The Continuous Spectrum in Baroclinic Models with Uniform Potential Vorticity Gradient and Ekman Damping

Abstract

Analytic solutions of the continuous spectrum are obtained for quasigeostrophic models in which the basic-state meridional potential vorticity (PV) gradient is uniform but nonzero. The modes that form the continuous spectrum?continuum modes?are baroclinically neutral, singular solutions of the linear dynamical equations, which have an interior critical level. Although most inviscid shear flows support continuous spectra, previous studies have largely been restricted to models in which the interior PV gradient is zero. In that situation, continuum modes are formed by a superposition of boundary potential temperature anomalies and an interior PV δ function at the critical level. Here it is shown how a nonzero interior PV gradient and Ekman damping nontrivially affect the vertical structure of continuum modes. A consideration of the perturbation PV further rationalizes their vertical structure.