For a simplified model of the Gulf Stream front along a vertical-walled continental slope of a constant-depth ocean basin, the dynamics governing frontal instabilities, meanders, and eddies depend primarily on (i) L0/ R0, the ratio of the cross-stream distance of the stream axis from the slope, L0, to the Roosby radius of deformation, L0, and (ii) h0/ H, the ratio of the depth L0 of upper layer of light water to ocean basin depth H. A nonlinear, time-dependent three-dimensional model is used to study this interdependency. Two different types of meander solutions are found, depending on the value of the (nondimensionalized) initial available potential energy per unit alongfront length and per unit “Rossby area,” HR0, APE = ( L0/ R0)(h0/ H)/2. For small APE, the meanders and their associated cyclones are slope-bounded as they propagate downstream. This solution has characteristics similar to observed Gulf Stream meanders south of a topographic feature at 31.5°N (the so-called “Charleston Bump”) on the southeastern continental margin. For large APE, the meander displays branching surface currents upstream of its associated cyclone. One branch is deflected seaward while the other, weaker, branch hugs close to the slope. The two branches envelop the cyclone as they propagate downstream in unison. This solution has features similar to observed Gulf Stream meanders north of the Charleston Bump.
The growth rate σ, of instability depends on whether L0/ R0 is less or greater than one. For L0/ R0 > 1, σ depends only on h0/H and increases with h0/H like (h0/H)n, with n < 1. For L0/ R0 > 1, σ decreases because, with effects of rotation now diminished, a larger fixation of the initial available potential energy is converted to mean kinetic energy without formation of energetic, unstable meander waves and eddies. The instability is of baroclinic origin in all cases studied and, in agreement with field observations and laboratory experiments, computed meander wavelengths are of the order of 2π R0 irrespective of values of h0/H and L0/ R0. These results on the growth rates and wavelengths of meander waves agree with analytical, ageostrophic linear models of density fronts.
Model results show features like asymmetric frontal meanders, propagating cyclones and warm filaments, which have their counterparts in the Gulf Stream frontal system along the southeastern continental margin from the Florida Straits to Cape Hatteras. Computed growth rates, phase speeds, wavelengths, and mean/perturbation energy conversions are consistent with available field and laboratory data.