|Date: Tuesday, November 09, 2010
Title: Convective flows under strong rotational constraints
Abstract: Current models and simulations of fluid turbulence in the atmosphere and oceans
are conducted at parameters that do not closely resemble observed realistic
values. Thermal and rotational forces are sometimes orders of magnitude too
small. Improvements in computing power through Moore's laws will produce
minimal advances with present-day models (specifically, a doubling of
resolution in each direction every six years for three-dimensional problems).
It is therefore clear that advances must occur through new model development
and associated simulations utilizing extreme parameter values in an asymptotic
manner. This will require a body of knowledge gained from large-scale direct
numerical simulations that explore the nature of extreme values in controlled
One such area has been that of convection under the influence rotation. In
general numerical simulations of rotationally constrained flows are unable to
reach realistic parameter values (e.g., Reynolds Re and Richardson Ri numbers).
In particular, low values of Rossby number Ro, defining the extent of
rotational constraint, compound the already prohibitive temporal and spatial
restrictions present for high-Re simulations by engendering high-frequency
inertial waves and the development of thin (Ekman) boundary layers.
Recent work in the development of reduced partial differential equations
(PDEs) that filter fast waves and relax the need to resolve boundary layers
has been extended to construct a hierarchy of balanced equations that span the
stably and unstably stratified limits. By varying the aspect ratio for
spatial anisotropy characterizing horizontal and vertical scales, rapidly
rotating convection and stably stratified quasi-geostrophic motions can be
described within the same framework.
In this talk, the asymptotic PDEs relevant for rotating convection are
explored. Special classes of fully nonlinear exact solutions are identified
and discussed. Direct numerical solutions that correctly capture the regular
vortex columnar and irregular geostrophic turbulence regime of recent
laboratory experiments are also presented and discussed.
Speaker: Keith Julien
Institution: University of Colorado at Boulder