Linear stability and enhanced dissipation for the two-jet Kolmogorov type flow on the unit sphere

We consider the Navier–Stokes equations on two-dimensional unit sphere and study linear stability of two-jet Kolmogorov type flow which is a stationary solution given by zonal spherical harmonic function degree two. prove for an arbitrary viscosity coefficient showing exponential decay to linearized equation towards equilibrium grows as tends zero. The main result this paper nonexistence nonzero eigenvalues perturbation operator appearing in equation. By making use mixing property expressed recurrence relation harmonics, we show that does not have only nonreal but also real eigenvalues. As application result, get enhanced dissipation sense rescaled time decays arbitrarily fast