Ashwin Vishnu Mohanan*, Pierre Augier^, Erik Lindborg*
* Linne Flow Center, Department of Mechanics, KTH, Stockholm, Sweden
^ LEGI / CNRS, Université Grenoble Alpes, Grenoble, France
Article [2] selected as featured research by AIP (Nov 22, 2017)
Gage (1979) & Lilly (1983): inverse energy cascade as in Kraichnan (1967)
Dewan (1979):forward energy cascade as in Kolmogorov (1941)
3D Boussinesq equation simulations in Lindborg (2006) demonstrated that
Explain many geophysical phenomena, including waves
Conserves potential vorticity and enstrophy.
Shallow water equation is often studied as QG equations:
$$\frac{D}{Dt}\left(\nabla^2 \psi + \beta y - \frac{1}{L_d^2} \psi \right)= \frac{D}{Dt}\left(\zeta + \beta y - f_0 \eta \right)=0$$Important assumptions:
While allowing, $|\zeta| \sim |d|$ in contrast with QG where $|\zeta| >> |d|$
where, $\theta = c\eta$
Pros: No shocks, KE and APE are quadratic and conserved, linearised potential vorticity conserved in the limit $Ro \rightarrow 0$: $q = \zeta - f\eta$
Cons: Full potential vorticity $Q$ is not exactly conserved
Python framework to run sequential and parallel (MPI) CFD simulations for a variety of problems (Navier-Stokes, Shallow Water, Föppl von Kármán equations, ...).
highly modular, object-oriented structure, on-the-fly postprocessing
specialized in pseudo-spectral methods (based on fluidfft),
user friendly, documented
efficient (much faster than Dedalus, faster than SpectralDNS).
Hierarchy of C++ and Cython classes to use different FFT libraries: FFTW, P3DFFT, PFFT, CuFFT .. possibly more?
Python operators classes (2d and 3d) to write code independently of the library used for the computation of the FFT.
Pythran to speedup critical code. Performance $\simeq$ Fortran.
Command line utilities (fluidfft-bench
and fluidfft-bench-analysis
).
Unit tests!
Top view of setup used for 2 sets of experiments
Carriage:
Study of wave-vortex interactions using shallow-water and toy-model equations
Large simulation of the toy model over a sphere
Study of cyclonic/anticyclonic assymetry using the toy model
Toy model reproduces $k^{-5/3}$ energy spectra similar to atmospheric mesoscale spectra.
FluidDyn open-source project
MILESTONE project