Acoustic backscatter from bubbles as a (quasi)passive tracer of turbulent mixing in high-flow tidal channels

In high-flow tidal channels, the water column tends to be well-mixed vertically due to the high levels of turbulence. Under favorable circumstances, such as those in which wind waves incident at the channel entrance from the adjoining open ocean or large embayment are opposed by the tidal flow, the waves steepen and break as they propagate upstream, resulting in bubble injection at the sea surface. These bubbles are then mixed downward by the tidally generated turbulence, resulting in pronounced, surface-connected, downward-propagating plumes of high backscatter in records from bottom-mounted upward-looking acoustic Doppler current profilers, typically operating at 100s of kHz. Letting the backscatter amplitude represent a pseudo-concentration, C, we demonstrate that the vertical turbulent diffusivity, K, can be estimated from the vertical turbulent flux i < c′w′> along the axis of the vertical beam, and the mean vertical gradient, dC/dz. Intriguingly, and despite the fact that bubbles are positively buoyant, the resulting estimates of K are very close to the values of momentum diffusivity required to obtain good agreement between the observed tidal velocities and a data-validated numerical tidal circulation model for the particular channel in question