Newsletter  2021.3  Index

Theme : "The Conference of Fluid Engineering Division (March issue)” Preface (T. HASHIMOTO，S. MATSUDA，H.J. PARK) Direct Numerical Simulation and Linear Processes of Stably Stratified Sheared Turbulence Aoi NAKAMURA, Shinya OKINO and Hideshi HANAZAKI (Kyoto University) Synthesis of microcapsules containing temperature-sensitive magnetic particles and understanding of flow characteristics Kazuki OGURA, Keiko ISHII and Koji FUMOTO (Aoyama Gakuin University) Flight simulation game of micro air vehicle Yoshitaka ISODA , Takuma SADANAGA , Makoto KAWANO (Kyoto Institute of Technology) Meisei Tennyo, Dance in the Air! Atsuki FUKUHARA (Meisei University)

 

Direct Numerical Simulation and Linear Processes of Stably Stratified Sheared Turbulence

Aoi NAKAMURA, Shinya OKINO and Hideshi HANAZAKI Kyoto University

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 Fourier-spectral method. The computational domain is much larger than the initial integral scale to resolve the large-scale structures which develop in stratified shear flows. The stratification and shear have linear effects on the flow since the buoyancy term and the mean-shear 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 large-scale motion and suppresses the small-scale 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.

Table 1 Parameters and the computed box size in DNS.

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_i²/2 (red) and the potential energy  ρ²/(2Fr²)(blue) obtained by DNS (Case Sh1Fr1). (a,d) t=U^*₀t^*/L^*₀=2, (b,e) t = 10 and (c,f) t = 20.

Figure 3  DNS and RDT results of the kinetic-energy spectrum E_K(k) and the potential-energy 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 kinetic-energy spectrum E_K(k) and the potential-energy 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  Shear-parameter dependence of the energy spectra (a)E_K(k), (b)E_P(k) and (c)E₃₃(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^3/2Fr^3/2k_O) in all the figures.