A three‐dimensional model of the M₄ tide in the Irish Sea: The importance of open boundary conditions and influence of wind

A fully nonlinear three‐dimensional hydrodynamic model of the Irish Sea is used to examine the processes determining the spatial variability of the M 4 tide in the Irish Sea. The model is based upon a mixed spectral/finite difference approach, with an expansion of functions in the vertical (yielding a continuous current profile) and a finite difference grid in the horizontal. The model has a sufficiently fine grid to enable the nonlinear advective terms to be resolved in their finite difference form, and the spatial variability of the M 4 tide to be represented. Computed M 4 elevations and currents determined using a radiation open boundary condition with both M 2 mid M 4 elevation and current input and a flow dependent viscosity are found to be in satisfactory agreement with observations considering the limited grid resolution of the model, and the level of noise in the M 4 tide as a percentage of the signal is much higher than for M 2 . This agreement is good enough to establish the credibility of using the model to examine the processes influencing the M 4 tide, which are discussed in detail. The importance of an M 4 current input to the radiation condition, and the difficulty of using an elevation specified open boundary condition to reproduce the M 4 tide in this region are considered in some detail. The nonlinear advective terms are shown to have a limited local influence (namely, around headlands) in generating the M 4 tide. The influence of wind effects upon M 4 tidal currents, particularly through the nonlinear term associated with a time dependent eddy viscosity, is examined, and shown to produce a significant increase in the M 4 near surface tidal current, and a modification of the current profile. In essence, the change of the M 4 tidal current by meteorological effects will give rise to noise in any observed M 4 current due to the random nature of the wind fields.