Turbulence & Mixing in Shelf Seas
A characteristic feature of ROFI systems is the occurrence of a marked semi-diurnal oscillations in stability of the water collumn. The amplitude of these oscillations in some cases is comparable to the mean stability so that the water column approaches, or even attains, complete vertical homogeneity once during each tidal cycle. This minimum in stability occurs close to the time of low water in the Southern North Sea Rhine ROFI where the tide is dominated by a progressive Kelvin wave moving up the Dutch coast. By contrast, minimum stratification in Liverpool Bay is observed at the time of local high water where the tides are dominated by a standing wave.
For the simpler case of a tidal standing wave, as in Liverpool Bay, the fresher surface water is moved seaward faster than underlying more-saline water on the ebb tide creating a stratified water column (Fig. 1.). In the absence of mixing this reaches a maximum stability at, or soon after, low water. Then, on the flood tide, the shear acts to produce a reverse differential advection which tends to reduce stratification reaching a minimum at, of near high water.
The situation in the Rhine ROFI is more complicated. When the water column is mixed, the tidal ellipses are close to the degenerate, in a straight line form at all levels inside and offshore of the ROFI region. With the onset of stratification, the surface ellipse becomes markedly anticyclonic (clockwise) while near the seabed the flow becomes more cyclonic. These differences in ellipticity imply an out-of-phase component of cross-shore velocity that is the origin of the strong cross-shore shear required for tidal straining. The maximum stratification occurs for the largest positive straining effect, i.e. when the surface off-shore displacement relative to the lower layers is maximal.
It can be shown that since we are dealing with a progressive Kelvin wave the straining displacement is in phase with the alongshore velocity and, hence the surface elevation. Therefore, for this type of ROFI regime, the largest strain induced stratification is at the time of local highwater in contradistinction to the standing wave regime of Liverpool Bay. An intriguing link between the mean and periodic components of the stratification in the Rhine ROFI is illustrated in Fig. 2. Reduced mixing allows relaxation of the water column. This then sets up mean stratification, which in turn modifies the tidal ellipses. The resulting cross-shore velocity components produce a strong straining effect in the direction of the density gradient and hence induce the periodic component of stratification.