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The effect of surface buoyancy gradients on oceanic Rossby wave propagation

Motivated by the discrepancy between satellite observations of coherent westward propagating surface features and Rossby wave theory, this paper revisits the planetary wave propagation problem, taking into account the effects of lateral buoyancy gradients at the ocean's surface. The standard theory for long baroclinic Rossby waves is based on an expansion of the quasigeostrophic stretching operator in normal modes, $ϕ_n(z)$, satisfying a Neumann boundary condition at the surface, $ϕ_n'(0) = 0$. Buoyancy gradients are, by thermal wind balance, proportional to the vertical derivative of the streamfunction, thus such modes are unable to represent ubiquitous lateral buoyancy gradients in the ocean's mixed layer. Here, we re-derive the wave propagation problem in terms of an expansion in a recently-developed "surface-aware" (SA) basis that can account for buoyancy anomalies at the ocean's surface. The problem is studied in the context of an idealized Charney-like baroclinic wave problem set in an oceanic context, where a surface mean buoyancy gradient interacts with a constant interior potential vorticity gradient that results from both $β$ and the curvature of the mean shear. The wave frequencies, growth rates and phases are systematically compared to those computed from a two-layer model, a truncated expansion in standard baroclinic modes and to a high-vertical resolution calculation that represents the true solution. The full solution generally shows faster wave propagation when lateral surface gradients are present. Moreover, the wave problem in the SA basis best captures the full solution, even with just a two or three modes.