##### 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 2048^{3} 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 paper in Physics of Fluids, and in another paper in 2014. We also published recently a paper in Science Magazine on inverse cascades in rotating and stratified flows.

##### 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 1536^{3} grid points, and compare the effect of rotation in helical and in non-helical flows. We also studied the recovery of isotropy at small scales in a simulation or rotating turbulence at very large Reynolds number, using 3072^{3} 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 FLOWS

^{3}and 4096

^{3}grid points to study the evolution of helicity in the flow, and its cascade towards small scales.

**CONDUCTING FLUIDS**

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 1536^{3} grid points, and to study the development of current sheets and magnetic field reconnection with resolutions of 4096^{3} and 6144^{3} grid points.

##### FLUIDS IN SPHERICAL VESSELS

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.

##### LABORATORY EXPERIMENTS

Led by Pablo Cobelli, we built a laboratory to study geophysical turbulence and wave turbulence. The laboratory has a tank to study surface wave turbulence, a von Kármán experiment, and several fast cameras to do surface profilometry, PIV and PTV. The first paper using only data from our laboratory was published in 2015.