Direct simulation of stably stratified wall-bounded turbulence using the lattice Boltzmann method

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The lattice Boltzmann method (LBM) is employed to simulate stratified plane Couette (SPC) flows in their statistically stationary turbulent state. The aim is to assess the suitability of the LBM for direct simulation of wall-bounded, sheared turbulence under the influence of stable stratification. The SPC flow is generated by two parallel plates moving in opposite directions with velocities ± U w, and the buoyancy is fixed at ± b w at the upper and lower plates, respectively. The Reynolds number Re = U w h / ν, where h is the half-gap height, and ν is the kinematic viscosity, varies from 1000 to 3000. The Richardson number Ri = b w h / U w 2 is set to 0 or 0.01. The LBM results are compared to direct numerical simulations using the conventional pseudo-spectral method, and good agreement is found in various turbulence statistics, such as mean and fluctuation velocity and buoyancy, Reynolds stress, turbulent heat flux, dissipation rate, wall fluxes of momentum and heat, and longitudinal and transverse turbulence spectra. The results from grid-sensitivity tests indicate that the uniform isotropic grid spacing Δ x in LBM needs to be no greater than approximately the near-wall viscous length scale δ ν to achieve adequate resolution of stratified wall-bounded turbulence.