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

This presentation: focus on “wave” forcing

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:

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

2. Pseudo-spectral Fourier solvers (ns2d, ns3d, ns3d.strat, sw1l, …).

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

Numerical methods

• 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 and small isotropy coefficients

Large scale isotropy

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

Small scale isotropy

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

Isotropic turbulence \(\Rightarrow I_{velo} = I_{diss} = 1\)

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

Turbulence \(\Rightarrow U^3 \sim \varepsilon L\)

Energy in “vortices”

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