Stable and unstable Rossby waves in the North Pacific current as inferred from the mean stratification

We have determined free Rossby waves in the North Pacific Current by numerical methods. We have found only two stable solutions — the barotropic and first-order baroclinic Rossby shear modes. The influence of the current on the dispersion features of these waves is small for the barotropic shear mode, but is significant for the baroclinic shear mode. An explicit comparison of the dispersion relations for the baroclinic wave in case of vanishing and non-vanishing current is given. We have found at most one unstable solution per wave number. The unstable wave with largest growth rate has an e-folding time of 1.1 year. We have calculated vertical profiles of the stream function and the temperature for the various shear modes at various wave numbers. The temperature shear modes have been calculated for later usage in a Rossby wave model to be fitted to observed temperature data from the North Pacific Current area.