F Gauthier

P.-E Roche

Evidence of a boundary layer instability at very high Rayleigh number

Keywords: numbers: 47.27.Te , 44.25.+f , 67.90.+z Natural convection, Thermal convection, Ultimate Regime, Kraichnan's regime, Rayleigh-Bénard, Turbulence, Heat transfer, Boundary layer

In 1997, a Rayleigh-Bénard experiment evidenced a significant increase of the heat transport efficiency for Rayleigh numbers larger than Ra ∼ 10 12 and interpreted this observation as the signature of the Kraichnan's "Ultime Regime" of convection. According to Kraichnan's 1962 prediction, the flow boundary layers above the cold and hot plates -in which most of the fluid temperature drop is localized-become unstable for large enough Ra and this instability boosts the heat transport compared to the other turbulent regimes. Using the same convection cell as in the 1997 experiment, we show that the reported heat transport increase is accompanied with enhanced temperature fluctuations of the bottom plate, which was heated at constant power levels. Indeed, for Ra < 10 12 , the bottom plate fluctuations can simply be accounted from those in the bulk of the flow. In particular, they share the same spectral density at low frequencies, as if the bottom plate was following the slow temperature fluctuations of the bulk, modulo a constant temperature drop across the bottom boundary layer. Conversely, to account for the plate's temperature fluctuations at higher Ra, we no-longuer can ignore the fluctuations of the temperature drop across the boundary layer. The negative skewness of fluctuations at high Ra supports the picture of a boundary layer instability. These observations provide new evidence that the transition reported in 1997 corresponds to the triggering of the Ultimate Regime of convection.

I. INTRODUCTION

Natural convection forces turbulence in the atmosphere, in the oceans as well as in numerous geophysical, industrial and astrophysical flows. Understanding the convection regimes settling on such large scales is a major scientific challenge, directly impacting our ability to assess heat and mass transfer in the environment, for example. One of the simplest laboratory paradigm to explore the basic mechanisms of turbulent convection is the Rayleigh-Bénard cell. It consists in an horizontal layer of fluid between two isothermal plates imposing a temperature difference ∆ destabilizing the fluid. Dimensional analysis shows than the main control parameter in such cells is the Rayleigh number (Ra) which is proportional to ∆ and to the cube of the fluid layer height (the complete definition of Ra is given later). Unfortunately, due to this geometrical dependence, the reachable Rayleigh numbers in laboratory experiments are decades smaller than those estimated for environmental flows (typically Ra ∼ 10 20 in the atmosphere for example). Thus, our confidence in extrapolating laboratory findings to such flows depends on the understanding of very high Ra ex-periments.

Since 1997, a few Rayleigh-Bénard experiments [1,2,3,4] reported a significant enhancement of heat transport efficiency across the cell above Ra ∼ 10 12 within Boussinesq conditions. These observations were interpreted as the signature of the "Ultimate Regime" of convection, predicted in 1962 by R. Kraichnan [5]. Qualitatively, this regime is characterized by the turbulent state of the two boundary layers laying close to each plate but the precise conditions for triggering this boundary layer instability are difficult to predict [5]. The interpretation presented in 1997 [1] was motivated by the observation of an unprecedented heat transfer scaling versus Ra, compatible with the onset of Kraichnan's regime and significantly more efficient than any other observed or predicted scaling. In another paper, the authors of [1] reported another signature of the transition on the local temperature statistics at mid-height within the cell [6]. In 2001, the observation of the asymptotic heat transport scaling of the Ultimate Regime was reported in a similar cell with a calibrated corrugated surface [2]. For usual velocity turbulent boundary layers, such surfaces are well known to set the viscous sub-layer height constant and thus to reveal the asymptotic transport scaling [START_REF] Schlichting | Boundary-Layer Theory[END_REF]. This experiment therefore supports the 1997 interpretation of the occurrence of the Ultimate Regime of convection.

But a more direct evidence of a laminar-to-turbulent transition of the boundary layers near Ra = 10 12 is still missing, which motivated the present work. Direct local measurements within the boundary layers are difficult for practical reasons : the thermal boundary layer is very thin (typically smaller than 100 µm in the experiments discussed above) and its temperature profile is Ra dependent. To bypass the difficulties of local invasive measurements within the boundary layer, we use the low frequency fluctuations of the bottom plate to probe the stability of the bottom boundary layer. More precisely, we apply a constant heating power J on the bottom plate and monitor its temperature fluctuations of order one percent of ∆. We focus on times scales longer than the turn-over time of the mean flow circulation, for which the lack of spatial resolution of the "plate-probe" is not a limitation. We find that above Ra ∼ 10 12 , such fluctuations become significantly larger than those in the bulk of the flow, while both have the same intensity for lower Ra. Besides, the probability density function of the bottom plate temperature becomes increasingly skewed towards negative values above Ra ∼ 10 12 , corresponding to more and more frequent intense cooling events. We show that both observations are straightforwardly interpretable by the occurrence of an instability in the boundary layer for Ra ∼ 10 12 , which is consistent with the scenario of a transition to the Ultimate Regime of convection.

For reference, we mention that three Rayleigh-Bénard experiments explored Ra larger than 10 13 and didn't find any significant enhancement of the heat transfer [START_REF] Wu | [END_REF][START_REF] Ashkenazi | [END_REF]10]. In [START_REF] Wu | [END_REF], a transition of the local temperature statistics have been reported for Ra ≃ 10 11 and 10 13 [11]. In [12], the authors report an enhancement of heat transport at high Ra but, according to the authors themselves, the data are not fulfilling the Boussinesq conditions and therefore are difficult to compare to others. For references on numerical simulations, see [13,14]. The reason for such a scatter between experiments at very high Ra is still not understood and this issue is not addressed in this paper. We just note that the laminar -turbulent transition of velocity-driven boundary layers is known to be highly sensitive to experimental conditions [START_REF] Landau | Fluid Mechanics 2nd[END_REF] and the same could remain true for "temperature-driven" boundary layers.

