On the use and misuse of the Osborn model: Implications for improved estimates of ocean mixing rates

The Osborn model is widely used for quantification of diapycnal diffusivity K_ρ in in oceanic flows.Two main simplifications are routinely made when estimating mixing rates in stably stratified flows when using the Osborn model. First, a constant value is frequently assumed for the mixing coefficient Γ. Second, dissipation rates of turbulent kinetic energy ε are inferred using either the Thorpe length scales or from microstructure measurements using the isotropy assumption. Data from three independent direct numerical simulations of homogeneous stratified turbulence are used as a testbed to highlight impacts of these assumptions on estimates of K_ρ. A systematic analysis is used to evaluate the inferred diffusivities to exact DNS diffusivities as a function of the turbulent Froude number Fr_t. Use of a constant mixing coefficient Γ results in an under-prediction of K_ρ by up to a factor of 5 for strongly stratified conditions (i.e., at low Fr_t) and an over-prediction of K_ρ by up to two orders of magnitude in weakly stratified conditions (i.e., high Fr_t). The use of inferred dissipation rates ε based on the assumption of isotropy results in an over-prediction of K_ρ by a factor of 2 for low Fr_t and converges on the exact K_ρ for Fr_t > 1. However, the use of kinematic length scales, such as the Thorpe scale, to infer ε result in significant errors. The implications of these findings for improved estimates of ocean mixing rates are illustrated using an example application.