On the Equilibration in Nonlinear Barotropic Instability

Non-Linear Aspects of a Barotropically Unstable Polar Vortex in a Forced-Dissipative System

“…Decrease of dominant zonal wavenumber from 3 to 2 along the U axis at c0=35 is consistent with the result obtained by Kwon and Mak (1988). Figure 2 shows an example of the evolution of domain-averaged kinetic energy associated with zonal mean zonal flow and planetary waves (see IY94 for the definition) for the vacillation of U=270m/s, B=4, and c50=55.…”

“…Throughout this study, we fix the relaxation time as a-1=10 days and the viscosity coefficient v at a small constant which gives the dissipation time of 1 day at the largest total wavenumber (N=85) in our model. We employ a damping rate a that is rather smaller than the realistic value for middle and upper stratosphere in order to examine various flow regimes which depend on the external parameters; when a is too large, the variety of flow regimes is limited because the damping has a stabilizing effect on the system (see, e.g., Kwon and Mak, 1988).…”

“…With such a forcing and dissipation, several kinds of flow regimes are expected to exist, depending on some experimental parameters as in the B-channel experiments by Kwon and Mak (1988). We sweep a parameter space which determines the prescribed jet profiles of the forcing.…”

Non-linear Evolution of a Barotropically Unstable Circumpolar Vortex

“…Such competitions among unstable waves occur when the wave of smaller wavenumber has a little smaller growth rate than the most unstable mode (see Tables 1 and 4 for the above examples). This scale selection in the non-linear evolution of barotropically unstable flow has been already reported by Niino and Misawa (1984) with a laboratory experiment and Kwon and Mak (1988) with a numerical experiment. As Niino and Misawa (1984) discussed, the mechanism of the scale selection can be conjectured as follows: Initially, the most unstable wave grows and stabilizes the unstable basic state to a certain extent.…”

“…These stud-ies showed the linear unstable modes have similar properties to the observed eastward-moving waves. However, to our knowledge, there are few studies on the non-linear phase of the instability at which the linear unstable modes grow to have a finite amplitude and non-linear interactions become important, except for the work by Kwon and Mak (1988). They investigated the non-linear phase of the instability in a 3-channel as a general problem but had no application to the polar night jet.…”