A Numerical Verification of Self-Similar Multiplicative Theory for Small-Scale Atmospheric Turbulent Convection

The self-similar multiplicative theory(SSM theory), aims to interpret the scaling behavior of the temperature structure function. In the present paper, the author report results from a numerical simulation of atmospheric turbulent convection in order to verify this theory. The simulation was based on a shell model which was deduced from simplified atmospheric convection equations. The numerical results agreed well with the theory prediction of scaling law from the first order to the eighth order. They also showed that the prediction of this theory was better than that given by the Kolmogorov's theory in 1941, log-normal, and β model theories.

INTERMITTENCY AND SCALING IN TURBULENT CONVECTION

Both the velocity and temperature measurements taken in turbulent Rayleigh-B'enard convection experiments have been analyzed. It is found that both the velocity and temperature fluctuations are intermittent and can be well-described by the She-Leveque hierarchical structure. A positive correlation between the vertical velocity and the temperature differences is found both at the center, near the sidewall and near the bottom of the convection cell, supporting that buoyancy is significant in the Bolgiano regime. Moreover, the intermittent nature of the temperature fluctuations in the Bolgiano regime can be attributted to the variations in the temperature dissipation rate. However, the relations between the velocity and temperature structure functions and their correlations implied by the Bolgiano-Obukhov scaling are not supported by experimental measurements.

Effects of Prandtl number in two-dimensional turbulent convection

We report a numerical study of the Prandtl-number(Pr)effects in two-dimensional turbulent Rayleigh-Bénard convection.The simulations were conducted in a square box over the Pr range from 0.25 to 100 and over the Rayleigh number(Ra)range from 10^(7) to 10^(10).We find that both the strength and the stability of the large-scale flow decrease with the increasing of Pr,and the flow pattern becomes plume-dominated at high Pr.The evolution in flow pattern is quantified by the Reynolds number(Re),with the Ra and the Pr scaling exponents varying from 0.54 to 0.67 and-0.87 to-0.93,respectively.It is further found that the non-dimensional heat flux at small Ra diverges strongly for different Pr,but their difference becomes marginal as Ra increases.For the thermal boundary layer,the spatially averaged thicknesses for all the Pr numbers can be described byδθ~Ra^(-0.30) approximately,but the local values vary a lot for different Pr,which become more uniform with Pr increasing.

Attractive fixed-point solution study of a shell model for turbulent convection

Different scaling behaviors, such as Kolmogorov (K41) scaling and Bolgiano and Obukhov (BO) scaling, have been reported in various shell models proposed for turbulent thermal convection. However, two coexistent subranges with K41 and BO scaling are not set up with Bolgiano scale interlaying between the largest scale and the dissipation scale. In this paper, we summarize fixed-point solution study of the Brandenburg model with small perturbation theory by introducing a small disturbance term as the impact of buoyancy. Three groups of fixed-point solutions with different locations of the so-called buoyancy scale, above/below which buoyancy is significant/insignifant. Both theoretical and numerical results show that a modified K41 scaling, instead of K41 and BO coexistent scaling, is set up even though buoyancy may be significant over the scaling range, which suggests that the buoyancy scale is not related exactly to the Bolgiano scale. Thus, a K41 and BO coexistent scaling behavior is not setup for the Brandenburg model.

Space-time correlations in turbulent Rayleigh–Bnard convection

The recent development of the elliptic model （He, et al. Phy. Rev. E, 2006）, which predicts that the space-time correlation function Cu（r, r） in a turbulent flow has a scaling form Cu（rE, 0） with re being a combined space-time separa- tion involving spatial separation r and time delay T, has stimulated considerable experimental efforts aimed at testing the model in various turbulent flows. In this paper, we review some recent experimental investigations of the space-time correlation function in turbulent Rayleigh-Benard convection. The experiments conducted at different representative locations in the convection cell confirmed the predictions of the elliptic model for the velocity field and passive scalar field, such as local temperature and shadowgraph images. The understanding of the functional form of Cu（r, v） has a wide variety of applications in the analysis of experimental and numerical data and in the study of the statistical properties of small-scale turbulence. A few examples are discussed in the review.

