Author(s): M. Eletta Negretti; Scott A. Socolofsky; Gerhard H. Jirka

Linked Author(s): Scott A. Socolofsky

Keywords: Stratified flows; Interfacial waves; Shear layers; Hydrodynamic instability

Abstract: A dense fluid flowing along a sloping bottom is a geophysical process found in many natural water bodies and in the atmosphere. Predicting the rate of this flow exchange and the mixing and fate of the exchanged inflows into their neighboring water bodies is important in environmental and ecological studies such as water quality modeling and pollution remediation. In this study, preliminary numerical results using linear stability analysis are presented for a two-layer stratified shear flow, which is described with a hyperbolic tangent function for both the velocity and density profiles. Different numerical methods were tested, namely a pseudospectral method employing Chebyshev Polynomials (Socolofsky and Jirka 2004) and a finite difference method. Finally, a central, second-order finite difference method with an irregular grid is employed. The stability is studied from a temporal frame of reference. Preliminary results show that the unstable regions grow with increasing slope angles at a given wavenumber. Moreover, it introduces in the unstable regions the coexistence of two types of instabilities: KH instabilities characterized with higher temporal amplification rates and which decrease for increasing Richardson numbers, and Holmboe instabilities, which exist at higher Richardson numbers and which have a finite, non-zero phase speed.

DOI:

Year: 2007