Inertia-gravity wave radiation from the merging of two co-rotating vortices in the f-plane shallow water system

Abstract

Inertia-gravity wave radiation from the merging of two co-rotating vortices is investigated numerically in a rotating shallow water system in order to focus on cyclone–anticyclone asymmetry at different values of the Rossby number (Ro). A numerical study is conducted on a model using a spectral method in an unbounded domain to estimate the gravity wave flux with high accuracy. Continuous gravity wave radiation is observed in three stages of vortical flows: co-rotating of the vortices, merging of the vortices, and unsteady motion of the merged vortex. A cyclone–anticyclone asymmetry appears at all stages at smaller Ro (≤20). Gravity waves from anticyclones are always larger than those from cyclones and have a local maximum at smaller Ro (∼2) compared with that for an idealized case of a co-rotating vortex pair with a constant rotation rate. The source originating in the Coriolis acceleration has a key role in cyclone–anticyclone asymmetry in gravity waves. An additional important factor is that at later stages, the merged axisymmetric anticyclone rotates faster than the elliptical cyclone due to the effect of the Rossby deformation radius, since a rotation rate higher than the inertial cutoff frequency is required to radiate gravity waves.

Inertia–gravity wave radiation from the elliptical vortex in the f -plane shallow water system

“…Moreover, cyclone-anticyclone asymmetry in IGWs from a corotating vortex pair has been recently found (Sugimoto et al 2015). This asymmetry was also reported by the numerical simulation of a vortex merger (Sugimoto 2015; note that Pallàs-Sanz and Viúdez (2008) investigated spontaneous IGW radiation in a vortex merger for the first time). However, since analytical derivation was performed only for an idealized case of a co-rotating point vortex pair, and numerical verifications were done for cases of a co-rotating vortex pair and its merger as a numerical extension, it is not evident whether this asymmetry appears in complicated vortical flows.…”

Nonlinear Interaction Between Vortex and Wave in Rotating Shallow Water

“…(27) and (28) [22,23]. Furthermore, additional numerical simulations have been performed for the cases of merging of (equal or unequal) vortices, in which analytical solution cannot be derived [24,25]. In this section, the results of numerical simulation as well as model settings are introduced.…”

“…Then the phenomena on a two-dimensional unbounded plane can be calculated on a sphere with an ordinary spectral method of spherical harmonics by this mapping. Since grid points are arranged nonuniformly (many grid points are positioned in the near field of vortical flows, while few are in the far field of gravity waves), this method enables us to simulate nonlinear interactions between vortical flows and gravity waves with high accuracy [22][23][24][25].…”

“…As extended experiments, the results of the merging of (equal and unequal) vortices are introduced here [24,25]. As an initial state, a pair of corotating Gaussian vortices expressed by Eq.…”

“…In this chapter, recent results of the inertia-gravity wave radiation from nearly balanced vortical flows as an extension of sound wave generation from vortical flows are reviewed. Inertia-gravity wave radiation from various types of vortical flows, such as a corotating vortex pair [22], elliptical vortex (Kirchhoff vortex) [23] and merging of (equal or unequal) vortices [24,25], are investigated in a wide range of parameter space. All these works have reported that cyclone-anticyclone asymmetry in spontaneous emission and a local maximum of intensity of gravity waves emitted from anticyclones at intermediate value of the Coriolis parameter f.…”