Turbulent forced convection in a heat exchanger square channel with wavy-ribs vortex generator

Turbulent forced convective heat transfer and flow con figurations in a square channel with wavy-ribs inserted diagonally are examined numerically. The in fluences of the 30° and 45° flow attack angles for wavy-ribs, blockage ratio, R B= b/H = 0.05–0.25 with single pitch ratio, R P= P/H = 1 are investigated for the Reynolds number based on the hydraulic diameter of the square channel, Re = 3000–20000. The use of the wavy-ribs, which inserted diagonal in the square channel, is aimed to help to improve the thermal performance in heat exchange systems.The finite volume method and SIMPLE algorithm are applied to the present numerical simulation. The results are presented on the periodic flow and heat transfer pro files, flow con figurations, heat transfer characteristics and the performance evaluations. The mathematical results reveal that the use of wavy-ribs leads to a higher heat transfer rate and friction loss over the smooth channel. The heat transfer enhancements are around 1.97–5.14 and 2.04–5.27 times over the smooth channel for 30° and 45° attack angles, respectively. However, the corresponding friction loss values for 30° and 45° are around 4.26–86.55 and 5.03–97.98 times higher than the smooth square channel, respectively. The optimum thermal enhancement factor on both cases is found at R B= 0.10 and the lowest Reynolds number, Re = 3000, to be about 1.47 and 1.52, respectively, for 30° and 45° wavy-ribs.

Efficient turbulent compressible convection in the deep stellar atmosphere

We report on an application of gas-kinetic BGK scheme to the computation of turbulent compressible convection in the stellar interior. After incorporating the Sub-grid Scale （SGS） turbulence model into the BGK scheme, we tested the effects of numerical parameters on the quantitative relationships among the thermodynamic variables, their fluctuations and correlations in a very deep, initially gravity-stratified stellar atmosphere. Comparison indicates that the thermal properties and dynamic properties are dominated by different aspects of numerical models separately. An adjustable Deardorff constant in the SGS model cu, = 0.25 and an amplitude of artificial viscosity in the gas-kinetic BGK scheme C2 = 0 are appropriate for the current study. We also calculated the densityweighted auto- and cross-correlation functions in Xiong＇s turbulent stellar convection theory based on which the gradient type of models of the non-local transport and the anisotropy of the turbulence were preliminarily studied. No universal relations or constant parameters were found for these models.

Characteristics of convection and overshooting in RGB and AGB stars

Based on the turbulent convection model （TCM） of Li ＆ Yang, we have studied the characteristics of turbulent convection in the envelopes of 2 and 5M⊙ stars at the red giant branch and asymptotic giant branch phases. The TCM has been successfully applied over the entire convective envelopes, including the convective unstable zone and the overshooting regions. We find that the convective motions become progressively stronger when the stellar models are located farther up along the Hayashi line. In the convective unstable zone, we find that the turbulent correlations are proportional to functions of a common factor （V - V^d）T, which explains similar distributions in those correlations. For the TCM we find that if the obtained stellar temperature structure is close to that of the mixing length theory （MLT）, the convective motion will have a much larger velocity and thus be more violent. However, if the turbulent velocity is adjusted to be close to that of the MLT, the superadiabatic convection zone would be much more extended inward, which would lead to a lower effective temperature of the stellar model. For the overshooting distance, we find that the e-folding lengths of the turbulent kinetic energy k in both the top and bottom overshooting regions decrease as the stellar model is progressively located farther up along the Hayashi line, but both the extents of the decrease are not obvious. The overshooting distances of the turbulent correlation /u＇rT＂ are almost the same for the different stellar models with the same set of TCM parameters. For the decay modes of the kinetic energy k, we find that they are very similar for different stellar models based on the same set of TCM parameters, and there is a nearly linear relationship between lg k and In P for different stellar models. When Cs or α increases while the other parameters are fixed, the obtained linearly decaying distance will become longer.

