enjoy their physical proximity to the line in remote places where the dwellers, linked by solidarity links, can defend themselves against utility workers intervention against hook-ups and tampering. Such strategies, described and conceptualized in Nicaragua [START_REF] Cupples | Shifting Networks of Power in Nicaragua: Relational Materialisms in the Consumption of Privatized Electricity[END_REF], are to be found in many places. In recent years, the managers of several Jordanian utilities have reported, for instance, a rise in "non-technical losses" which is the coded phrase for theft, hook-ups and tampering6 . This is happening in a context of tariff hikes not only for electricity but also for the gas canisters used for heating. In winter, people resort to individual electrical heaters whose consumption is very high and therefore add to their invoices. But facing electricity rates hikes, they also shift to less expensive fuels, sometimes through illegal means. Hajjaj's cartoon ironically emphasizes the agency of Jordanian people coping with energy challenges (figure 1). The cartoon displays the "mourabahaniah" stove, which allows the customer to avoid any fuel shortage. The legend says : "Out of stock today ! With the "mourabahaniah" stove specifically designed to cope with the Jordanian winter. It burns all available fuels from free markets" ( ©Emad Hajjaj, 2012) The connection between the network and the customer isn't solely a physical device: it is also the collector that goes to the streets, reads the index and distributes the bill to the customer. Here again, the customer can display his power by refusing to pay in due time. In so doing, he exposes himself to the possibility of being cut off. But such a move can only be achieved with a team of utility workers coming to the field to physically disconnect the line, where they risk being resisted or assaulted. In Tunisia, non-payment, which already existed, has jumped to unusual levels after the revolution. In certain neighbourhoods, more than one third of customers did not pay their dues. 204 cases of assaults against STEG's workers have been recorded since the revolution 7 . The government and the utility were forced to soften their usual way of fighting what they call 'uncivic' behaviours. They gave more time to customers in arrears to pay their delayed bills while reducing the usual fines and publicly stating they wouldn't disconnect them, and wouldn't charge the (heavy) reconnection fees which are usually applied8 . Nevertheless, these behaviours have persisted, highlighting the power of the customers. In 2011, the unpaid sums amounted to 368 million DT of which 183 from the residential and small professional users like merchants, informal workers, etc. From 2011 to 2012, the deficit of the STEG rose from 303 million DT to 407 million9 .

The workers in the electricity distribution sector also have power that comes from their function in maintaining the wires and collecting the bills, thus making the reverse circulation electricity and of money in the circuits -an infrastructure which has a material but also a financial nature. In Tunisia, in the above mentioned events, the electricity union made claims that 'uncivic' behaviours and aggressions endangered the workers and should stop. The union strongly argued that during the revolution, its workers never ceased maintaining the infrastructure. Implicitly, it pointed out that continuous threatening of the workers could lead to intervention refusal, thus pressing both the customers and the managers to take measures that would help cool the tension -which was indeed implemented. In so doing, the union recalled its own power in the sustaining of the grid.

In Jordan, in April 2012, a similar strategy was successfully implemented by JEPCO's workers, the electric utility in Amman10 , as they went into strike to defend their benefits. A specific aspect of their strike was to retain the money collected from the customers, causing a loss in income for the company and therefore forcing her to come to the negotiation table. This highlights again the power of end-line workers.

In ways similar to Timothy Mitchell's demonstration of the power of coal workers and their ability to fight for their democratic rights, these different examples show how the physical and political configuration of the network creates various forms of vulnerability in which a range of end-line users (workers or customers) can assert their power in order to advance social rights. Periods of massive protests like those experienced in Arab cities create momentum for such struggles but conversely, outrage can also be stirred by the lack of, or rising prices, of fuel.

Conclusion

This article has made the argument that energy politics is of the greatest significance to understand the current revolts in Arab cities. Going away from traditional account on rentierism and oil geopolitics, it is suggested here that understanding the urban material politics and experience of energy is a necessary step that is missing in national or regional level analyses. It means reintroducing space, the materiality of the urban and the complex and shifting networks of social and political relations that constitutes it and to unravel its entanglements in the shifts urban energy system are undergoing. In so doing, the article has connected Mitchell's call for following the energy circuits, conceptualized as complex assemblages of material and discursive, human and non-human elements, highly subjected to political vulnerability at the connection points of circuits, with Swyngedouw's proposal to read cities as metabolic processes infused by configuration of power.