For convenience, we recall here the definitions of the main dimensionless parameters. The Rayleigh number Ra = (gh 3 α∆)/(νκ) and the Prandtl number P r = ν/κ characterize the buoyancy force and the molecular transport properties where g is the gravity acceleration, ∆ is temperature difference across the cell of height h and α, ν, κ are respectively the isobaric thermal expansion coefficient, the kinematic viscosity and the thermal diffusivity. The Nusselt number N u = Jh/(Sk∆) characterizes the heat transport efficiency across the cell, where J is the mean heat flux (in practice, the applied Joule heat-ing), k the thermal conductivity of the fluid and S the surface of the plate-fluid interface.

II. EXPERIMENTAL SETUP

The convection apparatus used in the present work has been described in [6]. The fluid is confined in a cylindrical volume of height 20 cm and diameter 10 cm with top and bottom oxygen free high conductivity copper (OFHC) plates of thermal conductivity 1090 W.m -1 .K -1 at 4.2 K [START_REF] Gauthier | Proc. 11th EUROMECH Eur. Turbulence Conf[END_REF]. The seamless stainless steel side wall is 500 µm thick and its measured thermal conductance is 327 µW.K -1 at 4.7K. Its parasitic contribution on N u has been corrected using the correction formula proposed in [17]. The cell is hanging in a cryogenic vacuum : the top plate is cooled by an helium bath at 4.2 K through a calibrated thermal resistance (3 W/K at 6 K). Its temperature is regulated by a PID controller and we apply a constant and distributed Joule heating on the bottom plate. The heat leaks from the cell in such set-up (about 200 nW at 4.7 K) are at least 4 decades smaller than this heating and are essentially due to the radiative transfer as shown in [18]. The temperature difference ∆ between the plates is measured with 0.1 mK accuracy thanks to a thermocouple ; for comparison the smallest ∆ used in this work is 18 mK. The cell is filled with 4 He which properties are calculated based on Arp & McCarty works [START_REF] Carty | Advances in Cryogenic Engineering[END_REF] and later improvements [START_REF] Roche | [END_REF]. The cell has been operated for 3 mean density and temperature conditions : 19.15 kg/m 3 at 6.0 K (P r ≃ 1.0), 19.15 kg/m 3 at 4.7 K (P r ≃ 1.3) and 70.31 kg/m 3 at 6.0 K (P r ≃ 2.8). These values are a compromise to obtain the best accuracy of helium properties, a 3 decades range of Ra around Ra = 10 12 and a limited range of P r.

We now show that the temperature of the bottom plate T plate is a well defined and measurable global quantity in such a set-up, accounting for the homogeneous temperature fluctuations of the whole plate. Two germanium thermistances are inserted into thermometers holders screwed on this copper plate [START_REF]Two different types of thermistances are used on each plate : LakeShore GR -200B -2500 and Cryocal CR1500 -P B. Special attention is dedicated to the thermalization using standard cryogenics techniques[END_REF]. The thermal response time of each thermistance is measured with the 3ω technique (for example see [START_REF] Lu | Review of Scientific Instruments 72[END_REF]). We find cut-off frequencies at -3 dB between 16 Hz and 32 Hz which is consistent with the thermistances' specifications. Thus thermometry has enough dynamics to reflect the plate's temperature fluctuations up to a few Hz, which is above frequencies of interest. The main intrinsic response time of the plate is τ p = d 2 p /κ p where d p = 10 cm is the plate's diameter and κ p is the thermal diffusivity of copper. At 4.7 K, τ -1 p is about 120 Hz which is also larger than the frequencies of interest. Although the plate's diffusive response time is small, the non-homogeneous nonstationary heat fluxes at the fluid/plate interface can still generate temperature gradients in the plate (for example, see [START_REF] Chillà | [END_REF]). We checked that this effect was negligible for the frequency range of interest : the coherence function between one thermometer located on the cell axis and the other one located on the plate edge is larger than 97% (or 99% if we discard the 3 lowest ∆). T plate is therefore a measurable and well defined quantity in this set-up, at least up to a few Hz. Each thermistance is polarized with an AC current of a few µA (to prevent significant overheating) and the resulting voltage is demodulated with a lock-in amplifier of 20 ms time constant, connected in a bridge configuration (insert of Fig. 1). The output signal is anti-alias filtered and recorded continuously during 5 or 10 h, corresponding typically to a few thousands of turn-over times.

III. RESULTS

As a preliminary test, we checked that the heat transport law N u(Ra) across the cell is consistent with the previous measurements with the same apparatus [6], in particular regarding the occurrence of a heat transfert enhancement slightly below Ra = 10 12 . Figure 1 illustrates this agreement by representing the compensated heat transfer N uRa -1/3 versus Ra for both experiments (data from [6] are restricted to those for which temperature time series in the bulk are available).

Figure 2 shows the power spectrum density of the bottom plate temperature T plate for various Ra. At low frequencies, spectra saturate on what we shall refer as "plateaus". These plateaus will be characterized by their spectral densities P . The cut-offs at high frequency are steeper than -3 dB/dec and they can be characterized by the frequencies F 20dB at -20 dB below the plateaus, or more conveniently by F c = 0.2 × F 20dB which roughly corresponds to the cross-over between the plateau and the cut-off regions. In pratice, P has been determined as the value ensuring the best merging of all spectra, when the spectral density is divided by P and the frequency by F c (solid lines Fig. 2 insert). Dimensionless cut-off frequencies F ⋆ c and plateaus P ⋆ are defined by : c can be seen as the Reynolds number associated with the distance h and the velocity hF c . Figure 3 presents this quantity compensated by Ra 0.5 to illustrate that the scaling of F ⋆ c is close to a power law Ra 1/2 for a given P r. Similar scaling have already been reported for other Reynolds numbers [6,23] measured in the same window of Ra. In particular, the Reynolds number Re associated with a mean velocity V of the large scale circulation at mid-height (at 2.5 cm from the axis) has been measured and fitted in the present cell as [6] :

