Baroclinic Buoyancy-Inertia Joint Stability Parameter

Abstract

At present, the barotropic buoyant stability parameter has been derived from a vertical virtual displacement of a water parcel. The barotropic inertial stability parameter in the eccentrically cyclogeostrophic, basic current field was derived in 2003 from a horizontal cross-stream virtual displacement of a parcel. By expressing acceleration of a parcel due to a virtual displacement, which is arbitrarily sloping within a vertical section across the basic current, in terms of natural coordinates, we derived the vertical component of baroclinic buoyant stability parameter B22, the horizontal component of baroclinic inertial stability parameter I22, the baroclinic joint stability parameter J2, its buoyant component B2 and its inertial component I2. B2 is far greater than I22, and when neglecting relative vorticity except for vertical shear, a downward convex curve of J2 plotted against the slope of a virtual displacement follows a trend of B2 curve. If a parcel displaces along a horizontal surface or an isopycnal surface, however, B2 vanishes, and J2 becomes equal to I2. Actual parcel is apt to displace not only along the bottom slope, but also along the sea surface and an isopycnal interfacial surface, which is approximately equivalent to an isentropic surface, preferred by lateral mixing and exchange of momentum. Such actual displacement makes B2 vanishing, and grants I2 an important role. The present analysis of I2 examining effects due to curvature and horizontal and vertical shear vorticities are useful in deepening our understanding of baroclinic instability in actual oceanic streams.