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.

:cite:t:`boyd_equatorial_1980`

::

    # define SOLITON

CPP options:

::

    # 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

**Settings :**

**Results :**    

.. figure:: figures/test_cases/test_cases_soliton.png
            :scale: 50 %

            SOLITON results : sea surface evolution


.. raw:: latex

    \clearpage