By using the direct numerical simulation method, the characteristics of counter-gradient heat transport in homogeneous shear turbulence under stable thermal stratification were investigated. The cluster connectivity method was employed to thoroughly examine the statistical properties of counter-gradient heat transport structures, including their geometric features and spatial distribution. The Reynolds number was set at Rex=5 000, and the Richardson numbers Ri were set to 0, 0.1, and 0.2, respectively. The simulation results reveal significant impacts of stable thermal stratification on turbulence structures. The number of counter-gradient transport regions significantly increases by introducing thermal stratification, and the relevant structures are elongated in the streamwise direction. Furthermore, the inclination angle between the structures and the streamwise direction is reduced by stable stratification. In the vertical direction, "ejection" and "sweep" heat fluxes exhibit a characteristic of paired distribution along the diagonal direction, and with increasing stratification intensity, "sweep" structures tend to appear below "ejection" structures. The flndings of this study deepen the understanding of counter-gradient heat transport in stratified shear turbulence and are useful for further exploration of the physical mechanisms underlying the counter-gradient transport phenomenon.
[1] Peltier W R, Caulfield C P. Mixing e-ciency in stratifled shear flows [J]. Annual Review of Fluid Mechanics, 2003, 35(1): 135-167.
[2] Gerz T, Schumann U, Elghobashi S E, et al. Direct numerical simulation of stratifled homogeneous turbulent shear flows [J]. Journal of Fluid Mechanics, 1989, 200: 563-594.
[3] Holt S E, Koseff J R, Ferziger J H, et al. A numerical study of the evolution and structure of homogeneous stably stratifled sheared turbulence [J]. Journal of Fluid Mechanics, 1992, 237: 499-539.
[4] Jacobitz F G, Sarkar S, van Atta C W, et al. Direct numerical simulations of the turbulence evolution in a uniformly sheared and stably stratifled flow [J]. Journal of Fluid Mechanics, 1997, 342: 231-261.
[5] Diamessis P J, Nomura K K. Interaction of vorticity, rate-of-strain, and scalar gradient in stratifled homogeneous sheared turbulence [J]. Physics of Fluids, 2000, 12(5): 1166-1188.
[6] Webster C A G. An experimental study of turbulence in a density-stratifled shear flow [J]. Journal of Fluid Mechanics, 1964, 19(2): 221-245.
[7] Lin J T, Pao Y H. Wakes in stratifled fluids [J]. Annual Review of Fluid Mechanics, 1979, 11(1): 317-338.
[8] 金海生. 温度分层剪切流的试验和数学模型研究[J]. 河海大学学报(自然科学版), 1991, 19(4): 59-67.
[9] Spedding G R, Browand F K, Fincham A M, et al. Turbulence, similarity scaling and vortex geometry in the wake of a towed sphere in a stably stratifled fluid [J]. Journal of Fluid Mechanics, 1996, 314: 53-103.
[10] 邱翔, 黄永祥, 卢志明, 等. 稳定分层湍流的PIV实验研究[J]. 实验流体力学, 2008, 22(2): 1-9.
[11] Rogallo R S. Numerical experiments in homogeneous turbulence [M]. Washington D C: National Aeronautics and Space Administration, 1981.
[12] Starr V P. Physics of negative viscosity phenomena [M]. New York: McGraw Hill, 1968.
[13] Komori S, Ueda H, Ogino F, et al. Turbulence structure in stably stratifled open-channel flow [J]. Journal of Fluid Mechanics, 1983, 130: 13-26.
[14] Komori S, Nagata K. Efiects of molecular difiusivities on counter-gradient scalar and momentum transfer in strongly stable stratification [J]. Journal of Fluid Mechanics, 1996, 326: 205-237.
[15] Gerz T, Schumann U. A possible explanation of countergradient fluxes in homogeneous turbulence [J]. Theoretical and Computational Fluid Dynamics, 1996, 8: 169-181.
[16] Lozano-Duran A, Flores O, Jim enez J, et al. The three-dimensional structure of momentum transfer in turbulent channels [J]. Journal of Fluid Mechanics, 2012, 694: 100-130.
