Modal Response of Reservoirs to Wind Stress

An analysis of the response of a density‐stratified reservoir to surface shear stress is presented. The reservoir is assumed to be two‐dimensional and to have a constant depth. In the limit that the bulk Wedderburn number WB and the bulk Richardson number RiB are both infinite, the resulting equations are linear and solutions can be found in terms of the individual responses of a set of orthogonal normal modes. For the case of a steady wind stress, the solution consists of periodic motions and steady isopycnal displacements. However, the steady‐state isopycnal slope at the base of the mixed layer is infinite, implying that upwelling can occur when the Wedderburn number is quite large. This is attributed to blocking of the stratified fluid below the mixed layer by the endwall. The modal theory presented in this paper is compared with experimental observations made using a belt to impart shear stress to a stratified fluid contained in a box. The comparison shows that the present theory is qualitatively correct in that upwelling is observed when WB≫1. However, the modal theory best predicts the first‐mode seiche amplitude; the higher‐mode response is not accurately predicted.