Lagrangian Spectra and Diapycnal Mixing in Stratified Flow

Abstract

Taylor's single-particle dispersion model is revisited and applied to unstratified and density stratified flows using observationally based and theoretical models of the Lagrangian velocity and density spectra, which are compared with existing parameterizations of diapycnal diffusion in these flows. For unstratified homogeneous turbulence, the vertical particle dispersion coefficient Kz computed from model Lagrangian velocity spectra agrees well with contemporary estimates of the diffusivity. For internal waves with no mixing, a large apparent dispersion occurs for times somewhat larger than the inverse buoyancy frequency 1/N. No dispersion occurs at long times. For stratified homogeneous turbulence with energy dissipation rate ε, Kz = ΓdεN?2, the same form as Osborn, but with Γd of about 2.5. This high value is attributed to apparent dispersion due to internal waves and an improper form of the model spectra that allows internal waves to exist at low frequencies. A diapycnal dispersion coefficient K? is formulated based on a white spectrum of Lagrangian density change D?/Dt with level ???, where ? is the rate of dissipation of density variance. This yields K? = (π/2)???/??2z, where ?z is the mean vertical density gradient. This has the same form as the Osborn and Cox model for diapycnal diffusivity if ?? = 1/π.