Reynolds Stress and Turbulent Energy Production in a Tidal Channel

Abstract

A high-frequency (1.2 MHz) acoustic Doppler current profiler (ADCP) moored on the seabed has been used to observe the mean and turbulent flow components in a narrow tidally energetic channel over six tidal cycles at neap and spring tides. The Reynolds stress has been estimated from the difference in variance between the along-beam velocities of opposing acoustic beams with a correction for the sampling scheme and bin size. Shear stress was found to vary regularly with the predominantly semidiurnal tidal flow with the stresses on the spring ebb flow (up to 4.5 Pa) being generally greater than on the flood flow (<2 Pa) when the currents are weaker. The vertical structure approximated to linear stress profiles decreasing from maximum values near the bed to almost zero stresses just below the surface. The variation in the bed stress was well represented by a quadratic drag law, based on the depth-mean current, with an estimated drag coefficient of 2.6 ± 0.2 ? 10?3. The production of turbulent kinetic energy (TKE) followed a regular cycle at the M4 frequency with maximum values exceeding 1 W m?3 near the bed during ebb flow at spring tides and decreasing with height to ?10?3 W m?3 at 2 m below the surface. Production was generally lowest (?10?4 W m?3) at low water slack, which was longer than high water slack, and is marked by a rapid transition from flood to ebb. During peak ebb and flood the vertical distribution of production and the eddy viscosity Nz are reasonably well described by a proposed model based on the law of the wall and a steady balance between the pressure gradient and a uniform shear stress gradient. The stress values have been incorporated into a trial dynamical balance based on the vertically integrated linearized equation of motion along the channel. The pressure gradient term is determined by two tide gauges separated by 5 km in the along-channel direction. The stress variation is in the correct phase to match the combined slope and acceleration term but is only about 60% of the magnitude required for balance. It is suggested that this discrepancy may result from an overestimation of the local pressure gradient, which may vary significantly between the tide gauges due to changes in the channel cross section.