We perform a direct numerical simulation (DNS) of interacting Kelvin–Helmholtz instabilities (KHI) that arise at a stratified shear layer where KH billow cores are misaligned or exhibit varying phases along their axes. Significant evidence of these dynamics in early laboratory shear-flow studies by Thorpe ( Geophys. Astrophys. Fluid Dyn. , vol. 34, 1985, pp. 175–199) and Thorpe ( J. Geophys. Res. , vol. 92, 1987, pp. 5231–5248), in observations of KH billow misalignments in tropospheric clouds (Thorpe, Q. J. R. Meteorol. Soc. , vol. 128, 2002, pp. 1529–1542) and in recent direct observations of such events in airglow and polar mesospheric cloud imaging in the upper mesosphere reveals that these dynamics are common. More importantly, the laboratory and mesospheric observations suggest that these dynamics lead to more rapid and more intense instabilities and turbulence than secondary convective instabilities in billow cores and secondary KHI in stratified braids between and around adjacent billows. To date, however, no simulations exploring the dynamics and energetics of interacting KH billows (apart from pairing) have been performed. Our DNS performed for Richardson number $Ri=0.10$ and Reynolds number $Re=5000$ demonstrates that KHI tubes and knots (i) comprise strong and complex vortex interactions accompanying misaligned KH billows, (ii) accelerate the transition to turbulence relative to secondary instabilities of individual KH billows, (iii) yield significantly stronger turbulence than secondary KHI in billow braids and secondary convective instabilities in KHI billow cores and (iv) expand the suite of secondary instabilities previously recognized to contribute to KHI dynamics and breakdown to turbulence in realistic geophysical environments.
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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 = LO/LT between the Thorpe scale LT, derived from the sounding measurements, and the Ozmidov scale LO. It is the determination of LO that enables determination of the dissipation rate of turbulence kinetic energy ε. 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.
more » « less- