15.9. Equatorial Rossby Wave¶
This test problem considers the propagation of a Rossby soliton on an equatorial beta-plane, for which an asymptotic solution exists to the inviscid, nonlinear shallow water equations. In principle, the soliton should propagate westwards at fixed phase speed, without change of shape. Since the uniform propagation and shape preservation of the soliton are achieved through a delicate balance between linear wave dynamics and nonlinearity, this is a good context in which to look for erroneous wave dispersion and/or numerical damping.
The problem is nondimensionalized with: H = 40 cm, L=295 km, T = 1.71 days and U=L/T=1.981 m/s. Theorical propagation speed is 0.4 (0.395) so that at t=120, the soliton should be back to its initial position after crossing the periodic channel of length 48.
Boyd J.P., 1980: Equatorial solitary waves. Part I: Rossby solitons. JPO, 10, 1699-1717
# define SOLITON
# undef OPENMP # undef MPI # define UV_COR # define UV_ADV # define ANA_GRID # define ANA_INITIAL # define AVERAGES # define EW_PERIODIC # define ANA_SMFLUX # define NO_FRCFILE