Beyond Lighthill: three ways to stay close to balance
Seminar Room 1, Newton Institute
This talk proposes to discuss the recently discovered cases of hybrid propagating structures consisting of vortex dipoles and co-moving gravity waves undergoing wave capture. It is shown how these cases fall outside the scope of the Lighthill theory of spontaneous imbalance and, concomitantly, outside the scope of shallow-water dynamics. Besides the fact that going from shallow water to continuous stratification allows disparate vertical scales -- small for inertia-gravity waves and large for vortical motion -- the key points are (a) that in contrast with cases covered by the Lighthill theory the wave source in these cases feels an order-unity radiation reaction, hence cannot be prescribed in advance, when Rossby numbers R \sim 1; (b) that cases of this sort will supply exceptions to the general rule that spontaneous imbalance is exponentially small in R; and (c) that unsteady vortical motion in continuous stratification can stay close to balance thanks to three quite separate mechanisms. These are
(1) the near-suppression, by Lighthill interference, of large-scale imbalance (inertia-gravity waves of large horizontal scale) where "large" means relative to Rossby deformation lengths L_D characterizing the vortical motion,
(2) the low-group-velocity flaccidity hence near-steadiness of L_D-wide jets that meander and form loops, Gulf-Stream-like, on streamwise scales >> L_D, and
(3) the dissipation of small-scale imbalance by wave capture leading to wave breaking, generically likely in an environment of random shear and straining.
Shallow-water models include the first two mechanisms but exclude the third.