The structures and energetics of fully nonlinear symmetric baroclinic waves

Abstract

A finite-difference Navier-Stokes model has been used to study rotating baroclinic flow for Richardson number [lsim ] 1, assuming no variations except in the vertical plane wholly containing the density-gradient vector. A section of a horizontally infinite channel has been studied, assuming periodic boundary conditions at the vertical computational boundaries and no-slip conducting horizontal boundaries. Two configurations were studied, both of which have an analytic basic solution with no horizontal variations in the velocities or density gradients. Symmetric baroclinic waves developed in the flows, as long as the Richardson number was not too large and the thermal Rossby number was large enough (for fixed diffusion parameters), consistent with linear theory. The structures and energetics of the fully developed waves were found to be especially dependent upon the Prandtl number Pr. Potential energy was the ultimate wave-energy source in all cases, and the average zonal flow was never much affected by the waves. For Pr > 1 the conversion from potential energy to wave kinetic energy was direct, via temperature and vertical-motion correlation. For Pr < 1 the conversion was from potential energy, to average kinetic energy by virtue of an induced meridional flow, to wave kinetic energy. For Pr = 1 the energy conversion was by either or both of the above, depending upon the other parameters.