**Pierre Augier**, Vincent Labarre,

Giorgio Krstulovic and Sergey Nazarenko

GAFDEM, 11-15 Sept. 2023

\[ \newcommand{\R}{\mathcal{R}} \newcommand{\FhR}{(F_h,\ \R)} \]

Internal gravity waves turbulence proposed to explain ocean measurements

…

Internal gravity waves (IGW), “vortices”, shear modes, small-scale turbulence

Horizontal Froude number \(F_h\) and buoyancy Reynolds number \(\R = Re {F_h}^2\)

LAST regime \(F_h<0.02\), \(\R>20\):

- downscale energy cascade
- anisotropic spectra

Brethouwer, Billant, Chomaz & Lindborg (2007)

\(\rho'(x, z)\)

**Questions**

- Regime corresponding to the oceanic waves?

- Effect of forcing, universality?
- Regimes in \((F_h, \R)\) space?

- IG wave turbulence? Nonlinearity?
- Mixing modeling?

**Would be good to have “Foundational” open datasets**

- Span the \(\FhR\) space

- Different forcing schemes

We built 2 first datasets with \(\neq\) forcing (as Waite & Bartelo, 2004, 2006, Lindborg & Brethouwer, 2007)

- forced in vortices

- forced in IG waves

Previous studies

This dataset (“wave” forcing)

Reproductibility

Reusability

auto-documented standard file formats.

software easy to extend.

Easily understandable/usable: not only raw states. Open software to compute, read, load and represent advanced outputs.

**FluidDyn:** a project to foster open source and Python in fluid mechanics. A set of open source collaborative Python packages: fluidsim, fluidimage, fluidlab, …

**Fluidsim:**

A framework to create CFD solvers from whatever (for ex. Snek5000, Fluidsimfoam)

Pseudo-spectral Fourier solvers (

`ns2d`

,`ns3d`

,`ns3d.strat`

,`sw1l`

, …).

Documented, tested, very efficient, dev hosted in foss.heptapod.net

`ns3d.strat`

Fluidsim solver(Navier-Stokes equations with constant \(N\), pseudo-spectral Fourier)

Forcing

Slow internal gravity waves (\(\omega/N \simeq 0.3\))

Large horizontal scales

Constant energy injection rate (\(P_K = 1\))

Time correlated

Shear modes removed from the dynamics

Input parameters: \(N\) and \(\nu\) (\(F_h\) and \(Re\))

Diffusion

Mostly DNS or quasi DNS (\(k_{max} \eta \simeq 1\)) but hyperviscosity for few simulations

Large scale isotropy

\[I_{velo} = \frac{3 E_{K_z}}{E_K}\]

Small scale isotropy

\[I_{diss} = \frac{1 - \varepsilon_{Kz}/\varepsilon_K}{ 1 - 1/3}\]

Brethouwer et al. (2007), …

Forced in waves

Forced in vortices

Maffioli (2017), Garanaik & Venayagamoorthy (2019), Le Reun, Favier & Le bars (2018)

Forced in waves

Forced in vortices

Slightly different \(F_h\) values for the regimes…

Same forcing (energy injection rate and scales) for all simuls

Forced in waves

Forced in vortices

Forced in waves

Forced in vortices

\(F_h = 0.024\) and \(\R = 13\) (**LAST like**)

- Strongly anisotropic
- \({k_h}^{-5/3}\) and steep vert. spectra
- Large toroidal spectra (vortices)

Forced in waves

Forced in vortices

\(F_h = 0.024\) and \(\R = 13\)

\(F_h = 0.003\) and \(\R = 7.1\)

(from spatiotemporal spectra)

2 datasets for 2 forcing schemes:

forced in large scale vortices

forced in large scale slow waves (\(\omega/N\simeq 0.3\))

More than 40 simulations (spanning the \((F_h,\ \R)\) space) for each forcing type, soon available as

**open**datasets!Fluiddyn / Fluidsim

Many different types of outputs and in particular

**spatiotemporal spectra**

**5 regimes**(Viscosity affected, LAST, Optimal, Weakly strat., Passive scalar)Lindborg (2006), Brethouwer et al. (2007), Maffioli et al. (2016), Garanaik-Venayagamoorthy (2019)

Indisputable observation of the \(\Gamma \sim {F_h}^{-1}\) and \({F_h}^{-2}\) scalings

For \(F_h\ll 1\) and \(\R>10\) (relevant for oceans),

**not a pure wave cascade**:- Weak forcing but strong, non-linear flows
- Strong vortices, LAST like
- Weakly non-linear waves dominated by other processes