F ⋆ c = F c .h 2 /ν and P ⋆ = P.ν/(h 2 ∆ 2 ) (1) 10 -2 10 -1 Fc
Re = hV /ν ≃ 0.206 × Ra 0.49 P r -0.70 (2)
The lower plot of Fig. 3 gives an estimate of the number N of turn-overs of the mean flow circulation during a time period 1/F c . Assuming that the circulation path is 2h long and using the previous mean velocity V fit, we get N ≃ V /2hF c = Re/2F ⋆ c . The insert shows that N is close to 2, indicating that the cross-over between the plateaus and the cut-off region of the T plate spectra is of the order of one turn-over frequency. The compensated plot of the spectral densities P ⋆ on Fig. 4 is the first important result of this paper. For Ra < 10 12 , the spectral densities dependence P ⋆ (Ra) is compatible with a Ra -2/3 scaling while it has no obvious Ra dependence for Ra > 2 × 10 12 , as illustrated by the 2/3 slope (dash line). For comparison, we also plotted the corresponding spectral density calculated from temperature time series recorded at mid-height within the cell in the previous experiment [6]. Similar spectral plateaus can also be evidenced in these times series below the frequency corresponding to a turn-over time typically. Within experimental uncertainty, the spectral densities plateaus in the bulk overlap with the plate's ones below Ra = 10 12 , but they significantly diffe r above Ra = 10 13 . The insert shows 4P ⋆ N u 2 P r -1 versus Ra. This quantity can be seen as P made dimensionless with ∆ and the molecular thermal diffusion time across a boundary layer of heigh h/(2N u). Within uncertainty, such a compensation of P ⋆ also cancels the Ra -and maybe P r-dependences in the low Ra region.

Figure 5 shows a representative sample of the probability density functions (pdf) of T plate -T plate normalized by its standard deviation, where overline stands for time averaging. The Rayleigh numbers range from 5.6 × 10 10 (top) up to 5.7 × 10 13 (bottom) where vertical offsets are introduced for clarity. The first three pdf are close to Gaussian (the solid line corresponds to a gaussian distribution), while the others become increasingly skewed as Ra increases : intense coolings of the plate occur more and more frequently than the corresponding overheating events. The insert presents the skewness

ζ = (T plate -T plate ) 3 (T plate -T plate ) 2 3/2 (3)
versus Ra. It illustrates that the absolute value of the skewness is no longuer significantly smaller than unity above Ra ∼ 10 12 .

IV. DISCUSSION

We assume that, on time scales longer than a few turnover times, the temperature fluctuations locally recorded in the bulk of the flow reflect temperature variations spanning over the whole bulk of the flow. Accordingly, we interpret the spectral density plateaus of T bulk below F c as a global characteristics of the bulk temperature, rather than local one. Since we operate the bottom plate at constant heating power, its temperature T plate is referenced by the fluid's bulk temperature and the temperature drop across the bottom boundary layer. At frequencies smaller than F c , we can define a time-dependent temperature drop δT bl across the bottom boundary layer, which mean value is ∆/2 and which fulfills (by definition) :

T plate = T bulk + δT bl (4)
Below Ra ≃ 10 12 , we conjecture that the bottom plate temperature fluctuations follow the ones of the bulk with negligible noise introduced by the temperature drop δT bl across the bottom boundary layer, that is :

T plate ≃ T bulk + ∆T /2 (5)
This is supported by the overlapping spectral densities plateaus of T bulk and T plate reported on Fig. 4. The open circle of the insert of Fig. 2 presents a typical spectrum of the temperature T bulk for Ra = 1.35 × 10 12 and P r = 1.3 recorded during the previous experiment with the same cell. The Y axis rescaling has been done with the same procedure as previously. The frequency axis is rescaled by F c = 0.068 Hz, which was obtained from an interpolation between the solid symbols of Fig. 3. The cut-off of the T bulk spectra for F > F c is less steep than for T plate spectra. This is consistent with a spatial filtering by the plate of the fluid's temperature inhomogeneities extending over less than typically one cell diameter. Estimations of the thermal characteristics of the fluid-plate system also corroborate our conjecture. Indeed, the expected time response of the plate to a slow variation of T bulk can be estimated as RC, where C ≃ 1J/K is the (measured) plate's heat capacity and R is the bottom boundary layer dynamical thermal resistance R :

R = ∂∆/2 ∂J ≃ 1 1.3 ∆/2 J (6)
We find that RC is always more than one decade smaller than 1/F c . Since the heat capacity of the bottom plate is significantly smaller than the heat capacity of the fluid, the plate represents a negligible thermal load for the slow temperature variations of the bulk fluid. Thus the plate can indeed follow quasistatically the temperature variation of the bulk, modulo the offset introduced by the temperature drop across the boundary layer.

Above Ra ≃ 2 × 10 12 , the spectral density plateaus P ⋆ of T plate get increasingly larger than their counterpart in the bulk (Fig. 4). We interpret this strong enhancement of fluctuations in the plate as the contribution of the temperature drop δT bl across the boundary layer. At high Ra, the frequent intense cooling events evidenced with the probability distributions of Fig. 5 are interpreted considering that the thermal contact between the plate and the bulk is greatly enhanced during short periods of time, corresponding to brief thinning of the boundary layer. This strongly suggests that the boundary layer is unstable.

We now discuss and discard the possibility that this boundary layer instability was already present at lower Ra but that the corresponding temperature fluctuations of δT bl were simply masked by the fluctuations of the bulk T bulk . Within this hypothesis of this "masking-effect", Fig. 4 could be interpreted without resorting to a flow transition occurring near Ra ∼ 10 12 .

A first argument is that both enhancements of Nu and T plate fluctuations nearly occur for the same Ra. If we accept that this coincidence is not fortuitous, both events should be accounted by a single mechanism which cannot be a simple masking-effect hypothesis.

As a second argument, the small -if any-dependence of P ⋆ (Ra) for Ra > 10 12 , seems in contradiction with our knowledge of boundary layers physics in the hard turbulence regime, which preceeds the Ultimate one. This contradiction suggests that the observed high Ra regime is not the hard turbulence one. Indeed, in the hard turbulence regime, the typical length scales of convection, such as the plumes various characteristic sizes, are known to decrease continuously as Ra increases, yielding to an increase of the number of degrees of freedom in a given cell [24]. In physical systems, one expects the relative fluctuations of global variables to decrease as the number n of degrees of freedom contributing to this variable increases [28], which is not the case of P ⋆ for Ra > 10 12 . To make this argument more concrete, we present below an illustrative model for boundary layer noise in the hard turbulence regime and we show that it leads to a contradiction if we apply it to the high Ra region.

