Normal-Mode Instabilities of a Time-Dependent Coastal Upwelling Jet

Abstract

Abstract The linear stability of a nearly time-periodic, nonlinear, coastal upwelling–downwelling circulation, over alongshore-uniform topography, driven by a time-periodic wind stress is investigated using numerical methods. The near-periodic alongshore-uniform basic flow is obtained by forcing a primitive equation numerical model of coastal ocean circulation with periodic wind stress. Disturbance growth on this near-periodic flow is explored in linear and nonlinear model simulations. Numerous growing normal modes are found in the linear analyses at alongshore scales between 4 and 24 km. These modes vary in cross-shore structure and timing of maximum disturbance growth rate. One group of modes, in the 6.5–8.5-km alongshore-scale range, bears strong resemblance to the ensemble average disturbance structures observed in perturbed nonlinear model simulations. These modes are of a mixed type, exhibiting both strong baroclinic and barotropic energy exchange mechanisms, with maximum disturbance growth occurring during the transition from upwelling favorable to downwelling favorable winds. Nonlinear disturbance growth is characterized by similar structures at these same scales, but with significant exchange of energy between disturbances at different alongshore scales, such that overall disturbance energy accumulates at the longest (domain) scales, and gradually propagates offshore mainly in the pycnocline over numerous forcing cycles.