Advective velocity and energy dissipation rate in an oscillatory flow

Characterizing the transport processes at the sediment-water interface along sloping boundaries in lakes and reservoirs is of fundamental interest in lake and reservoir water quality management. The turbulent bottom boundary layer (TBBL) along a slope, induced by the breaking of internal waves in a linearly stratified fluid, was investigated through laboratory measurements. Fast response micro-scale conductivity and temperature probes in conjunction with laser-Doppler velocimetry were used to measure the time series of salinity, temperature, and velocity along a sloping boundary. Turbulent energy spectra were computed from the velocity data using a time-dependent advective velocity and Taylor's hypothesis. The energy spectra were used to estimate the energy dissipation rate at different positions in the TBBL. The advective velocity in this near-zero mean shear flow is based on an integral time scale (T(int)). The integral time scale is related to the average frequency of the spectral energy density of the flow velocity. The energy dissipation rate estimated from the variable advective velocity with an averaging time window equal to the integral time scale (T=T(int)) was 43% higher than the energy dissipation rate estimated from a constant advective velocity. The estimated dissipation rates with T=T(int) were comparable to values obtained by curve-fitting a theoretical Batchelor spectrum for the temperature gradient spectra. This study proposes the integral time scale to be used for the oscillatory flows as (a) a time-averaging window to estimate the advective velocity and associated energy dissipation level, and (b) a normalizing parameter in the energy spectrum.