A Numerical Method for Solving the Forced Baroclinic Coastal-Trapped Wave Problem of General Form

Abstract

The determination of baroclinic coastal-trapped wave modes reduces to an eigenvalue problem quadratic in the eigenvalue if the long-wave assumption is not made. This problem can be expressed as a linear eigenvalue problem of expanded dimension. Consideration of the expanded problem permits direct determination of the set of functions orthogonal to the baroclinic eigenmodes sought. Using this set, the forced baroclinic response problem can be expressed as a series of first-order, ondinary differential equations, one for each forced eigenmode. The method presented represents two significant advances. First, the solution technique permits the calculation of complex wavenumbers directly as they would result from the determination of evanescent solutions or of solutions including bottom friction. Second, the forcing of waves that are solutions to equations nonlinear in the eigenvalue can be determined. Although the method has been described in the context of baroclinic coastal-trapped waves, it has more general applicability. For example, the problem of frontal stability involving equations cubic in the eigenvalue could be solved using a straightforward extension to the technique.