Effect of the nonlinear interaction of tidal harmonics on their spatial structure as applied to the system of the white and Barents Seas

Abstract

Using the three-dimensional nonlinear finite-element thermohydrodynamic model QUODDY-4, we obtain two solutions giving an idea of the role of the nonlinear interaction of tidal harmonics in the formation of their spatial structure. The first solution is induced by the total tide (M2 + S2 + K1 + O1) at the open boundary and by the total static tide inside the area under consideration; then, the solution obtained is subject to harmonic analysis. The second solution is obtained by specifying such tidal sea level elevations at the open boundary that meet individual tidal harmonics. These two solutions are compared. It is shown that the differences between the solutions for the S2, K1, and O1 waves can be significant, especially near the open boundary between the White and Barents seas. This conclusion remains valid also for the maximum velocities (major semiaxes of the ellipses) of the barotropic (depth-average) tidal current as well as for the average (over the tidal cycle) densities of the total tidal energy and components of the tidal-energy budget. The emergence of this feature indicates that there are resonance modes with frequencies that differ from those of the S2, K1, and O1 harmonics to a lesser extent than the M2 harmonic frequency. The same conclusion can be made by comparing the values of the amplification factor, which is defined as the ratio between the actual and static tides, for the system of the Barents and White seas as a whole and for Mezen Bay in the White Sea and Czech Bay in the Barents Sea, taken separately.