Turbulence properties in the solar convection envelope:properties of the overshooting regions

We apply the turbulent convection model （TCM） to investigate properties of turbulence in the solar convective envelope, especially in overshooting regions. The results show TCM gives negative turbulent heat flux uτ＇T＇ in overshooting regions, which is similar to other nonlocal turbulent convection theories. The turbulent temperature fluctuation T＇T＇ shows peaks in overshooting regions. Most important, we find that the downward overshooting region below the base of the solar convection zone is a thin cellular layer filled with roll-shaped convective cells. The overshooting length for the temperature gradient is much shorter than that for element mixing because turbulent heat flux of downward and upward moving convective cells counteract each other in this cellular overshooting region. Comparing the models＇ sound speed with observations, we find that taking the convective overshooting into account helps to improve the sound speed profile of our nonlocal solar models. Comparing the p-mode oscillation frequencies with observations, we validated that increasing the diffusion parameters and decreasing the dissipation parameters of TCM make the p-mode oscillation frequencies of the solar model be in better agreement with observations.

Cold filament frontogenesis and frontolysis induced by thermal convection turbulence using large eddy simulation

The frontogenetic processes of a submesoscale cold filament driven by the thermal convection turbulence are studied by a non-hydrostatic large eddy simulation.The results show that the periodic changes in the direction of the cross-filament secondary circulations are induced by the inertial oscillation.The change in the direction of the secondary circulations induces the enhancement and reduction of the horizontal temperature gradient during the former and later inertial period,which indicates that the frontogenetical processes of the cold filament include both of frontogenesis and frontolysis.The structure of the cold filament may be broken and restored by frontogenesis and frontolysis,respectively.The magnitude of the down-filament currents has a periodic variation,while its direction is unchanged with time.The coupling effect of the turbulent mixing and the frontogenesis and frontolysis gradually weakens the temperature gradient of the cold filament with time,which reduces frontogenetical intensity and enlarges the width of cold filament.

Anisotropy and Dissipation of Turbulence and Their Effects on Solar Models

Based on a dynamic model for turbulent convection, we investigate the effects of dissipation and anisotropy of the turbulence on the convective energy transport. We introduce two time scales to describe the dissipation of the turbulence, and approximate the anisotropy of the turbulence by Rotta's proposal of 'return to isotropy'. The improved turbulence model results in an equation to determine the temperature gradient in the convection zone, which is of similar form as that of the MLT. We apply the improved MLT to solar models, and find that the increases of the anisotropy and decreases of the dissipation of the turbulence reduce the value of the convection parameter a, because these processes enhance the convective energy transfer rate. Compared with the observed solar p-mode frequencies, it is plausible that the dissipation of the turbulence in the solar convection zone should be fairly strong, while the degree of anisotropy of the turbulence plays a less significant role on the structure of the solar convection zone.

Measurements of heat transport by turbulent Rayleigh-Bénard convection in rectangular cells of widely varying aspect ratios

High-precision measurements of the Nusselt number Nu for Rayleigh-B6nard （RB） convection have been made in rectangular cells of water （Prandtl number Pr ≈ 5 and 7） with aspect ratios （F~, Fy） varying between （1, 0.3） and （20.8, 6.3）. For each cell the data cover a range of a little over a decade of Rayleigh number Ra and for all cells they jointly span the range 6x105 〈 Ra 〈1011. The two implicit equations of the Grossmann-Lohse （GL） model together with the empirical finite conductivity cor- rection factorf（X） were fitted to obtain estimates of Nu∞ in the presence of perfectly conducting plates, and the obtained Nu∞ is independent of the cells＇ aspect ratios. A combination of two-power-law, Nu∞= O.025Ra0.357＋O.525Ra0.168, can be used to de- scribe Nu∞（Ra）. The fitted exponents 0.357 and 0.168 are respectively close to the predictions 1/3 and 1/5 of the 11μ. and 1Vμ re- gimes of the GL model. Furthermore, a clear transition from the II. regime to the IVμ regime with increasing Ra is revealed.

