The Modification of Background Density Profiles in Thermohaline Convection
Abstract
Density profile modification in thermohaline convection is examined with a sixteen coefficient spectral model derived from the two dimensional, shallow Boussinesq equations. These density modifications significantly alter the depth and location of the near surface sound channel. A linear stability analysis of the conductive solution gives a characteristic equation which determine the Hopf bifurcation points signalling the onset of convective, or temporally periodic, solutions. Two horizontal wave numbers are included to allow the existence of a double Hopf point, which when separated, may yield diffeo- Hopf points on the periodic solutions and so allow for secondary branching, or toral, solutions. The periodic solutions associated with the Hopf bifurcations are the toral solutions associated with the diffeo-Hopf points are then studied. An example using parameter values corresponding to those of melting sea ice is presented. The toral solutions are always unstable owing to the existence of the diffeo-Hopf point exclusively on the unstable periodic solution that branches second from the conductive solution. The competition between the stabilizing salinity gradient and destabilizing temperature gradient allows only stable steady and stable periodic solutions, which modify the background density profiles. The periodic solutions are characterized by an unstable density profile moving alternately between the interior and the boundaries. the sound channel alternately increases the decreases in depth and in location relative to the surface. In contrast, the steady solutions produce an unstable density gradient in the interior of the domain. In the steady case, there is always a near surface sound channel. (JHD)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1990
- Accession Number
- ADA228490
Entities
People
- H. N. Shirer
- J. L. Schramm
- R. Wells
Organizations
- Pennsylvania State University