Residual flows and elevations in the southern North Sea

Abstract

The distribution of residual flow and the variation in mean sea level in the southern North Sea have been simulated by using a two-dimensional, vertically integrated, numerical model. The tidal residuals (i.e. the nonoscillatory tidal component) associated with the principal, M 2 , constituent were calculated from a fully nonlinear model and in specifying the boundary conditions for this model, the technique used by Proudman (1957) to accommodate residual terms was adopted. The residual flows computed for the M 2 constituent were found to account for approximately one half of the net computed residuals and the flow distribution produced by the model was shown to be in excellent agreement with both observations and previous calculations (Nihoul & Ronday 1975). A linearized model was used to simulate the effect of the major non-tidal forcing phenomena, namely wind, density and sea-surface gradients. The magnitudes of the friction coefficients in the linearized model were evaluated in terms of the M 2 tidal velocities. In simulating the response of the region to an imposed wind field, boundary conditions were calculated by reference to the method of characteristics. The relation, calculated from the model, relating the wind speed to the resulting flow and the elevation gradient in the Dover Strait, was found to be in close agreement with the corresponding relation deduced from observations by Bowden (1956). Similarly, the long-term variation in mean sea level due to wind forcing calculated by the model was found to be in good agreement with the variation computed from observations by Rossiter (1967). It was shown that, subject to the assumption of vertical homogeneity implicit in the model, the residual flows and elevations generated by horizontal density gradients were of only a minor significance. The net residuals were obtained by superimposing the separate components, namely those of tidal, wind and sea-surface gradient origin. The magnitude of the sea-surface gradient was determined by ensuring a best fit between the computed and recorded variations in mean sea level along the Continental coast. The difference in mean sea level between the Continental and English coasts was then calculated directly and was found to be in agreement with the earlier estimate by Cartwright & Crease (1963). In addition, the corresponding datum differences between the English and Continental levelling networks were computed and were found to be in good agreement with the value calculated by using the most recent British and French levellings of the tidal datums at Dover and Dunkirk. The magnitude of the net residual flow, computed in conjunction with these net sea-level gradients, was also in excellent agreement with the net residual derived from over 9 years of cross-Channel cable recordings (Alcock & Cartwright 1977). In addition, the net residual flow computed for wind-free conditions was in close agreement with the results from current meter recordings under similar conditions (Prandle & Harrison 1975). The distribution of this net residual flow was found to be consistent with previous observations and estimations based on ( a ) temperature and salinity distributions, ( b )current meter measurements, ( c ) sea-bed drifters, ( d )distribution of caesium 137, ( e ) movement of sand waves and ( f ) independent modelling studies. In conclusion, the results of this study provide a framework which both connects and relates the established studies of residuals in the Southern Bight. In addition, for the first time, a complete and comprehensive description is presented of the contribution of each of the major residual forcing phenomena.