GAFD Seminar: Edgar Knobloch

Rotating convection is a prototypical system at the core of geophysical fluid dynamics. However, the parameter values for geophysical flows take values that are far outside those that can be studied in the laboratory or via state of the art numerical simulations. In this talk I will describe a formal asymptotic procedure that leads to a reduced system of equations valid in the limit of very strong rotation. These equations describe four regimes as the Rayleigh number Ra increases: a disordered cellular regime near threshold, a regime of weakly interacting convective Taylor columns at larger Ra, followed for yet larger Ra by a breakdown of the convective Taylor columns into a disordered plume regime characterized by reduced heat transport efficiency, and finally by a type of turbulence called geostrophic turbulence. Properties of these states will be described and illustrated using direct numerical simulations of the reduced equations. These simulations reveal that geostrophic turbulence is unstable to the formation of large scale barotropic vortices or jets, via a process known as spectral condensation. The details of this process will be quantified and its implications explored. The predictions from the reduced equations have been corroborated via direct numerical simulations of the Navier-Stokes equations, albeit at much more modest rotation rates, confirming that the reduction procedure captures the essence of the problem. Moreover, rescaling the Navier-Stokes equations using the aforementioned scales serves as an excellent preconditioner that allows us to perform fully resolved direct numerical simulations of very rapidly rotating convection at unprecedented Ekman numbers, some six orders of magnitude smaller than the current state of the art, approaching geophysically realistic values for the very first time. The computations reveal a new transition at Ek~10-9 towards symmetry between cyclonic and anticyclonic large scale vortex structures, and show that in the statistically stationary state the solutions converge to the predictions of the asymptotically reduced equations.