INCIPIENT INSTABILITY CRITERION OF 2 CONFINED SUPERPOSED FLUIDS

The problem of stability for the interface of two superposed fluids is determined by several parameters, for example, gravity, density diffe rence, interfacial tension, depth of flow field, and shape of boundary constraint. The present paper studies the effects of boundary shapes on the incipient stability criterion of the interface between two flui d layers with different densities confined within a vertical container . When the interface is disturbed, its shape is easily destroyed by un symmetric disturbances or due to the sloshing mode of disturbances. In the present study, two different wave-like boundaries are transformed to circular contours by conformal mapping. As the concept that some p roeprties of any successive transformations still remain unchanged is applied, we obtain the eigenvalues for the incipient stability criteri a under the constraints of wavelike contours.