Breakdown of hydrostatic assumption in tidal channel with scour holes

Abstract

Hydrostatic condition is a common assumption in tidal and subtidal motions in oceans and estuaries. Theories with this assumption have been largely successful. However, there is no definite criteria separating the hydrostatic from the non-hydrostatic regimes in real applications because real problems often times have multiple scales. With increased refinement of high resolution numerical models encompassing smaller and smaller spatial scales, the need for non-hydrostatic models is increasing. To evaluate the vertical motion over bathymetric changes in tidal channels and assess the validity of the hydrostatic approximation, we conducted observations using a vessel-based acoustic Doppler current profiler (ADCP). Observations were made along a straight channel 18 times over two scour holes of 25 m deep, separated by 330 m, in and out of an otherwise flat 8 m deep tidal pass leading to the Lake Pontchartrain over a time period of 8 h covering part of the diurnal tidal cycle. Out of the 18 passages over the scour holes, 11 of them showed strong upwelling and downwelling which resulted in the breakdown of hydrostatic condition. The maximum observed vertical velocity was ~ 0.35 m/s, a high value in a tidal channel, and the estimated vertical acceleration reached a high value of 1.76 × 10-2 m/s2. Analysis demonstrated that the barotropic non-hydrostatic acceleration was dominant. The cause of the non-hydrostatic flow was the steep slopes. This demonstrates that in such a system, the bathymetric variation can lead to the breakdown of hydrostatic conditions. Models with hydrostatic restrictions will not be able to correctly capture the dynamics in such a system with significant bathymetric variations particularly during strong tidal currents.