The influence of changing stratification conditions on barotropic tidal transport and its implications for seasonal and secular changes of tides

Ocean tides are changing on secular and seasonal time scales with much larger magnitudes than we would expect from changes in the gravitational forcing. In order to understand the impact of seasonal and long term changes of stratification on ocean tides, the influence of eddy viscosity and bottom drag on the barotropic transport of an oscillating flow is analyzed by analytical and numerical models. The shallow water equations without the advective terms are solved and analytical solutions are obtained in cases of vertically and temporally constant eddy viscosity, and linearized bottom drag. The numerical model (General Ocean Turbulence Model, GOTM) allows for a more realistic consideration of eddy viscosity, non-linear bottom friction and vertical density profiles. Results of analytical and numerical models are consistent and show that changing stratification conditions, which in turn change the eddy viscosity profile and bottom drag, modify the barotropic transport by 1–5%. Specifically, the analytical model points out that eddy viscosity Av is negative (positive) correlated with the barotropic transport if A v ω / α b 2 < 1 ( A v ω / α b 2 > 1 ) , where α b describes the bottom friction coefficient and ω the frequency of the oscillating flow. Generally, these results suggest that in shallow seas the seasonal variations in stratification are a major factor for the observed seasonal modulation in tides. Further, a deepening of the mixed-layer depth by only 10 m can change tidal transport by 1–2%, which might be relevant to understand secular trends of tides in a warming ocean.