Our model assumes that δT bl fluctuations can be described as resulting from the shot noise of plumes across the boundary layer, where plumes are defined as independent coherent structures erupting from the plates and responsible for all the heat flux transport. By analogy with the electronic shot noise crossing barriers (for example see [25,26]), shot noise from plumes of heat content q 0 is accounted by a white noise source of heat flux with a power spectral density 2q 0 J, which is in parallel with the boundary layer resistance R. At the low frequency of interest, the inertia C of the plate can be neglected as shown earlier (RCF c ≪ 1). Thus we predict a white noise spectrum for δT bl with a power spectral density P bl = R 2 2q 0 J. For consistency, the plateau extent F c should be to smaller or equal to the inverse of the autocorrelation time of each plume. Since F c corresponds to 2 turn over times typically, this requirement is not stringent. With this model, it is possible to infer the number n of independent plumes arising from the plate at a given time, which can be seen as the number of degrees of freedom of the boundary layer. We assume that q 0 corresponds to a n th of the thermal boundary layer heat content Q with :

Q = ρc p ∆ 4 Sλ (7)
where S = πh 2 /16 and λ ≃ h/2N u are the surface and thickness of the boundary layer in the hard turbulence regime. Neglecting the 1.3 prefactor in Eq.6, a bit of algebra gives :

n = P r 16P ⋆ bl N u 2 (8)
where P ⋆ bl = P bl .ν/(h 2 ∆ 2 ). For Ra > 2.10 12 , the bulk contribution P ⋆ is reflected so we have P ⋆ ∼ P ⋆ bl and we note that this value is roughly independent of Ra. Then, the above formula indicates that the number of degrees of freedom n of the boundary layer scales as N u -2 , that is a decreasing function of Ra. This is in contradiction with experience in the hard turbulence regime [24], which weakens the initial hypothesis of the existence of "hardturbulence" boundary layers above Ra ≃ 10 12 .

As a final argument, we note that the strong departure from gaussianity for Ra > 10 12 is not consistent with the continuous increase of the number of degrees of freedom of the boundary layer in the hard turbulence regime. Indeed, such an increase should favor the convegence to a gaussian of the pdf of global quantities such as P ⋆ ∼ P ⋆ bl , which is not the case.

V. CONCLUSIONS

A constant heating is applied to the bottom plate of a Rayleigh-Bénard cell and this plate's temperature fluctuations are analysed. We focus on times scales larger than typically 2 turn over times of the large scale circulation. Below Ra ≃ 10 12 , we give evidence that the plate's fluctuations follow the temperature fluctuations of the bulk of the cell. This implies that the temperature drop across the bottom boundary layer has negligible low frequency fluctuations. Above Ra ≃ 2 × 10 12 , the bottom plate fluctuation abruptly increase compared to the fluctuations in the bulk. This change is interpreted as an extra noise contribution brought in by the boundary layer. We discussed and discarded the possibility that this noise was present but simply masked at lower Ra. The negative skewness of the plate's temperature -which absolute value quickly increases in the high Ra regimesupports the picture of a boundary layer becoming unstable for Ra ∼ 10 12 The transition of the heat transfer law has already been reported with this cell [1]. These authors interpreted this as the triggering of Kraichnan's Ultimate Regime of convection, which is associated with a laminar to turbulent transition of the boundary layer [5]. The present results are fully consistent with such an interpretation and they provide new evidences supporting it based on dynamical measurement conducted "on" the boundary layer.

FIG. 1 :

 1 FIG. 1: Compensated Nu versus Ra. Solid symbols : present work. • : Pr=1.0, : Pr=1.3, : Pr=2.8. * : data from [6]. Insert : measuring circuit of each thermistance sensor.

FIG. 2 :

 2 FIG.2: Power spectra of the bottom plate temperature T plate . Insert : same spectra normalized by the adjusted plateau value P (y axis) and by Fc (x axis). • is a power spectrum of T bulk for Ra = 1.35 × 10 12 recorded in a previous run.

FIG. 3 :

 3 FIG.3: Upper plot : compensated cut-off frequency F ⋆ c versus the Rayleigh number. Lower plot : estimated number of turnovers corresponding to Fc F ⋆ c can be seen as the Reynolds number associated with the distance h and the velocity hF c . Figure3presents this quantity compensated by Ra 0.5 to illustrate that the scaling of F ⋆ c is close to a power law Ra 1/2 for a given P r. Similar scaling have already been reported for other Reynolds numbers[6,23] measured in the same window of Ra. In particular, the Reynolds number Re associated with a mean velocity V of the large scale circulation at mid-height (at 2.5 cm from the axis) has been measured and fitted in the present cell as[6] :

8 FIG. 4 :

 84 FIG.4: Compensated plateau level P * versus Rayleigh number (same symbols as on Fig.1). Insert : alternative normalisation of P (see text).

FIG. 5 :

 5 FIG. 5: Probability density functions of T plate -T plate normalised by its standard deviation. A vertical offset of one decade is introduced between each datasets. From top to bottom : ( ) Ra = 5.6 × 10 10 ,(⋄) Ra = 5.5 × 10 11 ,(△) Ra = 1.7 × 10 12 ,(•) Ra = 4.5 × 10 12 ,(⋆) Ra = 1.6 × 10 13 ,(▽) Ra = 5.7 × 10 13 . The insert shows the skewness versus Ra (same symbols as on Fig.1)

Acknowledgments

We thank B. Chabaud, B. Hébral, S. Aumaitre, P. Diribarne, Y. Gagne, and more especially B. Castaing for discussions and inputs. We thank the authors of [1] for sharing their raw data. This work was made possible thanks to the Région Rhône-Alpes support under contract 301491302.


Md Shahinur Rahman
email: srahman.bu367@gmail.com

Factors Affecting Price Fluctuation of Rice and Exploring the Rice Market in Barishal from the Consumer and Wholesaler Point of Views

Keywords: Price Fluctuations, Exploring the Rice Market, Consumer and Wholesaler

Rice is the staple food of Bangladesh. Although Bangladesh has achieved self-sufficiency in rice, the supply chain and logistics management of rice reveal inefficiency resulting in continuous fluctuation of price and artificial crisis. The main purpose of this paper is to explore the factors affecting the price volatility and prospects of rice market from the context of consumer and wholesaler. This study employed an in-depth interview with 50 consumers who reside in the three different villages and 30 rice wholesalers of Barishal city, Bangladesh. The findings of this study illustrated that the price fluctuation of rice is caused due to improper management and syndication among the channel members which leads a situation where a farmer sells paddy at a lower price in contrast a consumer buys rice paying a high price.

