Spontaneous generation of inertia–gravity wave packets by balanced geophysical flows

Abstract

The generation and propagation of a packet of small-amplitude inertia-gravity waves (IGWs) in a rotating stratified balanced flow is described. The initially balanced geophysical flow is an unstable baroclinic jet which breaks up into a street of cyclonic and anticyclonic vortices. The small-amplitude unbalanced component of the flow is extracted from the large-amplitude mesoscale balanced flow using the optimal potential vorticity balance approach. This analysis reveals that during the instability the balanced flow spontaneously emits bursts of IGWs. The emission occurs along two directions, into and out of the anticyclonic vortices. The inward-waves remain trapped inside the vortices while the outward-waves propagate away from them as a packet of small-amplitude IGWs with a three-dimensional helical structure. The wave packet emission is confirmed for different spatial resolutions (128 3 , 160 3 , 192 3 and 256 3 grid points). The ratio between the balanced vertical and horizontal velocity components is of the order of 10 −3 , as is typical of mesoscale geophysical flows. The ratio between the unbalanced vertical and horizontal components is about 0.1. Since the unbalanced horizontal and the balanced vertical velocity components are of similar magnitude, the vertical velocity of the IGWs is about 10 −4 times the balanced horizontal velocity. The IGWs are dominated by frequencies close to the inertial frequency and have a clockwise-rotating horizontal velocity, similar to plane wave solutions.

Emission of Inertial Waves by Baroclinically Unstable Flows: Laboratory Experiments with Altimetric Imaging Velocimetry

“…We believe that this causes the emission (albeit very weak) of the inertial waves. Note that the curvature of the meander is large which is consistent with the observations by Viudez and Dritschel (2006) in their numerical simulations. The interaction (collision) of the meanders creates a complex multilayered vorticity distribution.…”

“…A few recent numerical simulations (O'Sullivan and Dunkerton 1995, Zhang 2004, Viudez and Dritschel 2006 describe the emission of inertia-gravity waves by unstable baroclinic jet. In simulations by Viudez and Dritschel (2006) the emission is highly localized in space and occurs only "at the largest curvature side of the emerging highly ageostrophic anticyclonic vortex". Their observation of large curvature is consistent with the notion of large acceleration of fluid parcels required for the emission of waves.…”

Gravity Waves in a Horizontal Shear Flow. Part II: Interaction between Gravity Waves and Potential Vorticity Perturbations

“…Spontaneous emission of gravity waves has also been seen in observational studies (Uccellini and Koch 1987;Guest et al 2000;Pavelin et al 2001;Plougonven et al 2003) and numerical simulations (O'Sullivan and Dunkerton 1995;Zhang 2004;Plougonven and Snyder 2007;Viudez and Dritschel 2006) of baroclinic life cycles. The term ''spontaneous generation'' refers to emission of gravity waves occurring abruptly during the evolution of an initially balanced flow as distinct from emission of gravity waves during geostrophic adjustment of an initially unbalanced flow.…”

Exponential Smallness of Inertia–Gravity Wave Generation at Small Rossby Number

“…O'Sullivan & Dunkerton 1995, Zhang 2004, Plougonven & Snyder 4 2005, Viudez & Dritschel 2006, Viudez 2006. To date, however, the amplitude dependence of the IGW on the Rossby number has not been established in these models.…”