Three‐dimensional Numerical Model of the Irish Sea

Summary The model computes the dynamic response of the Irish Sea to a stationary wind‐stress field suddenly applied to the sea surface. The currents at any depth are determined as well as surface elevations, evaluations being made through time at positions on a uniform horizontal grid of mesh 7.5 nautical miles square. This calculation of the three‐dimensional current structure marks an advance on earlier numerical sea models which, generally, have solved the vertically‐integrated equations of motion and continuity to yield depth‐mean flows without reference to the vertical distribution of current. The method employed solves the hydrodynamical equations, taken in linearized form, by first transforming them to eliminate the depth co‐ordinate z . The resulting set of differential equations, involving two horizontal co‐ordinates x, y and time t , are then expressed in terms of finite‐differences for numerical solution using the familiar initial‐value technique of iterating, from one state of motion to the next, across successive time increments δ t . Finally, an inverse transformation applied to the computed values restores dependency on the z co‐ordinate, expressing the vertical current structure in terms of a set of eigenfunctions (or modes). The water is assumed to be homogeneous. Also, the coefficient of vertical eddy viscosity which determines the system of internal stresses is regarded as functionally independent of z and t . A slip condition is postulated at the sea bed. Along the open‐sea boundaries of the model, elevation and current are related by a radiation condition. A series of numerical experiments has been carried out with the model to determine the response of the Irish Sea to uniform southerly and westerly wind fields. In each case the surge motion generated has been computed and, after the transient oscillations have been damped down by friction, the steady‐state circulation maintained by the wind has been obtained.