Furthermore, seasonal productivity and natural calamities expand the gap between demand and supply of rice. Therefore, the paper will help the policymakers to form an overall understanding of the structure of the rice market in Bangladesh and undertake necessary strategies to meet price fluctuations. Additionally, the study will support prospective marketers to design market strategies to meet consumers' needs efficiently.

Introduction

Rice dominates a larger portion of diet for a large portion of world's human population, especially in Asia [START_REF] Faisal | Power Efficient Distant Controlled Smart Irrigation System for AMAN and BORO Rice[END_REF]. In Bangladesh, rice is regarded as the staple food, which covers almost three-quarters of the total cropped area in Bangladesh. Also, Bangladesh is the world's fourth-largest rice-producing country, yielding a total of 34.18 million metric tons. Cultivating rice three times a year, the average production of rice in our country is 4.2 metric tons per hectar [START_REF] Brri | Modern Rice Cultivation[END_REF]. According to the annual report of the Bangladesh Bureau of Statistics [START_REF] Bbs | Hand Book of Agriculture Statistics[END_REF] the per capita consumption of rice in Bangladesh is one of the highest in the world which is estimated at 188 kg yearly . The World Bank (WB, 2017) survey showed that the population of Bangladesh in 2016 was 162.95 million which has been growing at a yearly rate of 1.09%. This rapidly growing population is the major factor driving the market while the consumption rate of rice of consumers is increasing year by year.

The consumption rate in 2016 was 36.3 million metric ton and is expected to reach 39.7 million metric ton.

According to [START_REF] Murshid | RICE PRICES AND GROWTH AND POVERTY REDUCTION IN BANGLADESH[END_REF], rice cultivation accounts for 48 percent of total rural employment which is expected to rise even more if rice trading, transport, and processing activities are also taken into account. Furthermore, rice provides two-thirds of the caloric needs of the nation along with half the protein consumed. Also, the contribution of rice to agricultural GDP is about 70% while its share of national income is one-sixth. Therefore, rice is playing a robust role in Bangladesh even though the long-term trajectory is one of declining [START_REF] Faruqee | Stock-Taking of Major Studies and Reports on Agriculture and Rural Development in Bangladesh[END_REF].

In recent times, more than 13 million farms grow rice covering some 10.5 million hectare (M. [START_REF] Hossain | Crop agriculture and agrarian reforms in Bangladesh: present status and future options[END_REF]. Despite rice production has increased in the last couple of decades with selfsufficiency in rice food security, the availability of rice to consumers has not been stabilized.

As a result, the fluctuations have been seen as a common phenomenon in the price of rice by days and even by minutes in Bangladesh. Additionally, the supply chain of rice does not meet the requirement at the right time at the right place, which creates an artificial crisis and price volatility. Moreover, the supply of paddy is significantly affected by natural calamities such as drought and flood [START_REF] Murshid | RICE PRICES AND GROWTH AND POVERTY REDUCTION IN BANGLADESH[END_REF].

On the other hand, according to the annual report of the FAO showed that the prices gradually declined after they soared to Tk 47.78 in September 2017. Just following the year in November 2018, the prices fell below the Tk 40 mark. Presently the average price of 1 kg rice is being sold at the price of 34 Tk. Thus, the market prices have gradually been declining due to good crop harvest, which creates a situation that hurts farmers but benefits consumers. For this reason, farmers are said to be in real trouble as they have to pay very high wages to hired workers to harvest paddy during this peak season, but they sell their paddy at nearly half the production cost. Therefore, it is necessary to identify the appropriate demand and meet them accurately in a profitable way and it is the primary concern of rice production and supply chain management.

However, the study intended to investigate the reasons behind the causes of fluctuating the price of rice in Bangladesh as well as identifying the prospects of offering the fair fixed price to the consumers throughout the year from the consumer and wholesaler context. Thus, the goal of the study was to explore the rice market in Barishal with the help of "Helping Hand Belgium". Hence, the study formulated the research question as "What are the factors affecting price volatility of rice and business prospects from consumer and wholesaler perspectives?"

Theoretical Background

Rice Production

Generally, rice production is operated in all districts of Bangladesh including Barishal which is well-known as the granary state. The rice areas in Bangladesh have remained mostly unchanged over the last three decades, although production seasonality has changed significantly [START_REF] Siddique | A study on rice marketing system in Bangladesh: An empirical analysis[END_REF]. Hence, the rice market of Bangladesh is dominated by Boro production (harvested in May-June). Presently it becomes the dominant rice-growing season in the country. Aman is harvested in (Noember-December). The introduction of irrigation has made it possible to grow rice heavily in the dry season. A third rice crop is also grown in some areas, namely the Aus crop, harvested in July-August [START_REF] Murshid | RICE PRICES AND GROWTH AND POVERTY REDUCTION IN BANGLADESH[END_REF]. The following figure 1shows that there Bangladesh has been experiencing an upward trend of rice production from 1997 to 2016, though there are some fluctuations.

Parties involved in the supply chain of rice market

The key structural aspects of the rice market involve several intermediaries or agents who perform different functions at different levels of the marketing channel. [START_REF] Murshid | RICE PRICES AND GROWTH AND POVERTY REDUCTION IN BANGLADESH[END_REF] found that several agents are involved in the rice market including Farias (small itinerant paddy traders, who normally purchase from farmers and sell to Beparis) and Beparis (large itinerant paddy wholesalers) are primary level market participants, whereas Paikers (rice wholesalers) and Aratdars (rice commission agents) are terminal market operators. Millers are secondary market agents that operate between paddy Beparis on one side and Pikers and Aratdars on the other side [START_REF] Chowdhury | Rice markets in Bangladesh: A study in structure, conduct and performance[END_REF]. The final consumers following the local rice retailers operate at the end stage of the supply chain. [START_REF] Siddique | A study on rice marketing system in Bangladesh: An empirical analysis[END_REF] found several types of intermediaries in the rice supply chain which included Faria, Bepari, Paiker, Aratdar, wholesaler and retailer. According to [START_REF] Raha | Structure, Conduct and Performance of the Rice Market and the Impact of Technological Changes in Milling Co-Investigators[END_REF], in 1986, the BBS enumerated the total number of agents involved in rice trading and processing at 107,657.

