Numerical Modeling of Multiscale Dynamics at a High Reynolds Number: Instabilities, Turbulence, and an Assessment of Ozmidov and Thorpe Scales

Abstract

Abstract A high–Reynolds number direct numerical simulation (DNS) is employed to explore the instability and turbulence dynamics accompanying an idealized multiscale flow that approximates such environments observed throughout the atmosphere. The DNS describes the superposition of a stable gravity wave (GW) and a stable, oscillatory, finescale shear flow that together yield significant wave–wave interactions, GW breaking, Kelvin–Helmholtz instabilities (KHI), fluid intrusions, and turbulence. Larger-scale GW breaking and KHI events account for the strongest turbulence intensities, with intrusions competing with KHI and GW breaking at smaller spatial scales and later times. These dynamics drive a series of sheet-and-layer structures in the velocity, stability, and dissipation fields that persist for many buoyancy periods. Measures of local turbulence intensities include energy dissipation rates, Ozmidov and Thorpe scales (LO and LT, respectively), and a buoyancy Reynolds number sufficient to ensure sustained, strong turbulence events. These exhibit significant variability between and within instability events of different types. The Ozmidov and Thorpe scales for individual events are employed to assess variations of their ratio, C = LO/LT, with time. The value of C is highly variable with event type and time but typically increases with time because significant fluid overturning most often precedes turbulence. The value of C determined for the entire domain varies from 0 prior to instability to approximately 2 or larger at late times, with minima (maxima) prior to (following) significant instability and turbulence events. This appears to preclude an assumption that C is constant in stratified flows, except perhaps as an event average that may depend on event type.