Study of instability and turbulence development scenarios in a flow with stable stratification and two-dimensional obstacle

摘要

Computational study of a flow with an obstacle and stratification in various conditions was performed by means of the methods of large-eddy simulation (LES) and direct numerical simulation (DNS) implemented to solve the three-dimensional Navier-Stokes equations in the Boussinesq approximation, together with by the scalar diffusion equation. The results of scanning in the wide ranges of physical parameters (Reynolds number Re = UH/ν, Prandtl number Pr = ν/κ) are presented for instability and turbulence development scenarios in overturning internal lee waves generated by the two-dimensional cosine-shaped obstacle of height H in a stably stratified flow with the constant values of inflow density gradient and velocity U. These phenomena are explored by visualization of velocity and scalar (density) fields, and the analysis of spectra obtained from the DNS/LES data at 50 ≤ Re ≤ 40 000 and 1 ≤ Pr ≤ 700, relating to laboratory experiment cases, and atmospheric or oceanic situations. Based on the numerical simulation results, the power-law dependence on Reynolds number is demonstrated for the wavelength of the most unstable perturbation.