The motion of a non-isolated vortex on the beta-plane

Abstract

The trajectory of a non-isolated monopole on the beta-plane is calculated as an asymptotic expansion in the ratio of the strength of the vortex to the beta-effect. The method of matched asymptotic expansions is used to solve the equations of motion in two regions of the flow: a near field where the beta-effect enters as a first-order forcing in relative vorticity, and a wave field in which the dominant balance is a linear one between the beta-effect and the rate of change of relative vorticity. The resulting trajectory is computed for Gaussian and Rankine vortices.

Wavenumber-frequency analysis of single-layer shallow-water beta-plane quasi-geostrophic turbulence

“…(21) and its analogs have been studied for a variety of systems. [37][38][39][40][41][42][43][44][45][46][47][48][49] A solution to Eq. (21) that includes jets would not be spatially localized, however.…”

Playing pool on the beta-plane: how weak initial perturbations predetermine the long-term evolution of coherent vortices

“…Numerous subsequent investigations -theoretical, numerical and experimentalconfirmed this link and further elucidated the physical mechanisms at play (e.g. Reznik & Dewar 1994;Sutyrin & Flierl 1994;Llewellyn Smith 1997;Flór & Eames 2002). In particular, a series of analytical models have been developed (McWilliams & Flierl 1979;Nof 1981Nof , 1983Killworth 1986;Cushman-Roisin, Chassignet & Tang 1990;Benilov 1996) which express the migration rate of isolated vortices in terms of eddy structure and background stratification.…”

Dynamics of Vortex Rossby Waves in Tropical Cyclones, Part 2: Nonlinear Time‐Dependent Asymptotic Analysis on a β‐Plane

“…where A 1 and A 2 are constants. Since we are evaluating the solution near r = r c , we write the expressions in (31) in terms of (r − r c ) as…”

“…This term is present if the basic flow streamfunctionψ(r ) does not satisfy Equation (1). The influence of this term has been investigated, e.g., [27][28][29][30][31][32], in the context of the initial-value configuration where a vortex is specified at the initial time at some location in two-dimensional space and evolves forward in time. The inclusion of this term in the governing equation for the vortex results in the so-called beta drift or beta-gyre effect, where a secondary dipole circulation develops and forces the vortex to move along the dipole axis.…”