Shear Instabilities of Tidal Currents in Inlets and Estuaries

Tidal currents in narrow inlets and channels can have horizontal velocity gradients that produce instabilities in the flow (so-called shear waves) that can lead to the spinoff of large eddies. It is expected that shear instabilities will cause the tidal currents in narrow inlets and estuaries to meander along the channels varying in both time and space. The resulting vortices, or eddies, may impact navigation, transport of organic or inorganic matter (e.g. larvae, oil spills, etc.), and cause mixing of momentum in coastal estuaries. We analytically solved for linear shear instabilities of tidal currents in narrow estuarine channels following Bowen and Holman (1989), differing in three conditions here: (1) the current is bounded by structure or land on both sides of the channel (or cross-shore direction) (2) the cross-channel is split into regions and there is an additional region in this system leading to two cross-channel gradients in the along-channel velocity (3) there is an additional extremum, leading to the possibility of unstable, or growing, shear wave solutions on either side of the tidal current. The characteristic frequencies, growth rates, and wavelengths of the fastest growing shear wave modes are determined as a function of the cross-channel structure and speed of the along-channel tidal current in this theoretical analysis.