Turbulence Structure and Mixing in Strongly Stable Couette Flows over Thermally Heterogeneous Surfaces: Effect of Heterogeneity Orientation

Abstract Direct numerical simulations (DNS) of plane Couette flows over thermally heterogeneous surfaces at bulk Reynolds number $$Re=10^4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>R</mml:mi> <mml:mi>e</mml:mi> <mml:mo>=</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>4</mml:mn> </mml:msup> </mml:mrow> </mml:math> and bulk Richardson number $$Ri=0.25$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>R</mml:mi> <mml:mi>i</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.25</mml:mn> </mml:mrow> </mml:math> are performed. The focus of the present study (that extends previous work by the authors) is the effect of surface heterogeneity orientation on boundary-layer structure. The temperature of the upper and lower walls is either homogeneous or varies sinusoidally, where the temperature-wave crests are either normal or parallel to the mean flow (HETx and HETy cases, respectively). Importantly, the horizontal-mean surface temperature is the same in all simulations. The stratification is strong enough to quench turbulence over a homogeneous surface, but turbulence survives over heterogeneous surfaces. In all heterogeneous cases, both molecular diffusion and turbulence transfer momentum down the gradient of mean velocity. The total (turbulent plus diffusive) heat flux is down-gradient, but quasi-organized eddy motions generated by the surface thermal heterogeneity induce heat transfer up the gradient of the mean temperature. Comparative analysis of HETx and HETy cases shows that the configuration with the spanwise heterogeneity is more turbulent and more efficient in transporting momentum and heat vertically than its counterpart with the streamwise heterogeneity. Vertical profiles of mean fields and turbulence moments differ considerably between the HETx and HETy cases, e.g., the streamwise heat flux differs not only in magnitude but also in sign. A close examination of the second-order turbulence moments, vertical-velocity and temperature skewness, and the flow eddy structure helps explain the observed differences between the HETx and HETy cases. The implications of our DNS findings for modelling turbulence in stably-stratified environmental and industrial flows with surface heterogeneity are discussed.