Trade and milling

The unhusked rice is milled in semi-automatic and automatic rice mills and sold to both local and long-distance tradersthe bulk of it going to the latter [START_REF] Murshid | RICE PRICES AND GROWTH AND POVERTY REDUCTION IN BANGLADESH[END_REF].This was a huge change since 20 years before when marketed quantities were much smaller and when milling technology was much more basic with a significant "traditional" segment relying on small or minor processors for initial preparations before carrying out paddy crushing in semiautomatic mills.

According to the FAO (2004), the rice supply chain in Bangladesh is demand-driven. Although Bangladesh is self-sufficient in rice, the rice supply chain in Bangladesh mainly consists of milling sector, the wholesale sector, and the retail sector. The milling sector procures paddy from the farmers, whereas paddy traders and wholesalers and then prepare the milled rice. After that the wholesale sector procures the milled rice from this sector and sells the milled rice to the retail sector while the retail sector sells the milled rice to the consumers. The product turnover of retailers is about 22 kg per day. This compares with 10 tons per day for the wholesalers and up to 50 tons per day per mill [START_REF] Murshid | RICE PRICES AND GROWTH AND POVERTY REDUCTION IN BANGLADESH[END_REF].

According to the previous studies, [START_REF] Dawson | Testing for the law of one price: Rice market integration in Bangladesh[END_REF]Ahmed & Bernard, 1990;[START_REF] Goletti | STRUCTURAL DETERMINANTS OF MARKET INTEGRATION: THE CASE OF RICE[END_REF][START_REF] Hossain | Evaluation of Rice Markets Integration in Bangladesh[END_REF] it is found that the number of research related to identifying the factors causing price fluctuations and exploring the rice market in Bangladesh especially in Barishal from the consumer and wholesaler point of views has not been yet much explored. Therefore, the study aimed to explore the rice market from both of these perspectives.

Objectives of the Study

This study comprises some key objectives which are as follows; i. To investigate the causes of vulnerability of price of rice in Bangladesh.

ii. To identify the key parties involved in the supply chain and logistics management of the rice market in Barishal.

iii. To examine the financial viability of the wholesalers in Barishal. iv.

To illustrate the factors affecting consumers' intention to purchase rice when the price of rice fluctuates.

v. To find out new prospects and suggest some implications whether the consumers can be offered a fixed fair price throughout the year or not.

Methodology

This study was qualitative where the researcher attempted to explore new ideas and findings of the phenomenon through in-depth interview. According to [START_REF] Tiu Wright | Exploring the in-depth interview as a qualitative research technique with American and Japanese firms[END_REF] and [START_REF] Maxwell | :+An+Interactive+Approach,+Applied+Social+Rese arch+Method+Series,+Sage,+Thousand+Oaks,+CA,+Vol[END_REF], the in-depth interview is regarded as an effective tool to gain a detail understanding of a new phenomenon. All the participants participated in in-depth interview session willingly while they were selected randomly with judgmental sampling technique to remove the research bias.

Two sets of structured questionnaires were designed for the consumers (village people) and wholesalers, both of the interviewees were from Barishal.

A total of 50 village people, who are from 3 different villages, and 30 wholesalers of rice were interviewed to collect data for the study. The age level of all the respondents was above 18 years. For a single interviewee, the interview session took an average of 20 to 30 minutes. In these cases, all the research questions were translated into Bengali so that the respondents could understand and respond easily and smoothly. Furthermore, personal observation was also employed in this study. Both primary and secondary data were employed in this study.

Therefore, the primary data was analyzed by using the Microsoft spreadsheet program.

Result Analysis and Discussion

In this section, the results were analyzed for each research question along with illustrating the key findings of the study to make clearer and better understanding the real scenario of the rice market in Barishal. The study comprised of two sections. The first section illustrated the analysis from the corner point of consumers, who are the village people. On the other hand, the second section described the analysis and findings from the wholesaler point of views. Both of the sections are discussed as follows: The table-1 shows the demographic characteristics of the consumers. Total of 50 consumers precipitated in the interview session willingly as they were not provided any gift to overcome the response biases. Among the participated respondents 32 (64%) were male and 18 (36%) were female. However, the age level of all the respondents was above 18 years. According to the table-1, between 15-25 years old there were 2 participants and between 26-35 years, 36-45 years, 46-55 years, and 56 years or above were 12, 18, 14, and 4 participants respectively. In the case of income levels, the highest number of participants were ranged between the monthly of 0-10000tk, which were 25 along with the lowest number of participants was 1 falling between 300001-above. The occupation of the participants was ranged as farmers, housewives, businessmen, fishermen, teachers, and day-laborers.

Analysis from the consumer perspective

A. The frequency of going to shop to purchase rice

The figure 2 illustrates that among 50 participants, 48 mentioned that they have to purchase rice in different intervals while the other 2 participants told that they need not buy rice at all as they have enough lands for growing paddy which procures the source of rice for their family throughout the year. However, as it is shown in the figure-, almost 74%, the highest portion, consumers buy rice regularly whereas 21% of consumers purchase rice weekly, 5% of consumers buy rice monthly and no consumers buy rice on yearly basis.

B. The quantity of rice consumers purchase when they go for shopping

The quantity of purchased rice of a consumer varies because of different intervals when he or she goes for purchasing. As we find from figure 1 that around 74% of consumers buy rice daily that's why their quantity of purchasing rice falls between 0-5 kg. Furthermore, the consumers who purchase rice weekly generally their quantity ranges from 5 kg to 10 kg. On the other hand, the consumers who purchase rice monthly basis buy rice of 25 kg sacks or 50 kg sacks.

Almost 75% of consumers who buy rice monthly basis purchase 25 kg sacks.

C. The amount of rice cooked per day

The quantity of rice consumption depends on the number of family members the consumer has.

