Newsletter 2021.3 Index
Theme : "The Conference of Fluid Engineering Division (March issue)”

Direct Numerical Simulation and Linear Processes of Stably Stratified Sheared Turbulence
Aoi NAKAMURA,

Abstract
Unsteady turbulence under uniform stratification and uniform shear is analysed by direct numerical simulations (DNS) at a moderate Reynolds number (Re = 50) and a Prandtl number Pr = 1, to investigate the combined effects of stratification and mean shear, and discuss the applicability of the rapid distortion theory (RDT). Numerical scheme for the present DNS is the Fourierspectral method. The computational domain is much larger than the initial integral scale to resolve the largescale structures which develop in stratified shear flows. The stratification and shear have linear effects on the flow since the buoyancy term and the meanshear term are the linear terms in the governing equations. They have more significant effects on large scales, and the stratification is effective down to the Ozmidov scale, and the mean shear is effective down to the Corrsin scale. Then, the RDT, which is a linear theory, applies down to the Ozmidov or Corrsin scale. The DNS results also show that the mean shear enhances the largescale motion and suppresses the smallscale vertical motion, leading to a better applicability of RDT even at small scales.
Key words
Turbulence, Stratified Flow, Shear, Ozmidov Scale, Corrsin Scale
Figures
Figure 1 Sketch of the mean field.
Case 
Sh  Fr  L (DNS) 
Sh1Fr1 
1  1  30π 
Sh1Fr01 
1  0.1  30π 
Sh10Fr1 
10  1  30π 
Sh10Fr01 
10  0.1  40π 
Sh15Fr01 
15  0.1  40π 
Sh20Fr01 
20  0.1  40π 
Sh30Fr01 
30  0.1  40π 
Figure 2 Distribution of the kinetic energy u_{i}^{2}/2 (red) and the potential energy ρ^{2}/(2Fr^{2})(blue) obtained by DNS (Case Sh1Fr1). (a,d) t=U^{*}_{0}t^{*}/L^{*}_{0}=2, (b,e) t = 10 and (c,f) t = 20.
Figure 3 DNS and RDT results of the kineticenergy spectrum E_{K}(k) and the potentialenergy spectrum E_{P}(k) at (a) t=1 , (b) t=4 and (c) t=8 for Sh1Fr1. The symbol ● on the solid lines (DNS) indicates the Ozmidov wavenumber k_{O}=l_{O}^{1} which is equal to the Corrsin wavenumber( k_{C}=l_{C}^{1} ), and ○ indicates Kolmogorov wavenumber k_{K}=l_{K}^{1} (l^{*}_{K}=(ν^{*3}/ε*)^{1/4}: Kolmogorov scale).
Figure 4 DNS and RDT results of the kineticenergy spectrum E_{K}(k) and the potentialenergy spectrum E_{P}(k) at t=1.5 for (a) Sh1Fr01, (b) Sh10Fr1 and (c) Sh10Fr01. The arrows at the top of each figure indicate the Ozmidov, Corrsin and Kolmogorov wavenumbers.
Figure 5 Shearparameter dependence of the energy spectra (a)E_{K}(k), (b)E_{P}(k) and (c)E_{33}(k) at t=1 obtained by DNS. The arrows at the top of each figure show the four Kolmogorov wavenumbers and four Ozmidov wavenumbers corresponding to the four simulated cases. The Corrsin wavenumber satisfies k_{C} ≥ k_{O} (k_{C} = Sh^{3/2}Fr^{3/2}k_{O}) in all the figures.