Stability of the solar latitudinal differential rotation inferred from helioseismic data

We revisit the hydrodynamical stability problem posed by the observed solar latitudinal differential rotation. Specifically, we carry out stability analyses on a spherical shell for solar-like two-dimensional inviscid shear flow profiles of the form v = s₀ - S₂μ² - S₄μ⁴where μ is the sine of latitude. We find that stability is remarkably sensitive to the magnitude of the μ⁴ term. This allows us to reconcile apparently conflicting results found in the published literature. We then use latitudinal differential rotation profiles extracted from various helioseismic inversions of the solar internal rotation and investigate their stability as a function of depth from the base of the tachocline to the top of the convective envelope. In all cases considered, we find that the latitudinal differential rotation in the tachocline is stable while that in the bulk of the convective envelope is unstable. Under the assumption that the instability is not impeded by finite Reynolds number or three-dimensional effects not accounted for in our analysis, we speculate on possible observable consequences of the occurrence of the instability in the top half of the convective envelope.