On the hydraulics of Boussinesq and non-Boussinesq two-layer flows

Publisher Website
Google Scholar
Abstract
Exact expressions for the internal and external Froude numbers for two-layer flows are derived from the celerities of infinitesimal long internal and external waves, without recourse to the Boussinesq approximation. These expressions are functions of the relative density difference between the layers; the relative thickness of the layers; and the stability Froude number, which can be regarded as an inverse bulk Richardson number. A fourth Froude number, the composite Froude number, has been most often used in previous studies. However, the usefulness of the composite Froude number is shown to diminish as the stability Froude number increases. The potential confusion associated with having four Froude numbers of importance has been alleviated by deriving an equation interrelating them. This equation facilitates a comprehensive understanding of the hydraulics of two-layer flows.It is demonstrated that in substantial portions of some flows (both Boussinesq and non-Boussinesq exchange flow through a contraction are presented as examples), the stability Froude number exceeds a critical value. In this case hydraulic analysis yields imaginary phase speeds corresponding to the instability of long internal waves. Various implications of this result are discussed.