Stability of Finite-Amplitude Baroclinic Waves in a Two-Layer Channel Flow

Part II. Moderately Non-Linear Regime

Abstract

By using a two-layer channel model, the stability and behaviours of finite-amplitude baroclinic waves are investigated in the moderately non-linear regime. Two methods which are applicable to the moderately non-linear regime are adopted. One is the method in which steady wave solutions are first obtained and then their stabilities are examined with respect to various perturbations. The other is the numerical method in which time integrations of a grid model are performed as an initial value problem. We obtain many interesting results, although we treat some cases with particular values of non-dimensional parameters except the vertical shear U. The main results are summarized as follows: (1) The stability of steady finite-amplitude baroclinic waves is determined mostly by the sideband instability. (2) The dominant wavenumber seen in a finite-amplitude state is different from that predicted by the linear theory. (3) The beta effect reduces the stable region of finite-amplitude baroclinic waves in the (α, U)-plane, where a is wavenumber. (4) The wavenumber realized in the finiteamplitude state for given values of parameters depends on the initial conditions. Such a hysteresis phenomenon in wavenumber selection is seen when the stable region contains more than two wavenumbers. (5) Both wavenumber and amplitude vacillations are simulated by numerical experiments. The sideband instability can produce such time-dependent motions. The mechanism of vacillations produced by this instability is different from those proposed by Lorenz (1963) and Pedlosky. (1976, 1977).