Asymptotically reduced equations and numerical simulations for 3D rapidly rotating convective and stably stratied fluid layers
David Nieves
Applied Mathematics, University of Colorado Boulder
Date and time:
Monday, November 3, 2014 - 12:00pm
Location:
ECCR 257 Newton Lab
Abstract:
A single model for non-hydrostatic quasi-geostrophic motions is studied in two distinctly dierent physical
frameworks. The rst framework investigates coherent structures in the setting of rapidly rotating Rayleigh-
Benard convection while the second framework investigates motions of a rapidly stably stratied
fluid layer. These flows are of physical relevance to geophysical and astrophysical systems whose dynamics are strongly
inuenced by rapid rotation and thermal forcing such as interiors of giant planets, rapidly rotating stars, the
Earths outer liquid core, and open ocean deep convection.
In rapidly rotating convection four flow regimes with distinct characteristics have been identied via
simulations of asymptotically reduced equations as a function of the a reduced Rayleigh number fRa and
Prandtl number . In each regime the flow organizes, with varying intensity, into coherent vertical structures.
The identied morphologies, in order of increasing fRa, consist of the cellular regime, the convective Taylor
column (CTC) regime, the plume regime, and a regime characterized by geostrophic turbulence. Presently,
physical limitations on laboratory experiments and spatio-temporal resolution challenges on direct numerical
simulations of the incompressible Navier-Stokes equations inhibit an exhaustive analysis of the
flow morphology in the rapid rotating limit. Flow morphologies identied from simulations of an asymptotically reduced
equations have been investigated from a statistical perspective. Utilization of auto- and cross-correlations of
temporal and spatial signals that synthesize experimental data have been employed to (i) identify transitions
in flow morphology, (ii) recover radial proles of coherent structures, and (iii) extract transport properties
of these structures. These results provide a foundation for comparison and a measure for understanding
the extent to which rotationally constrained regime has been accessed by laboratory experiments and direct
numerical simulations.
Motivated by recent studies on rotating and stratied flows (Pouquet et al. (2013)) investigations of the
asymptotically reduced equations for non-hydrostatic quasi-geostrophic motions in a stably stratied setting
is a subject of ongoing and future work.