Comprehensive open datasets of stratified turbulence forced in vertical vorticity or wave modes
Pierre Augier, Vincent Labarre,
Giorgio Krstulovic and Sergey Nazarenko
GAFDEM, 11-15 Sept. 2023
\[ \newcommand{\R}{\mathcal{R}} \newcommand{\FhR}{(F_h,\ \R)} \]
Turbulence influenced by a stable density stratification
Motivations
Internal gravity waves turbulence proposed to explain ocean measurements
…
Summary
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)
\(\rho'(x, z)\)
Turbulence influenced by a stable density stratification
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
Span the \(\FhR\) space
Previous studies 
This dataset (“wave” forcing) 
Open datasets and Open-source software
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.
The FluidDyn project and Fluidsim
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
Numerical methods
ns3d.stratFluidsim 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 and small isotropy coefficients
\[I_{velo} = \frac{3 E_{K_z}}{E_K}\]
\[I_{diss} = \frac{1 - \varepsilon_{Kz}/\varepsilon_K}{ 1 - 1/3}\]
Regimes from small and large isotropy coefficients
Brethouwer et al. (2007), …
Comparison forcings: regimes
Forced in waves
Forced in vortices 
Mixing coefficient \(\Gamma\) and energy ratio \(E_A/E_K\)
Maffioli (2017), Garanaik & Venayagamoorthy (2019), Le Reun, Favier & Le bars (2018)
Comparison forcings: mixing coefficient
Forced in waves
Forced in vortices 
Slightly different \(F_h\) values for the regimes…
Total energy and toroidal energy
Same forcing (energy injection rate and scales) for all simuls
Comparison forcings: energies versus \(F_h\)
Forced in waves
Forced in vortices 
Comparison forcings: toroidal energy
Forced in waves
Forced in vortices 
Spatial and temporal spectra
\(F_h = 0.024\) and \(\R = 13\) (LAST like)
- Strongly anisotropic
- \({k_h}^{-5/3}\) and steep vert. spectra
- Large toroidal spectra (vortices)
Comparison forcings: spectra
Forced in waves
Forced in vortices 
Spatio-temporal spectra
\(F_h = 0.024\) and \(\R = 13\) 
\(F_h = 0.003\) and \(\R = 7.1\) 
Proportion of weakly nonlinear internal waves
(from spatiotemporal spectra)
Conclusions
Open data / open software
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
Conclusions
Results on strat. turbulence forced in waves
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
