Vertical overturns: A comparison of Thorpe and Ozmidov length scales

Abstract

An objective measure of the length scale of turbulent overturning events, the Thorpe scale, LT, is compared to the Ozmidov scale L0 = (ε/N3)1/2, where N is the buoyancy frequency and ε is the kinetic energy dissipation rate. Far from the surface in wind‐forced mixing layers and in the seasonal thermocline, L0 and LT are of the same order, but near the surface of a mixing layer, L0 is significantly larger than LT. The change in the ratio L0/LT is attributed to a decrease in the gradient Richardson number in the highly energetic zone near the surface. Another length scale, LB = (DCx/N)1/2, where Cx is the Cox number and D is the molecular diffusivity of temperature, is the same order as LT near the surface of a mixing layer as well as in the layer interior and in the seasonal thermocline. It is shown, by using the turbulent kinetic energy budget, that LB/LT is only weakly dependent on the gradient Richardson number as long as the ratio of eddy viscosity to eddy diffusivity is constant. The temperature variance dissipation rate is compared to the product of the buoyancy frequency and the existing temperature variance. Temperature fluctuations are defined as the temperature difference between the observed temperature profile and the Thorpe profile (the temperature profile which would result if an overturning patch gravitationally collapsed without dissipation). It is shown that the major balance in the temperature variance equation is between the rate at which variance is produced and the rate at which it is dissipated and that the rate of change of temperature variance can be an important modification to this balance only if the variance decays in a time much smaller than a buoyancy period.