Similarity scaling of turbulence in a temperate lake during fall cooling

Abstract

Abstract Turbulence, quantified as the rate of dissipation of turbulent kinetic energy (ε), was measured with 1400 temperature‐gradient microstructure profiles obtained concurrently with time series measurements of temperature and current profiles, meteorology, and lake‐atmosphere fluxes using eddy covariance in a 4 km 2 temperate lake during fall cooling. Winds varied from near calm to 5 m s −1 but reached 10 m s −1 during three storm events. Near‐surface values of ε were typically on the order of 10 −8 to 10 −7 m 2 s −3 and reached 10 −5 m 2 s −3 during windy periods. Above a depth equal to |L MO |, the Monin‐Obukhov length scale, turbulence was dominated by wind shear and dissipation followed neutral law of the wall scaling augmented by buoyancy flux during cooling. During cooling, ε z = 0.56 /kz + 0.77 J B0 and during heating ε z = 0.6 /kz, where is the water friction velocity computed from wind shear stress, k is von Karman's constant, z is depth, and J B0 is surface buoyancy flux. Below a depth equal to |L MO | during cooling, dissipation was uniform with depth and controlled by buoyancy flux. Departures from similarity scaling enabled identification of additional processes that moderate near‐surface turbulence including mixed layer deepening at the onset of cooling, high‐frequency internal waves when the diurnal thermocline was adjacent to the air‐water interface, and horizontal advection caused by differential cooling. The similarity scaling enables prediction of near‐surface ε as required for estimating the gas transfer coefficient using the surface renewal model and for understanding controls on scalar transport.