Our interest in this test problem is to investigate spurious dispersion effects, and how they relate to the choice of horizontal resolution and the order of the approximation used in the numerical solution. The model is initialized with the zeroeth order solution and integrated forward in time. The initial wave should propogate nearly unchanged to the west. There are errors due to both the numerical approximation and the neglect of the higher-order terms in the initial conditions. The standards of merit for this problem include the phase speed of the numerical wave and the rms error between the expected solution and the actual solution.

Perturbation solutions to the Rossby soliton problem are available to
both zeroeth (Boyd, 1980 [2]) and first order (Boyd, 1985
[3]). The problem as posed uses the zeroeth order solution.
Following Boyd, we nondimensionalize with *H* = 40 cm, *L*=295 km, *T* =
1.71 days and
*U*=*L*/*T*=1.981 m/s.
The asymptotic solution is constructed by adding the lowest and first
order solutions:

where

The zero-order solution is

while the first-order solution is given by

where

with the coefficients

Using the zeroeth order solution as initial conditions, we have
computed the evolution of the Rossby soliton for a total of 40 time
units. The solution for the lowest symmetric mode wave (*n*=1) is
used. During this interval, the soliton propagates westwards across
several of its characteristic widths. (Comparable results are
obtained for the more complete, first-order asymptotic solution.)