Baroclinic Instability and Thermohaline Gradient Alignment in the Mixed Layer

Abstract The density of the mixed layer (ML) is approximately uniform in the vertical, but there are dynamically important horizontal gradients. The subinertial mixed layer (SML) approximation is a small Rossby number filtering of the primitive equation that isolates the low frequency (ω ≪ f) dynamics. A linear stability analysis based on the SML approximation shows that the horizontal density gradients within the mixed layer (ML) support baroclinically unstable waves with inverse wavenumbers in the range 1 to 10 km. This conclusion follows from both a slab ML model, in which the horizontal velocity has no vertical shear, and a geostrophic ML model, in which the horizontal velocity is sheared according to the thermal wind relation. In the geostrophic case the instability is identical to the long wavelength limit of baroclinically unstable Eady waves. An interesting difference between the slab and geostrophic ML is the dynamics of thermal and saline anomalies. In the slab case, thermohaline anomalies are a...