According to the following figure-3, among total 50 participants, the highest number of participants ( 22) said that they need to cook approximately 1.6 kg to 2 kg rice per day following the second-highest number (11) of participants who need almost more than 2 kg rice per day In Bangladesh, the price of rice changes frequently over the year because of several reasons including natural disasters, strong syndicates, creating an artificial crisis, high-profit tendency, the high price of seeds and fertilizers, etc. In most of the cases, consumers enjoy low price in November, December and January because in this period of farmers pick up Aman paddy in their house.

On the contrary, in May, June, July and August consumers have to high price due to floods and other natural disasters though it's Boro cultivation period. But till on 20th July in 2019 the average of rice is 33 tk [START_REF] Parvez | Rice prices hit 3-year low[END_REF]. Because every year the government of Bangladesh purchases a huge amount of paddy from the local farmers to reduce the unusual price hike over the year. Besides, the government imports rice to meet local demand of a huge population.

The following figure-4 describes the average price of rice changes from 2016 to 2019. on 10th February 2019, the price rose up to $ 0.6 and went downward quickly in the following month. In the middle of July 2019, the price again crossed $ 0.5 level which was around $ 0.55 and lowered somewhat under $0.5 level.  What do consumers do when the price increases?

When consumers were asked what they do if price increases, almost 82% of them answered that they buy low priced rice-Bullet, Shorna, Hira. These types of rice are generally cheap and produced locally. Whereas some consumers do not change their purchasing pattern in terms of choosing rice although the price of rice changes. Some consumers agreed that they store rice when the price of is lower especially at the time of harvesting.

E. Do the consumers have a grocery in their village?

All the respondents participated in the study were asked whether they have a grocery in their village or not. All of them stated positively that they have at least one grocery in their village.

Most of the groceries are located in such a place where they can buy whatever they need. These types of groceries sell almost all the necessary items that the consumers need daily.

F. Do the consumers have to go further to buy their daily needs? What are the daily items they buy other than rice?

In response to this question, all of the 50 consumers answered that all of them have to go further for buying other daily items other than rice. In most of the time, they purchase salt, oil, dal, pepper, onions, garlic, potatoes, and other vegetables. The table-2 shows the demographic characteristics of the wholesalers of the rice market. A total of 30 wholesalers who are actively performing business activities in Barishal city precipitated in the interview session. Among 30 participants, all of them were male as no women are associated with rice wholesaling business in Barishal. The age level of all the participants was above 18 years. As per the table-2, 2 participants' age level was between 15-25 years and the age level between 26-35 years, 36-45 years, 46-55 years, and 56 years or above were 13, 8, 6, and 1 respectively. Besides, the lowest number of participants' income levels were ranged between the monthly 0-10000tk, which was 1 and the highest number of participants' income levels between 300001-above was 12. Among 30 respondents, their occupation comprised as 17 were owners, 8 were hired managers, 2 drivers and 3 were labors who are directly and indirectly related to the wholesaling business.

Analysis from the wholesaler perspective

Demographic Characteristics of the Participants

A. The number of wholesalers in Barisal currently selling rice

All of the participants in this section under this question demonstrated their opinions but the answers were somewhat varied from one participant to others. According to their responses, the average number of wholesalers who are presently selling rice within Barisal city to the retailers and consumers are approximately 60 to 70.

B. The price trend changed in per quantity in wholesaling

In most of the cases, the wholesalers of rice in Barisal purchase rice from the northern part of Bangladesh. As, in Barishal, there is very a few number Millers who process local paddy into rice .Besides, the output of these Millers are too poor to meet the local demand. That's why wholesalers have to buy rice from other parts. These regions include-Kushtia, Rajshahi, Bogra, Jhenaidah, Nator, satkhira because in these parts there are lots of Beparis, Aratdars , Millers of rice. In addition, some Rice Agents import rice from India. So, when they purchase from these rice intermediaries almost 84 % of respondents demonstrated that there is no relationship between the purchased quantity of rice and its price. Because every day the association of Beparis, Aratdars , Millers of rice set the price of rice. The wholesalers of use trucks to carry rice into their warehouse. After adding the transport and other costs, for 1 kg rice the wholesalers pay almost 22 BDT to 30 BDT. On the other hand, when wholesalers sell rice to the local retailers and consumers they offer almost 10% to 15% price off on their wholesaling price. Wholesalers sell 1 kg rice almost 32 BDT to 45 BDT as price varies based on the quality of rice.

C. In wholesaling, the percentage of rice comes in 25 KG sacks and 50 KG sacks

Rice is packed in two types of the sack-25 KG sack and 50 KG sack. According to the responses of the participants, almost 78% of rice comes in 25 KG sack as it is easy to carry and store as well as a large number of consumers are likely to buy rice of this quantity. On the other hand, 22% of rice comes in 50 KG sack.

E. To whom could "Helping Hand Belgium" buy rice if they decide to begin a business?

The rice mill owners act as a middle party among farmers, Farias and Paikers, retailers, consumers. Among 30 respondents, almost 75% of respondents noted that if anyone wants to start up a wholesaling business he or she needs to buy rice from the rice mill owners. 5% of the total respondents suggested that a new wholesaler can also buy rice from the rice agents (importers). Besides, paddy is needed to process it to make rice. Thus, it requires larger operations which are costly and time consuming. But if anyone has the paddy processing options, the idea is good.

F. Do "Helping Hand Belgium" need to sign a contract with farmers before they plant the rice? Do the wholesalers buy the harvest before seeding?

All the respondents agreed that no formal contract with farmers is needed to buy rice from the farmers before planting rice. Furthermore, there is no specific time to buy rice as rice is stored for the year-round. Therefore, no one purchases rice before seeding.

G. Transportation the rice from the wholesalers' warehouse to the villages

All the parties involved in the supply chain of rice do business independently. Thus, there is no authorized agents who sell rice in the village areas. Therefore, every party has to bear the cost of transportation of their own. Furthermore, the wholesalers do not have any warehouse in the village areas.

