2d stratified turbulence and internal gravity wave turbulence

Miguel Calpe Linares, Pierre Augier, Nicolas Mordant

FluidSim and the FluidDyn project

Ashwin Vishnu, Cyrille bonamy

           

ANR DisET meeting (30-31 Jan 2019)

Ocean turbulence statistics interpreted as the signature of IG waves

"Garrett-Munk spectrum"

• vertical spectra $N^2 k_z^{-3}$

• temporal spectra, energy for $f < \omega < N$

Naive representation: soup - cascade of (weakly interacting) IG waves?

   

3d strongly stratified turbulence

• Kinematic decomposition: $\omega_z$, $\nabla_h u$ and shear modes

For oceanic parameters (strongly stratified, large Re):

• Strongly non-linear

• $\omega_z \sim \nabla_h u$

$$b(x,z)$$

Brethouwer, Billant, Chomaz & Lindborg (2007)

How to get "pure" IG wave turbulence?

• We don't want $\omega_z$

  $\Rightarrow$ we can use 2d stratified turbulence.

• We don't want shear modes

  $\Rightarrow$ we disable them

2D stratified turbulence to understand IG wave turbulence

Advantage: cheap so we can run several simulations at high Re

Goal: obtain IG wave turbulence

Which dissipation?

• Dissipation at small scales

• Hyper viscosity

Which forcing?

• force eigenmodes of the linearized equations

• correlation time $\sim$ wave period $T_N(k)$

• intermediate-scale (possibility of upscale and downscale cascades)

Problem standard forcing in a shell:

no well-defined $T_N(k)$

Anisotropic forcing

$\Rightarrow$ well-defined non-dimensional numbers

• direction of propagation $F = \frac{\omega_l}{N}$

• non-linearity $\gamma = \frac{\omega_f}{\omega_l}$

• dissipation

Few results

A dream: the "oceanic-like" limit

• strongly stratified
• weak dissipation at large horizontal scale (large buoyancy Reynolds number)

Warning:

Direction of propagation of forced waves! Here $F = \omega_l / N = 0.5$

We obtain statistically stationary flows

Dissipation only at small scales $\Rightarrow$ energy transfers towards small scales

   

It would not be the case without stratification!

Buoyancy fields at stationary state

   

Small vertical length scales for strong stratification

Warning: dissipation at large horizontal scale even for large $Re$

Horizontal and vertical spectra

   

Horizontal and vertical spectral energy budget

$\gamma = 1$ (strongly stratified), $n_x = 3840$

   

The code is interesting!

FluidDyn project

A project to foster open-science and open-source in fluid mechanics

   

A thesis:

• open-source never so strong,
• new tools and methods allowing collective work,
• possibility of collaborations on good quality research codes.

Some packages:

fluidimage, fluidlab, fluidsim, fluidfft, transonic, ...

The code is interesting: FluidSim

(Ashwin Vishnu, Cyrille Bonamy, Miguel Calpe)

• Open-source collaborative framework / library for writting solvers

• High quality code (tests run with continuous integration, proper documentation, issue tracker)

• Very user-friendly

• Developer friendly: mostly in Python, highly modular (object-oriented Python)

• Extensible (for example fluidsim-ocean)

• Specialized in pseudo-spectral (Fourier), but not only

• Very efficient

Under the hood:

• FluidFFT: Python / C++ library for (parallel) Fourier transforms (2D and 3D)

• Transonic and Pythran: "Make your Python code fly at transonic speeds!" (actually at good-C++ speed)

Conclusions

• Work in progress

• Dissipation dominated by vertical gradient $\Rightarrow$ not yet "geophysical" regime

• Very interesting tools (FluidSim, FluidFFT, Transonic)

• Outputs not shown here (for example spatio-temporal spectra)

Good tools and clean setup to answer these questions

• Can we obtain (weak?) internal gravity wave turbulence?

• Statistics similar as in the oceans?