[17] Sekimoto A, Dong S, Jimenez J, et al. Direct numerical simulation of statistically stationary and homogeneous shear turbulence and its relation to other shear flows [J]. Physics of Fluids, 2016, 28(3): 035101.
[18] Dong S, Lozano-Duran A, Sekimoto A, et al. Coherent structures in statistically stationary homogeneous shear turbulence [J]. Journal of Fluid Mechanics, 2017, 816: 167-208.
[19] Pumir A. Turbulence in homogeneous shear flows [J]. Physics of Fluids, 1996, 8(11): 3112-3127.
[20] Canuto C, Hussaini M Y, Quarteroni A, et al. Spectral methods: evolution to complex geometries and applications to fluid dynamics [M]. Berlin: Springer Science & Business Media, 2007.
[21] 董思卫, 程诚, 陈坚强, 等. 基于聚类连通法的湍流拟序结构研究进展[J]. 力学进展, 2021, 51(4): 792-830.
[22] Katul G, Kuhn G, Schieldge J, et al. The ejection-sweep character of scalar fluxes in the unstable surface layer [J]. Boundary-Layer Meteorology, 1997, 83: 1-26.
[23] Li D, Bou-Zeid E. Coherent structures and the dissimilarity of turbulent transport of momentum and scalars in the unstable atmospheric surface layer [J]. Boundary-Layer Meteorology, 2011, 140: 243-262.
[24] Chowdhuri S, Prabha T V. An evaluation of the dissimilarity in heat and momentum transport through quadrant analysis for an unstable atmospheric surface layer flow [J]. Environmental Fluid Mechanics, 2019, 19: 513-542.
[25] Moisy F, Jimenez J. Geometry and clustering of intense structures in isotropic turbulence [J]. Journal of Fluid Mechanics, 2004, 513: 111-133.
[26] del Alamo J C, Jimenez J, Zandonade P, et al. Self-similar vortex clusters in the turbulent logarithmic region [J]. Journal of Fluid Mechanics, 2006, 561: 329-358.
[27] Dong S, Tong F, Yu M, et al. Positive and negative pairs of fluctuating wall shear stress and heat flux in supersonic turbulent boundary layers [J]. Physics of Fluids, 2022, 34(8): 085124.
[28] Zhang S, Xia Y, Qiu X, et al. Secondary vortical structures statistics of near-wake region in cylinder/wall interaction [J]. Acta Mechanica Sinica, 2023, 39(8): 322375.
[29] Yoon M, Hwang J, Yang J, et al. Wall-attached structures of streamwise velocity fluctuations in an adverse-pressure-gradient turbulent boundary layer [J]. Journal of Fluid Mechanics, 2020, 885: A12.
[30] Dong S, Huang Y, Yuan X, et al. The coherent structure of the kinetic energy transfer in shear turbulence [J]. Journal of Fluid Mechanics, 2020, 892: A22.
[31] Cheng C, Li W, Lozano-Duran A, et al. On the structure of streamwise wall-shear stress fluctuations in turbulent channel flows [J]. Journal of Fluid Mechanics, 2020, 903: A29.
[32] Cheng C, Li W, Lozano-Duran A, et al. Uncovering Townsend’s wall-attached eddies in low-Reynolds-number wall turbulence [J]. Journal of Fluid Mechanics, 2020, 889: A29.
[33] Osawa K, Jimenez J. Intense structures of difierent momentum fluxes in turbulent channels [J]. Physical Review Fluids, 2018, 3(8): 084603.
[34] Jeong J, Hussain F, Schoppa W, et al. Coherent structures near the wall in a turbulent channel flow [J]. Journal of Fluid Mechanics, 1997, 332: 185-214.
[35] Jimenez J. Near-wall turbulence [J]. Physics of Fluids, 2013, 25(10): 101302
[36] Iida O, Nagano Y. Efiect of stable-density stratification on counter gradient flux of a homogeneous shear flow [J]. International Journal of Heat and Mass Transfer, 2007, 50(1/2): 335-347.
