Analysis of time-varying wind-induced currents in the North Channel of the Irish Sea, using empirical orthogonal functions and harmonic decomposition

Abstract

The response of the currents in the North Channel of the Irish Sea to time-dependent wind and open boundary forcing is examined using a three-dimensional model of the region. For wind-induced motion, we primarily consider currents produced by a clockwise rotating wind field with periods above, at, and below the inertial period. With the longer period wind forcing a calculation is performed with an anticlockwise rotating wind. Flow fields from the model, in particular currents in the centre of the Channel and at points in shallower water, are analysed using the harmonic method in time and an expansion of empirical orthogonal functions (EOFs) in the vertical. Results from the analysis show that with wind forcing at the inertial period, currents are produced throughout the water column, although with longer and shorter period forcing the depth of penetration of the wind's momentum is confined to a near surface layer. In the case of an anticlockwise rotating wind, for a given wind period (excluding the inertial), the thickness of the near surface layer is less than that for the clockwise wind. In the case of short period forcing, in deep water the wind stress and elevation gradient terms, are balanced by the acceleration term whereas at longer periods the acceleration term is small, and the balance is between rotational and elevation gradient terms and the wind stress. In shallow water, the bottom stress contributes to the balance of terms. Also the bottom Ekman layer occupies a significant proportion of the water column, and influences the profile of wind-induced currents. The analysis of current profiles using both harmonic methods, and fitting EOFs in the vertical shows that to first order the motion in the centre of the channel can be described by linear dynamics. However, non-linear coupling between the time-varying eddy viscosity and wind shear in the surface layer modifies the M 2 tidal current in this region. In shallower water the quadratic bottom friction term is important as are the non-linear advection of momentum terms. With open boundary forcing, the flow is to first order aligned with the orientation of the channel, and dominated by currents at the period of the boundary forcing. In the near bed region, higher frequency harmonics are generated, although the M 2 harmonic found in the wind-driven flow case does not appear at any depth. The highly sheared surface layer found with wind forcing is not present for currents induced by open boundary forcing, where shear is confined to the bottom boundary layer. The application of harmonic analysis methods, and the use of EOFs in the vertical are shown to be powerful techniques in understanding the physical nature of time-dependent flow in the North Channel.