Nakamura, N.,1993: An illustrative model of instabilities in meridionally
and vertically sheared flows. Journal of the Atmospheric Sciences,
50(3), 357-375.
Abstract: An analytic model is formulated to study the characteristics
of shear instabilities in meridionally and vertically sheared flows. The
model is based on the quasigeostrophic equations in two layers. The layers
are divided into sections of piecewise uniform potential vorticity. An
algebraic dispersion relation is obtained for the complex phase speed c.
The magnitude and the sign of the potential vorticity jumps, their meridional
separation, the barotropic shear, and the wavenumber of the modes determine
the stability of the system. Solutions describe not only pure baroclinic
and barotropic instabilities, but also mixtures of these instabilities.
The influences of linearly sheared barotropic flows on baroclinic instability
are studied in detail, with an emphasis on the direction of vertically
integrated momentum flux. The model's implications for the nonlinear life
cycle of baroclinic waves are also discussed.