Nonlinear barotropic instability of upper-tropospheric tropical easterly jet on the sphere

The nonlinear evolution of perturbation superimposed on the barotropic, unstable observed mean easterly jet at 100 hPa is studied over the sphere. The nondivergent barotropic nonlinear global spectral model with rhomboidal truncation at zonal wavenumber 21 is integrated for 120 days for initial random and linear unstable perturbations. The model includes a Rayleigh friction and restoring mechanism for zonal wind to its initial distribution. Time variations of eddy and zonal kinetic energy, zonal-wave and wave-wave interactions, and eddy and zonal kinetic energy dissipations are examined. The growth of perturbation begins with exponential increase in its kinetic energy for a short period, followed by a linear increase. The perturbations undergo oscillations before approaching a steady state. During the initial exponential phase, the nonlinear interactions further destabilize the jet, and this effect is more pronounced for the random initial perturbation. It is found that oscillations in kinetic energy are due to the time lag between energy source (zonal-wave interaction) and sink (frictional dissipation). It is noticed that the random initial perturbation is more efficient than the linear unstable modes in reaching the steady state. Nonlinear interactions shift the preferred wave towards the lower wavenumber 6. Wave 6 accounts for more than 98% of eddy kinetic energy of steady state. The role of wave-wave interaction is secondary to zonal-wave interaction. Steady-state wave 6 has an inviscid growth rate of 0.104 × 10-5 s-1, a phase speed of -20.9° day-1, and a meridional scale comparable to the half-width of the easterly jet. The zonal scale of the wave is close to the Rossby radius of deformation. The maximum meridional velocity associated with the wave is 3.8 m s-1. Nonlinear interactions modify the jet to a more asymmetric distribution, which induces a southward shift in the wave- amplitude maximum location. Strong correlation between latitude of maxima for wave amplitude and meridional gradient of basic-state potential vorticity is noticed. A close agreement is seen between observation and nonlinear preferred wave 6. The kinetic energy cycle for steady-state wave 6 on the sphere and in the latitude belt 10°S-40°N is computed and discussed. The kinetic energy of wave 6 in the latitude belt agrees well with the observed value