Exponentially Unstable Edge Modes at Large Froude Number: the Inertial-Gravity-Edge Instability

The existence of unstable edge modes on vortices with sharp PV gradients was first established by Ford (1994), who demonstrated that this instability couples an inner Rossby wave with an outer inertia-gravity wave at small Froude number. Although Ford concluded that these modes have little practical significance to geophysical applications, recent work in the "superspin" regime of large Froude and large Rossby numbers supports the relevance of this instability to hurricane dynamics at large hurricane category (Schecter, 2008; Hodyss & Nolan, 2008). Although the nomenclature "Rossby-inertia-buoyancy" or "RIB" instability has been applied to these modes, a formal connection with Rossby waves at large Froude number has never been established.

Using large Froude number asymptotics, I show that the RIB instability is, in fact, an edge mode living on a PV gradient that couples a retrograde inertial oscillation and a prograde gravity wave---the Inertial-Gravity-Edge (IGE) instability---in the high Froude number superspin regime relevant to hurricanes. Unlike the Kelvin wave, however, where inertial and gravity contributions to the momentum balance separate in cross-shore and along-shore directions, inertial and gravity influences fully merge in the IGE wave. Analytic expressions for the phase and group velocity of the IGE instability at a PV discontinuity are presented and validated using simulations of the linearized primitive equations. Simulations demonstrate a strong dependence of IGE growth rate on the base-state angular velocity at the PV edge, and a near negligible dependence on the vorticity (PV) jump, confirming the non-Rossby wave nature of this mode.