Note on the Propagation of Baroclinic Waves in a Zonal Ocean Current

In a zonal ocean current one sees Stationary or slowly moving baroclinic waves, with a wavelength of 1,000 km or more. These waves may be equivalent to a type of very long waves studied earlier in the atmospheric case. The wave speed is independent of the wave number but depends on the speed of the basic current, the stratification etc. For the case of a zonal current with exponential vertical profile, stationary waves are found for an eastward current. The wave perturbation normally decays downward in an exponential way. The parameter that decides the nature of the waves is λ = β/f² ΔAp₀/U₀ where U₀ is the amplitude of the basic current, ΔA the vertical variation of the specific volume, p₀ the scale pressure (the pressure variation that corresponds to the scale depth of the basic current), and f the Coriolis parameter. For a westward current travelling neutral waves exist but only for special values of λ that are not normally expected in the oceans.