H. The best cost-effective ways to transport rice to the villagers

According to the responses of the respondents, approximately 55% retailers use Pickups to carry rice to the village areas. Pickup is one of the most effective vehicles to carry up-to 1.5 ton rice. As Barishal a riverine region, engine boats are also effective transportations for carrying rice to the rural areas of Barishal. Furthermore, autos and three-wheeler vans are used to transport small quantity of rice from the wholesalers to the villagers. Three wheeler vans

I. The wholesalers monthly cost for maintaining their warehouse

The following figure-9 illustrates the monthly cost of maintaining a warehouse. Among 30 respondents, the highest number of respondents ( 16) mentioned that to maintain a warehouse their range of monthly cost falls between 20001 BDT to 30000 BDT following the second largest number of respondents (6) whose range of monthly cost is 10001 BDT to 20000 BDT.

In contrast, 1 participant, the lowest number of the respondent, noted that his cost of maintaining warehouse is between 000 BDT to 10000 BDT.

Recommendations

The major portion of the population in Bangladesh live in the village areas and most of them live from hand to mouth. For this reason, they have to all the daily necessities regularly. If the price of rice fluctuates on a continuous interval, these impoverished people's suffering no knew bounds. Therefore, it is a big opportunity to offer them all the daily necessities i.e. rice at a fixed lower price relative to the market price. As they buy rice daily with low quantity, a wide range of rice packaging can also be promoted like 5 kg bag, 10 kg bag, 15 kg bag and so on.

This packaging approaches may reduce the burden of spending more TK to buy rice at one time. Besides, in harvesting time when the farmers pick up new paddy in their house a huge amount of paddy can be purchased from them at a lower and fair price as the price of paddy remains lower due the peak season.

From the corner point of wholesalers, results showed that the rice market of Bangladesh is consisted of multiple channel members who individually add markup with their cost resulting in the high price of rice to the consumers. Additionally, they operate their business independently whereas there exist a lacking of effective supply chain and logistics The amount of monthly cost needed to maintain a wearhouse management. As a result, from farmer to consumers there is a huge supply and demand gap. In the last weeks of May 2019, farmers sold 40 kg (One Maund) average paddy at between 450 tk to 500 tk [START_REF] Khan | Govt. Farmers in a Fix over Low Paddy Price[END_REF]. That means 1 kg paddy is sold at around 12 tk. You get 25 kg to 27 kg rice from 40 kg paddy along with 15kg to 13 kg by products which are used as foods of animals and other purposes. If the retail price of this rice is 30 tk per kg that means the price of 25 kg rice is 750 tk. The average consumer price of rice is 34 tk to 48 tk per kg. This gap happens because of the intermediaries involved between farmers and consumers. Therefore, if effective management supply chain and logistics of rice can be ensured, the price of rice will be in affordable range of consumers.

However, the new marketers who want to start rice wholesaling business in Barishal, it would be an opportunity for them to sell rice at lower fixed price to the villagers as there are no businessmen who are still selling rice at a fixed price throughout a year. Also paddy can be purchased at lower price from the local farmers of Barishal since almost 80% of local paddy is sold to the Millers of northern parts of Bangladesh. Then after processing it backs to Barishal with higher price. In case of purchasing rice from the Millers and wholesalers, often retailers and consumers have to suffer a lot because they randomly create artificial crisis of rice and charge high price. This artificial crisis is caused due to the strong syndication of the Millers and wholesalers. Therefore, before starting a business it is important to assess the market trends and formulate contemporary strategies.

Conclusion

The study aimed to investigate the factors that play as the actors of price changes of rice as well as identify business prospects from the consumer and wholesaler point of views. The findings of the study revealed that the supply chain of rice is still a multi-agent system consisting of many actors, i.e. stakeholders such as a retailer, wholesaler, Faria, and miller. For this reason, there is a huge gap between the price of paddy of farmers and the price of rice of retailers, for which, farmers do not get the fair prices of paddy though they have to manage high production cost due to high price of fertilizers, high cost of labors and so on. On the other hand, consumers have to pay a high price when they buy rice from the retailers. Furthermore, the strong syndication among the stakeholders of rice creates complex conditions which also responsible for the instability of the price of rice. Therefore, if any newly established business in Bangladesh aims to sell rice at a fixed lower price than the other channel members throughout the year, it will be difficult to operate due to this strong syndication of the channel members.

Limitations

The sample size of the study was limited within three different villages of Barishal and Barishal city. As the data collection procedure was confined to in-depth interview which represents a qualitative research approach, a larger sample may generate more specific generalizations about the study. Furthermore, if the study is conducted further in other parts of Bangladesh and other developing countries the findings may be somewhat different.

Acknowledgement

This research study was financially supported by Helping Hand Belgium.

Figure 1 :

 1 Figure 1: Rice production of Bangladesh (Source: TRIDGE, 2019)

Figure- 2 :

 2 Figure-2: The frequency of going to the shop to buy rice (Source: Depth interview)

  . In contrast, and the lowest number of participants (3) mentioned that they require around less than or equal to 0.5 kg rice per day.

Figure- 3 :

 3 Figure-3: The amount of rice cooked daily by the respondents (Source: Depth interview)

Figure- 4 :

 4 Figure-4: The trend of average prices of rice from 2016 to 2019 (Source: Depth interview)

Figure- 5 :

 5 Figure-5: Bangladesh's Wholesale Price Trend (Source: TRIDGE, 2019)

Figure- 6 :

 6 Figure-6: The percentage of rice comes in 25 KG and 50 KG sacks (Source: Depth interview)

Figure- 7 :

 7 Figure-7: The number of group members involved in the supply channel of rice and their flow of operations (Source: Depth interview).

Figure- 8 :

 8 Figure-8: The best cost-effective ways to transport rice to the villagers (Source: Depth interview)

Figure- 9 :

 9 Figure-9: The amount of monthly cost needed to maintain a warehouse (Source: Depth interview)

The trend of average prices of rice from 2016 to 2019

									The amount of rice cooked per day
														5 kg		1.6-2 kg			2.01 kg or above
	40 60	41	45	44	35	42	46	47	34	42	45	48	34	41	44	43	36	35	39	33	34	36
	20
	0
			May			June			July		October	November	December
										2016	2017	2018	2019

Farmer Bepari Miller Local Wholesaler or Aratdar District Level Wholesaler or Paikers Retailer Consumer Faria to

  And the other 20% of respondents recommended that if the quantity of rice is relatively low, he or she may buy rice from the local wholesalers of Barishal. No one suggest buy rice from farmers as no one buy rice from farmers. Only one can buy paddy from them.