Hydrodynamic turbulence

These are some images of hydrodynamic turbulence (click on the images to see them at full resolution). Most are from numerical simulations using up to 20483 grid points and were published in 2005 and in 2008 (see also the references therein).  One of these images was used by Ian Stewart in his book “Visions of Infinity: The Great Mathematical Problems” to illustrate the complexity of a turbulent flow.

Rotating and stratified turbulence

Rotating and stratified turbulence develops slanted layers in the velocity and the temperature fields (and pancake-like structures in the absence of rotation). Below are some images of simulations of stratified turbulence, published in a recent paper in Physics of Fluids, and in another paper in 2014.

Rotating turbulence

Flows in a rotating frame transfer energy preferentially towards two-dimensional modes, developing strong anisotropy and column-like structures. The images below were rendered using data from simulations with up to 15363 grid points, and compare the effect of rotation in helical and in non-helical flows. Recently we also studied the recovery of isotropy at small scales in a simulation or rotating turbulence at very large Reynolds number, using 30723 grid points. Images from these simulations were used by Peter Davidson in his books “Turbulence in Rotating, Stratified and Electrically Conducting Fluids” and “Turbulence: An Introduction for Scientists and Engineers (2nd Edition)”.

Quantum turbulence is the chaotic and erratic spatio-temporal behavior observed in superfluids and Bose-Einstein condensates. Recently, we were able to extract the spatio-temporal spectrum of Kelvin waves from simulations of the Gross-Pitaevskii equation. With Marc Brachet and Patricio Clark di Leoni we also performed multiple simulations of quantum turbulence using 20483 and 40963 grid points to study the evolution of helicity in the flow, and its cascade towards small scales.


The magnetohydrodynamic (MHD) approximation can be used to study conducting flows in planetary cores and large-scale plasmas in the interplanetary and interstellar medium. In these plasmas, study of small-scale processes require two-fluid approximations, or kinetic plasma descriptions. We performed multiple simulations of MHD flows, to study turbulence with resolutions of up to 15363 grid points, and to study the development of current sheets and magnetic field reconnection with resolutions of 40963 and 61443 grid points.


Spherical containers are interesting for many astrophysical and geophysical applications. Using a purely spectral code, we performed multiple simulations of hydrodynamic and MHD flows in rotating spherical vessels. Although purely spectral methods are computationally expensive, the high accuracy and conservation of the method allowed us to study the long-time dynamics and statistics of planetary-like dynamos, including a comparison of magnetic field reversals stemming from the numerical simulations with data of terrestrial magnetic field reversals.


Recently, with Pablo Cobelli we started building a laboratory to study geophysical turbulence and wave turbulence. The laboratory already has a tank to study surface wave turbulence, and several fast cameras to do surface profilometry. The first paper using only data from our laboratory was published in 2015.