Impact of Cyclone Nilam on Tropical Lower Atmospheric Dynamics

A deep depression formed over the Bay of Bengal on 28 October 2012, and developed into a cyclonic storm. After landfall near the south coast of Chennai, cyclone Nilam moved north-northwestwards. Coordinated experiments were conducted from the Indian stations of Gadanki（13.5？N, 79.2？E） and Hyderabad（17.4？N, 78.5？E） to study the modification of gravity-wave activity and turbulence by cyclone Nilam, using GPS radiosonde and mesosphere–stratosphere–troposphere radar data. The horizontal velocities underwent large changes during the closest approach of the storm to the experimental sites. Hodograph analysis revealed that inertia gravity waves（IGWs） associated with the cyclone changed their directions from northeast（control time） to northwest following the path of the cyclone. The momentum flux of IGWs and short-period gravity waves（1–8 h） enhanced prior to, and during, the passage of the storm（±0.05 m2s-2and ±0.3 m2s-2, respectively）, compared to the flux after its passage. The corresponding body forces underwent similar changes, with values ranging between ±2–4m s-1d-1and ±12–15 m s-1d-1. The turbulence refractivity structure constant（C2n） showed large values below 10 km before the passage of the cyclone when humidity in the region was very high. Turbulence and humidity reduced during the passage of the storm when a turbulent layer at ～17 km became more intense. Turbulence in the lower troposphere and near the tropopause became weak after the passage of the cyclone.

Local Collocation Approach for Solving Turbulent Combined Forced and Natural Convection Problems

An application of the meshless Local Radial Basis Function Collocation Method(LRBFCM)[22,30–33]in solution of incompressible turbulent combined forced and natural convection is for the first time explored in the present paper.The turbulent flow equations are described by the low-Re number k−εmodel with Launder and Sharma[23]and Abe et al.[1]closure coefficients.The involved temperature,velocity,pressure,turbulent kinetic energy and dissipation fields are represented on overlapping 5-noded sub-domains through the collocation by using multiquadrics Radial Basis Functions(RBF).The involved first and second order partial derivatives of the fields are calculated from the respective derivatives of the RBF’s.The involved equations are solved through the explicit time stepping.The pressure-velocity coupling is based on Chorin’s fractional step method[11].The adaptive upwinding technique,proposed by Lin and Atluri[27],is used because of the convection dominated situation.The solution procedure is represented for a 2D upward channel flow with differentially heated walls.The results have been assessed by achieving a reasonable agreement with the direct numerical simulation of Kasagi and Nishimura[20]for Reynolds number 4494,based on the channel width,and Grashof number 9.6×105.The advantages of the represented mesh-free approach are its simplicity,accuracy,similar coding in 2D and 3D,and straightforward applicability in non-uniform node arrangements.

Interaction of Radiation and Turbulent Natural Convection:A Pseudo-Direct Numerical Study

This paper presents a hybrid lattice Boltzmann solver for turbulent buoyancy-driven flow coupled with surface thermal radiation.The two-relaxation time scheme for the Boltzmann equation combined with the implicit finite difference scheme for the energy equation is implemented to compute the heat transfer and fluid flow characteristics.The accuracy and robustness of the hybrid approach proposed in this study are assessed in terms of the numerical and experimental data of other researchers.Upon performing the simulation,the Rayleigh number is ranged from 108 to 1010 whereas the surface emissivity is changed from zero to unity.During computations,it is found that the overall temperature of the cavity is increased as a result of enhancing the surface radiation.Convective plumes are formed both at the isothermal and the thermally-insulated walls with the Ra109 and#0.6.In the conditions under study,the overall heat transfer rate is raised by around 5%when taking into account the surface thermal radiation.

Temperature fluctuations and heat transport in partitioned supergravitational thermal turbulence

We report an experimental study of the local temperature fluctuationsδT and heat transport in a partitioned supergravitational turbulent convection system.Due to the dynamics of zonal flow in the normal system without partition walls,the probability density function(PDF)at a position in the mixing zone exhibits a downward bending shape,suggesting that the multi-plume clustering effect plays an important role.In partitioned system,zonal flow is suppressed and the PDFs indicate that the single-plume effect is dominant.Moreover,statistical analysis shows that the PDF ofδT is sensitive to supergravity.Additionally,the thermal spectra follow P(f)∼f^(-5) in the normal system,which is relevant to the zonal flow.The absolute value of the scaling exponent of P(f)and the scaling range become small in the partitioned system,which provides another evidence for the influence of zonal flow on the energy cascade.Further,heat transfer enhancement is found in the partitioned system,which may result from zonal flow being restricted and then facilitating the radial movement of thermal plumes to the opposite conducting cylinder.This work may provide insights into the flow and heat transport control of some engineering and geophysical flows.

