Field and numerical study of entrainment laws for surface mixed layer

A steady deepening of the diurnal mixed layer was observed in a large Japanese freshwater lake Lake Biwa during nocturnal cooling. The observed dissipation rates normalized with surface buoyancy flux and wind stress are in good agreement with previously reported values. The observed time series of the water column was simulated using the Mellor–Yamada second-order turbulence closure scheme. The time series of the observed diurnal mixing layer depth agrees well with the simulated time series. The details of entrainment were investigated using both data sets. Because the deepening was due to both convection and wind stress, the entrainment was separated into two parts. Each part followed the empirical relationships reported from laboratory studies. In order to use both forcings, namely convection and wind stress, we propose a new entrainment diagram taking both into consideration.