Direct Numerical Simulation Guidance for Thorpe Analysis to Obtain Quantitatively Reliable Turbulence Parameters

Thorpe analysis has been used to study turbulence in the atmosphere and ocean. It is clear that Thorpe analysis applied to individual soundings cannot be expected to give quantitatively reliable measurements of turbulence parameters because of the instantaneous nature of the measurement. A critical aspect of this analysis is the assumption of the linear relationship C = L-O/L-T between the Thorpe scale L-T, derived from the sounding measurements, and the Ozmidov scale L-O. It is the determination of L-O that enables determination of the dissipation rate of turbulence kinetic energy epsilon. Single atmospheric and oceanic soundings cannot indicate either the source of turbulence or the stage of its evolution; different values of C are expected for different turbulence sources and stages of the turbulence evolution and thus cannot be expected to yield quantitatively reliable turbulence parameters from individual profiles. The variation of C with the stage of turbulence evolution is illustrated for direct numerical simulation (DNS) results for gravity wave breaking. Results from a DNS model of multiscale initiation and evolution of turbulence with a Reynolds number Re (which is defined using the vertical wavelength of the primary gravity wave and background buoyancy period as length and time scales, respectively) of 100 000 are sampled as in sounding of the atmosphere and ocean, and various averaging of the sounding results indicates a convergence to a well-defined value of C, indicating that applying Thorpe analysis to atmospheric or oceanic soundings and averaging over a number of profiles gives more reliable turbulence determinations. The same averaging study is also carried out when the DNS-modeled turbulence is dominated by turbulence growing from the initial instabilities, when the turbulence is fully developed, when the modeled turbulence is decaying, and when the turbulence is in a still-later decaying stage. These individual cases converge to well defined values of C, but these values of C show a large variation resulting from the different stages of turbulence evolution. This study gives guidance as to the accuracy of Thorpe analysis of turbulence as a function of the number of profiles being averaged. It also suggests that the values of C in different environments likely depend on the dominant turbulence initiation mechanisms and on the Reynolds number of the environment.