Ageostrophic instability in rotating, stratified interior vertical shear flows

Abstract

International audienceThe linear instability of several rotating, stably stratified, interior vertical shear flows U¯¯¯(z) is calculated in Boussinesq equations. Two types of baroclinic, ageostrophic instability, AI1 and AI2, are found in odd-symmetric U¯¯¯(z) for intermediate Rossby number (Ro). AI1 has zero frequency; it appears in a continuous transformation of the unstable mode properties between classic baroclinic instability (BCI) and centrifugal instability (CI). It begins to occur at intermediate Ro values and horizontal wavenumbers (k,l) that are far from l=0 or k=0, where the growth rate of BCI or CI is the strongest. AI1 grows by drawing kinetic energy from the mean flow, and the perturbation converts kinetic energy to potential energy. The instability AI2 has inertia critical layers (ICL); hence it is associated with inertia-gravity waves. For an unstable AI2 mode, the coupling is either between an interior balanced shear wave and an inertia-gravity wave (BG), or between two inertia-gravity waves (GG). The main energy source for an unstable BG mode is the mean kinetic energy, while the main energy source for an unstable GG mode is the mean available potential energy. AI1 and BG type AI2 occur in the neighbourhood of A−S=0 (a sign change in the difference between absolute vertical vorticity and horizontal strain rate in isentropic coordinates; see McWilliams et al., Phys. Fluids, vol. 10, 1998, pp. 3178–3184), while GG type AI2 arises beyond this condition. Both AI1 and AI2 are unbalanced instabilities; they serve as an initiation of a possible local route for the loss of balance in 3D interior flows, leading to an efficient energy transfer to small scales

Horizontal shear instabilities in rotating stellar radiation zones

“…The inflectional instability occurs when there exists an inflection point y i where U (y i ) = 0. On the other hand, the inertial instability can occur without an inflection point when there is an imbalance between the pressure gradient and the inertial force, the mechanism equivalent for the centrifugal instability in cylindrical geometry (Kloosterziel & van Heijst 1991;Billant & Gallaire 2005;Wang et al 2014). For the hyperbolic tangent shear flow (7) in stratified-rotating fluids, the inflectional instability is always present while the inertial instability exists only in the range 0 < f < 1 (Arobone & Sarkar 2012).…”

“…This allows us to assume that the horizontal gradients of the angular velocity (and of the fluctuations of temperature and chemical composition) are smoothed out, leading to the so-called "shellular" rotation, that only varies with the radius. Such a radial variation of rotation is pertinent to the vertical shear instability, which has been mostly studied on the local f -plane with vertical stratification (see e.g., Wang et al 2014). The horizontal shear instability with stellar differential rotation in latitudinal direction has also been studied (see e.g., Watson 1980;Garaud 2001;Kitchatinov & Rüdiger 2009), but the combined impacts of the rotation, stratification, and thermal diffusion on horizontal shear instability are not yet fully resolved.…”

Submesoscale currents in the ocean

“…GI and CI are well-known processes, and both have finite-amplitude forward energy cascade and dissipation; they are particularly apt in the weakly (or negatively) stratified SBL [ 56 , 67 ]. AAI is a less widely familiar instability type but by now has a variety of adduced flow examples (see [ 68 ] and its references), including the ageostrophic instability mode in Eady’s flow [ 69 , 70 ]. Unlike GI and CI, AAI does not have a sharp onset condition in a general fluid model, but rather can exhibit an exponentially small unstable growth rate, as , which is also relevant to the asymptotic fuzziness of the slow (momentum-balanced) manifold (§ 4 b; [ 10 ]), but with when Ro ∼1, indicating that the fuzziness can become thick for SMCs outside this Ro limit.…”

Horizontal shear instabilities in rotating stellar radiation zones

“…Such a thermal-wind balance has been adopted for cases where the rotation vector and the base shear are not aligned in stratified fluids; for instance, ageostrophic instability in vertical shear flows in stratified fluids in the traditional f -plane (Wang et al 2014). In addition to the thermal-wind balance, the base temper-atureΘ(y, z) is considered to be stably stratified with a linearly increasing profile in z; therefore, it has the form…”