We present high resolution (25 mm spatial, 8 Hz temporal) profiles of velocity measured over a shallow tidal flat using pulse-coherent Acoustic Doppler Profilers mounted on surface drifters. The use of Lagrangian measurements mitigated the problem of resolving velocity ambiguities, a problem which often limits the application of high-resolution pulse-coherent profilers. Turbulent dissipation rates were estimated from second-order structure functions of measured velocity. Drifters were advected towards, and subsequently trapped on, a convergent surface front which marked the edge of a freshwater plume. Measured dissipation rates increased as a drifter deployed within the plume approached the front. A drifter then propagated with and along the front as the fresh plume spread across the tidal flats. Near-surface turbulent dissipation measured at the front roughly matched a theoretical mean-shear-cubed relationship, whereas dissipation measured in the stratified plume behind the front was suppressed. After removal of estimates affected by surface waves, near-bed dissipation matched the velocity cubed relationship, although scatter was substantial. Dissipation rates appeared to be enhanced when the drifter propagated across small subtidal channels.