A comprehensive open dataset of stratified turbulence forced in vertical vorticity¶

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Pierre Augier$^1$, Jason Reneuve$^1$, Vincent Labarre$^2$

  1. Université Grenoble Alpes, CNRS, Grenoble INP, LEGI, Grenoble
  2. Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Nice
               
10 mai 2022
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Forced dissipated stratified turbulence¶

Forced at large $L_h$ and dissipated at small $l$ ($Re \gg 1$)

Forced in large vortices invariant over the vertical¶

  • Very standard

  • The system "chooses" the dominant vertical length scale (height of the layers)

  • As in real experiments (wakes of columnar objects, flaps creating dipoles)

Forcing computed in spectral space¶

  • $k_z = 0$ and $3 \leq k_h / \delta k_h \leq 4$

  • such that the energy injection rate is constant (nice but not as in experiments)

Non dimensional numbers and regimes¶

For large $Re$, 2 non-dimensional numbers:¶

  • $F_h$
  • $\mathcal{R} = Re {F_h}^2$

3 regimes:¶

  • Dissipated at large horizontal scale ($\mathcal{R} < 1$)
  • Layered Anisotropic Stratified Turbulence (LAST, $F_h < 0.02$, $\mathcal{R} > 10$ (?))
  • Weakly stratified ($F_h > 0.05$)

Consequences of $\mathcal{R} = Re {F_h}^2$¶

  • LAST ($F_h < 0.02$, $\mathcal{R} > 10$): $Re \gg 1$, difficult numerically and experimentally

  • Usually for a dataset, $\mathcal{R}$ and $F_h$ are strongly related

Need for a comprehensive dataset $[F_h, \mathcal{R}]$¶

More than 40 simulations available as an open dataset!

Numerical methods¶

  • Pseudo-spectral solver ns3d.strat of the CFD framework Fluidsim (Navier-Stokes under the Boussinesq approx. with homogeneous and constant $N$)

  • Time advancement: RK4

  • Shear modes removed from the dynamics (in Fourier space) for statistically stationnary states

Numerical methods: resolution and hyperviscosity¶

  • Proper DNS requires huge resolutions.

  • We use smaller resolutions to reach stationnarity. $\Rightarrow$ need for hyperviscosity (order 4)

  • Increase resolution (and decrease hyperviscosity) step by step.

Methods: resolution and $\nu_4$ versus $[F_h, \mathcal{R}]$¶

Numerical methods¶

Smaller aspect ratio $L_z / L_h$ for strongly stratified flows

2 isotropy coefficients¶

  • characterizing the large scales (based on velocity)
$$I_{velocity} = \frac{3 E_{Kz}}{E_K} $$
  • characterizing the small scales (based on dissipation)
$$ I_{diss} = \frac{1 - \varepsilon_{Kz} / \varepsilon_{K}}{1 - 1/3}$$

Large scale isotropy $I_{velocity}$ versus $F_h$¶

Small scale isotropy $I_{diss}$ versus $\mathcal{R}$¶

2 isotropy coefficients, versus $[F_h, R]$¶

Regimes... Thresholds/transitions

Mixing coefficient¶

$\displaystyle \Gamma = \frac{\varepsilon_A}{\varepsilon_K} \sim \left(\frac{b}{NU}\right)^2$
  • Weakly stratified turbulence (passive scalar)
$$D_t b \sim - N^2 w \Rightarrow b = N^2 L_h \Rightarrow \Gamma \sim {F_h}^{-2}$$
  • Strongly stratified turbulence (double energy cascade) $ \Rightarrow \Gamma \simeq 1 $
Maffioli, Brethouwer & Lindborg (2016)

Mixing coefficient versus $[F_h, R]$¶

Mixing coefficient versus $F_h$¶

=> 4 regimes at large $Re$ and $\mathcal{R}$!

Characterization of the LAST regime¶

Spectra and toroidal/poloidal decomposition¶

  • spatial
  • temporal
  • spatio-temporal

Presence and degree of nonlinearity of an internal wave field?

Data in Mycore