Thomas Haine (1), Greg Eyink (2), Dawn Ring (3)
(1) Department of Earth and Planetary Sciences, Johns Hopkins University US A, (2) Department of Applied Mathematics and Statistics, Johns Hopkins Univ ersity USA, (3) Department of Earth and Planetary Sciences, Johns Hopkins U niversity USA
ABSTRACT: A recent laboratory experiment of Williams, Haine, and Read has observed spontaneous generation of Inertia-Gravity Waves (IGWs) in a rotating two-layer annular fluid. We provide an explanation for these observations based upon the asymptotic renormalization theory of Wirosoetisno, Shepherd, and Temam JAS (2002), for the limit of small Rossby number (Ro). The first-order renormalized equation derived by those authors contains only resonant triplet interactions, and thus cannot generate IGWs from potential vorticity modes. In fact, if the initial IGW energy is zero, as it is in the Williams, Haine, Read experiment (at least to leading orde r in Ro), the equation reduces to Quasi-Geostrophic dynamics.
The renormalized solution contains also a first-order "slaved" term consisting only of IGWs, however. This term is zero initially, but increases in a few fast wave periods to be O(Ro). These IGWs are slaved to the vortical flow, but not balanced, so they oscillate rapid ly in time. By computing the analogue of this additional term in the partic ular geometry and boundary conditions of the Williams et. al. laboratory ex periment, we plot the results of a two-layer, Quasi-Geostrophic (QUAGMIRE) numerical model together with this first order IGW term. Comparison with the IGW activity observed by Williams, Hain e, and Read gives a decisive test if this source term is responsible for th e IGWs observed in the experiment.