Geostrophic turbulent convection
Buoyantly-driven rotating turbulence occurs in planetary and stellar interiors, where it is responsible for mixing and transport (of heat, composition, momentum, etc.), and can generate large scale magnetic fields via the dynamo effect in the case of electrically conducting fluids (planetary and stellar cores).
In these celestials objects, rapid global rotation strongly constrains the turbulence through the geostrophic balance --- the dominant force balance between pressure and the Coriolis force. This balance promotes rotational alignment : the degree of anisotropy along the rotation axis increases with rotation (Proudman-Taylor theorem), creating a scale separation in both space and time for geophysically-relevant regimes.
Mathematically, the standard governing equations become increasingly stiff (i.e. prone to large errors due to computer’s finite precision) as rotation increases towards geophysical values. In terms of control parameters, the ratio of viscous forces to the Coriolis force defines the Ekman number, inversely proportional to rotation : estimates for the Earth’s outer core are of order O(10^-15) while standard DNS are typically limited to Ek>(10^-8).
In this talk, I will show how asymptotically-informed non-dimensionalisation leads to an alternative formulation of the equations of motion coined RRRiNSE (Rescaled Rapidly Rotating incompressible Navier-Stokes equations), mathematically equivalent to the standard Navier-Stokes equations but with improved conditioning.
Using the RRRiNSE model, we have explored rapidly rotating regimes in previously inaccessible regions of parameter space, relevant for geophysical applications.
As the Ekman number decreases to small but finite values, the main findings include : (i) the convergence of the heat flux (Nusselt number) to the value predicted by quasi-geostrophic reduced models valid in the asymptotic limit Ek->0, accompanied by (ii) the restoration of the statistical symmetry between cyclone and anticyclones at low Ek.
The model above assumes that rotation and gravity are anti-parallel and thus pertains to polar regions. Time permitting, I will present recent advances in quasi-geostrophic models for convection with gravity and rotation at an angle, representative of fluid patches at arbitrary latitudes.
Contact Nathanaël Machicoane for more information or to schedule a discussion with the seminar speaker.