Heat transfer and flow structure of two-dimensional thermal convection over ratchet surfaces

This paper presents a numerical study of the Rayleigh-Benard convection(RBC)in two-dimensional cells with asymmetric(ratchet)roughness distributed on the top and bottom surfaces.We consider two aspect ratios of roughness y=1,2 and the range of the Rayleigh number 1.0 xlO6<Ra<2.0x1010 with the Prandtl number Pr=4.The influences of the roughness on the heat transfer and the flow structure are found to be strongly dependent on both Ra and the roughness geometry.We find that the roughness can have a significant influence on the organization of the secondary comer rolls,and the comer rolls are evidently suppressed by the roughness for intermediate values of Ra.In the presence of the roughness,a sharp jump of the Nu values is identified as the Ra value is slightly increased,accompanied with the dramatic changes of the large-scale flow structure and the plume dynamics.The influences of the ratchet orientation on the heat transfer and the flow structure are discussed and analyzed.

Double diffusive convection in the finger regime for different Prandtl and Schmidt numbers

In this work fingering double diffusive convection,i.e.the buoyancy-driven flow with fluid density being affected by two different scalar components,is investigated numerically with special efforts on the influences of the physical properties of two scalar components.We show that different scalar properties can affect the global transport behaviors.The concentration flux exhibits different exponents in their power-law scalings for different combinations of scalar components.The scaling exponents of heat flux,however,depend mainly on the ratio of the diffusivities of two scalars.If one uses the local parameters of the finger layer in the bulk,the behaviors are very similar to those found in the fully periodic simulations.The horizontal width of the fingers is consistent with the wavelength of the fast growing mode.For one case we observe evidences of the thermohaline staircase,namely,the typical width of the flow structures changes significantly in different layers within the flow domain.

Unsteady analysis of jet impingement under vibration conditions

The vibration of thermodynamic machinery will affect its cooling system.In this research,a high-resolution simulation of jet impingement was performed to quantify the unsteady turbulent convection under vibration conditions.A newly developed Self-Adaptive Turbulence Eddy Simulation(SATES)method was used.The Reynolds number was Re=23000,the jet-towall distance was fixed at H/D=2,and the vibrating frequency of the impinging wall f varied from 0 to 200 Hz.Compared with the static wall case,the maximum enhancement of the stagnation point and area averaged Nusselt number within r/D=1 could reach up to 5%due to the larger primary vortices,whereas it could reduce the heat transfer by 10%beyond r/D=3 due to the suppression of the wall vortices development.Based on the unsteady analysis and Proper Orthogonal Decomposition(POD)pattern,the modes controlled by vibration were recognized and their contributions to the heat transfer performance were also evaluated.The introduction of the vibration promoted the development of the primary vortices and changed the radial alternating motion to a vertical alternating motion at the wall jet region.The former was beneficial for the heat transfer,while the latter was unfavorable.

Convective heat transfer of nanofluids with correlations

To investigate the convective heat transfer of nanofluids, experiments were performed using silver-water nanofluids under laminar, transition and turbulent flow regimes in a horizontal 4.3 mm inner-diameter tube-in-tube counter-current heat transfer test section. The volume concentration of the nanoparticles varied from 0.3% to 0.9% in steps of 0.3%, and the effects of thermo-physical properties, inlet temperature, volume concentration, and mass flow rate on heat transfer coefficient were investigated. Experiments showed that the suspended nanoparticles remarkably increased the convective heat transfer coefficient, by as much as 28.7% and 69.3% for 0.3% and 0.9% of silver content, respectively. Based on the experimental results a correlation was developed to predict the Nusselt number of the silver-water nanofluid, with ＋10% agreement between experiments and prediction.