On the use of the Stokes number to explain frictional tidal dynamics and water column structure in shelf seas

Abstract. In recent years coastal oceanographers have suggested using the "Strouhal" number or its inverse, the "Stokes" number, to describe the effect of bottom boundary layer turbulence on the vertical structure of both density and currents. These are defined as the ratios of the frictional depth (δ) to the water column depth (h) or vice versa. Although many researchers have mentioned that the effects of the earth's rotation should be important, they have tended to omit it. Rotation may have an important influence on tidal currents, as the frictional depth from a fully cyclonic to a fully anticyclonic tidal ellipse can vary by up to an order of magnitude at mid latitudes. The Stokes number might appear smaller for cyclonic current ellipses (larger for anticyclonic) than it is without rotation, resulting in frictional effects being underestimated (overestimated). Here, a way to calculate a Stokes number is proposed, in which the effect of the earth's rotation is taken into account. The standard Stokes and the rotational Stokes numbers are used as predictors for the position of the tidal mixing fronts in the Irish Sea. Results show that use of the rotational number improves the predictions of fronts in shallow cyclonic areas of the eastern Irish Sea. This suggests that the effect of rotation on the water column structure will be more important in shallow shelf seas and estuaries with strong rotational currents.