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A Correction to this paper has been published: https://doi.org/10.1007/s10236-021-01446-z

The present work explores the applicability of an alternative eddy viscosity formulation in numerical models dealing with the dynamics of the coastal ocean. The formulation is based on the Reynolds stress anisotropy–anisotropy being an important tool for capturing turbulent mixing. Initially idealized entrainment scenarios are evaluated that are typical for shelf seas viz. entrainment in linearly stratified and two-layer fluids caused by surface wind stress or barotropic pressure gradient-driven bottom stress. An attempt is made to simulate the realistic semi-diurnal cycle of turbulent dissipation in Liverpool Bay Region of Freshwater Inflow (ROFI) in the Irish Sea characterized by strong horizontal gradients and interactions with tidal flow. Turbulent dissipation cycles with a 25-h period using free-falling light yo-yo (FLY) dissipation profiler exhibits a strong asymmetry between ebb and flood. The above dynamics involving tidal straining during the ebb and mixing during the flood has been simulated using k– $$ \varepsilon $$ and the alternative formulated turbulence scheme in a one-dimensional (1-D) dynamic model. The model is forced with observed tidal flow and horizontal gradients of temperature and salinity. Simulated dissipation cycles show good agreement with observation. The present work also involves a comparison of dissipation rate measurements in northern North Sea using the abovementioned turbulence schemes—the measurements being taken using free-falling shear probes and CTD (conductivity, temperature, and depth) sensors. The main forcing provided for the upper and bottom boundary layers are atmospheric forcing and tides, respectively. To compare the observations and model results, quantitative error measurements have also been studied which reveal the applicability of the alternative turbulence scheme.

To explore the feasibility of forescasting North Sea storm surges by integrating numerically a combined atmospheric-oceanographic physical model, the severe storm and the resulting water levels occurring on 3 January 1976 were simulated as a first step into this direction. For this purpose, the atmospheric model was run with a resolution of 8 levels in the vertical and a horizontal grid spacing of 1.4° in latitude and 2.8° in longitude on the hemisphere. The initial conditions are based upon observations of 2 January 1976, 12 GMT, i.e. about 24 hours before the storm reached its greatest intensity in the southern parts of the North Sea. The surface wind predicted by the atmospheric model was converted into stress values through a bulk formula which then entered the vertically integrated North Sea model, to yield the desired water elevations in a 22 km-grid. Moreover, also the observed wind, stemming from a careful re-analysis of the storm situation, was handled in the same way. The numerically obtained results were compared with gauge measurements at a number of coastal stations.

In this paper ERS-1 altimeter data are used for the calibration of a tidal model of the European Continental Shelf. The data assimilation procedure to estimate the uncertain parameters in the model is based on the adjoint method. Here the estimation problem is formulated as a large scale optimization problem, that is solved with a gradient based optimization method. The gradient is determined efficiently by using the solution of the adjoint problem. The data assimilation procedure is applied by using the ERS-1 data with and without other measurement information from water level stations.