Reviewing recent material, economic and political transformations of energy issues in Arab cities, this article has shown, by focusing on electricity, that a massive urban energy transition had taken place. Electricity nowadays has become an indispensable form of energy in cities, which shape urban landscapes and urban way of life. Electricity also spurred a new order, highlighting the role of the State as a broker of urban modernity, thanks to the engineering of subsidies. But the recent liberalisation of electricity tariff and, more broadly, the changing symbolical and political relationships between the State and the urban citizens, triggered strong mobilizations that converged with the current Arab revolts. The complex connections between the electricity grid and the urban also offer diverse agents -dwellers, utility workers -the opportunity to exploit their position in the circuit to resist such policies.

While the energy transition toward low carbon energy is seen as a new and strong imperative in a context of sustainable urban development and of oil peak, the current mobilizations point to the social challenges such policies would face. Not only would this involve a dramatic economic and financial reshuffling of the massive public subsidies, but also hurt habits and representations embedded in the urban circuits of energy (and electricity). The current revolts have shown the ability of various actors in these circuits to use the vulnerabilities of the circuits -and first the financial weaknesses of the electric utilities -to resist reforms hurting their rights to affordable energy, which is synonymous with the right to the city.

Figure 1 :

 1 Figure 1: The struggle for home heating in Jordan

Table 1 :

 1 Electricity access in the Arab world

		Electrification level (%) 2002	Electrification level (%) 2009	Population without electricity (2009) millions	Urban Population 2009 (%)
	Algeria	99	99		71
	Bahrain	100	99,4	0,0	89,0
	Egypt	98	99,0		43,0
	Iran	99	98,4	1,2	69,0
	Iraq	95	86,0	4,1	67,0
	Israel	100	99,7	0,0	92,0
	Jordan	95	99,9	0,0	82,0
	Kuwait	100	100,0	0,0	98,0
	Lebanon	96	99,9	0,0	87,0
	Lybia	100	?		77,0
	Morocco	77	97,0		56,0
	Oman	95	98,0	0,1	73,0
	Qatar	96	98,7	0,0	98,0
	Saudi Arabia	98	99,0	0,3	82,0
	Syria	87	92,7	1,5	55,0
	United Arab Emirates	97	100,0	0,0	84,0
	Tunisia	95	99,0		66,0
	Yemen	50	39,6	14,2	31,0
	Source: IEA, World Energy Outlook 2005, 2011 ; Urban Population from the World Bank

  Tuniscope, 2013. 204 cas d'agressions contre les employés de la STEG recensés depuis la Révolution. Tuniscope.com. Available at: http://www.tuniscope.com/index.php/article/31892/actualites/societe/steg-revolution-413712 [Consulté le septembre 25, 2013].

National statistical records.

See a recent account: "A merchant's tale recalls Amman electric revolution"[START_REF] Freij | A merchant's tale reveals Amman's electric revolution | The Jordan Times[END_REF]).

Bougoutayya I., Facturation STEG -Les raisons d'une facturation salée -, Le Quotidien, 2/4/2011.

Strikingly, the first demonstration in March 2011 led to the resigning of Prime minister Samir al-Rifai , who had been directly involved in the designing of the privatization policy as an adviser of the king, before becoming the CEO of a Jordanian-Emirati company who bought the majority of two former electricity stateutilities, and being lastly nominated as Prime minister in 2009.

Unusual and strongly felt power cuts took place in Tunisia and Jordan during the summer 2012[START_REF] Namrouqa | Power cuts witnessed as temperatures soar above 40 o C. The Jordan Times[END_REF]; La Presse de Tunisie 2012). The same goes about Egypt, where people have to cope with shortages of electricity, and natural gas delivery (Markoum Verdeil 2013).

Fieldwork interviews inAmman and Irbid, 2008-2010.

Debbar Z., 2011, La STEG ouvre une nouvelle page, Echo Journal, 1 avril 2011.

Kapitalis, 2011, Tunisie. Les impayés de la Steg s'élèvent à 213 millions de dinars, Turess, 17 août 2011, < http://www.turess.com/fr/kapitalis/5447 > ; Youssef B., 2012, Plus de 360 millions de dinars d'impayés pour la STEG, Tunisie Numérique, 13 janvier 2012, < http://www.tunisienumerique.com/plus-de-360-millions-de-dinars-d%E2%80%99impayes-pour-la-steg/95701 >.

10 Electricity workers end strike as union reaches deal with company, The Jordan Times, 23 april 2012 < http://jordantimes.com/electricity-workers-end-strike-as-union-reaches-deal-with-company >