Nongeostrophic baroclinic instability of two fluids

The interfacial stability of two fluids under differential rotation in a tall, right circular cylinder was investigated. The differential speeds are such that the Rossby number of the flow is small. Geostrophic conditions prevail in the interior, undisturbed flow and the results of interfacial shape calculations using the geostrophic velocity profiles in each fluid are compared with experimentally measured interface shapes. A linearized stability analysis, including interfacial tension and viscous effects at the interface and end caps was performed on the nongeostrophic equations of motion. Experiments were conducted in which instability regions corresponding to the wave numbers n = 1 and n = 2 are determined. Qualitative observations are made concerning the presence of amplitude and frequency vacillations characteristic of finite amplitude baroclinic waves under supercritical conditions.