(Received 14 March 2008; in revised form 27 June 2008)
Eigen modes of a linear shear flow in shallow water on an equatorial
β-plane are obtained over a wide parameter range.
High-order unstable modes, neutral modes,
and continuous modes are examined
based on the results of Taniguchi and Ishiwatari (2006)
that investigates mainly the lowest order most unstable modes.
The results are summarized as follows:
- With detailed examinations of mode structures,
it is shown that some continuous modes have
equatorial Rossby wave like structures.
This result confirms the discussion of
Taniguchi and Ishiwatari (2006) that all equatorial Rossby modes
assimilate into continuous modes.
- High-order zonally symmetric unstable modes obtained by Stevens (1983)
are described in terms of resonance between neutral waves.
The high-order modes are caused by resonance
between eastward mixed Rossby-gravity modes and continuous modes
or by resonance between eastward inertial gravity modes and
continuous modes.
- Neutral modes whose dispersion curves intersect
with nearby dispersion curves of other neutral modes
are examined.
These neutral modes do not resonate with contiuous
modes having pseudomomenta with opposite sign
in spite of intersection of dispersion curves of the neutral modes
and contiuous modes.
Such neutral modes appear when there exist regions
outside inertially unstable region,
and have large amplitudes
outside inertially unstable region.
- The behaviors of dispersion curves of equatorial Kelvin modes
and westward mixed Rossby-gravity modes are examined
in cases that the two curves come closer.
With narrowing calculational domains,
it is observed that
dispersion curves of equatorial Kelvin modes
kink, when equatorial Kelvin modes
and westward mixed Rossby-gravity modes resonate.