Time development of small disturbances to plane Couette Flow

The question of linear sheared-disturbance evolution in constant-shear parallel flow is here reexamined with regard to the temporary-amplification phenomenon noted first by Orr in 1907. The results apply directly to Rossby waves on a beta-plane, and are also relevant to the Eady model of baroclinic instability. It is shown that an isotropic initial distribution of standing waves maintains a constant energy level throughout the shearing process, the amplification of some waves being precisely balanced by the decay of the others. An expression is obtained for the energy of a distribution of disturbances whose wavevectors lie within a given angular wedge and an upper bound derived. It is concluded that the case for ubiquitous amplification made in recent studies may have been somewhat overstated: while carefully-chosen individual Fourier components can amplify considerably before they decay. a general distribution will tend to exhibit little or no amplification.

Mean motions induced by baroclinic instability in a jet

A study is made of the zonal-mean motions induced by a growing baroclinic wave in several contexts, under the framework of three different analysis schemes: the conventional Eulerian mean (EM), the transformed Eulerian mean (TEM), and the generalized Lagrangian mean (GLM). The effect of meridional shear in the initial jet on these induced mean motions is considered by treating the instability problem in the context of the two-layer model. The conceptual simplicity of the TEM formulation is shown to be useful in diagnosing the dynamics of instability, much as it has been found helpful in many problems of wave, mean-flow interaction. In addition, it is found that the TEM vertical velocity is a very good indicator of the GLM vertical velocity. However, the GLM meridional velocity is always convergent towards the centre of instability activity, and is not at all well represented by the nondivergent TEM meridional velocity. In comparing the results with Uryu's (1979) calculation of the GLM circulation induced by a growing Eady wave, it is found that the inclusion of meridional jet shear in the present work leads to some strikingly different effects in the GLM zonal wind acceleration. In the case of pure baroclinic instability treated by Uryu, the Eulerian and Stokes accelerations nearly cancel each other in the centre of the channel, leaving a weak Lagrangian acceleration opposed to the Eulerian one. In the more general case of mixed baroclinic-barotropic instability, however, the Eulerian and Stokes accelerations can reinforce one another, leading to a very strong Lagrangian zonal wind

The influence of ocean flow on newly forming sea ice

The heat and mass balance of the Arctic Ocean is very sensitive to the growth and decay of sea ice and the interaction between the heat and salt fields in the oceanic boundary layer. The hydraulic roughness of sea ice controls the detailed nature of turbulent fluxes in the boundary layer and hence is an important ingredient in model parameterizations. We describe a novel mechanism for the generation of corrugations of the sea ice–ocean interface, present a mathematical analysis elucidating the mechanism, and present numerical calculations for geophysically relevant conditions. The mechanism relies on brine flows developing in the sea ice due to Bernoulli suction by flow of ocean past the interface. For oceanic shears at the ice interface of 0.2 s−1, we expect the corrugations to form with a wavelength dependent upon the permeability structure of the sea ice which is described herein. The mechanism should be particularly important during sea ice formation in wind-maintained coastal polynyas and in leads. This paper applies our earlier analyses of the fundamental instability to field conditions and extends it to take account of the anisotropic and heterogeneous permeability of sea ice.

Baroclinic instability on hot extrasolar planets

We investigate baroclinic instability in flow conditions relevant to hot extrasolar planets. The instability is important for transporting and mixing heat, as well as for influencing large-scale variability on the planets. Both linear normal mode analysis and non-linear initial value cal- culations are carried out – focusing on the freely-evolving, adiabatic situation. Using a high- resolution general circulation model (GCM) which solves the traditional primitive equations, we show that large-scale jets similar to those observed in current GCM simulations of hot ex- trasolar giant planets are likely to be baroclinically unstable on a timescale of few to few tens of planetary rotations, generating cyclones and anticyclones that drive weather systems. The growth rate and scale of the most unstable mode obtained in the linear analysis are in qual- itative, good agreement with the full non-linear calculations. In general, unstable jets evolve differently depending on their signs (eastward or westward), due to the change in sign of the jet curvature. For jets located at or near the equator, instability is strong at the flanks – but not at the core. Crucially, the instability is either poorly or not at all captured in simulations with low resolution and/or high artificial viscosity. Hence, the instability has not been observed or emphasized in past circulation studies of hot extrasolar planets.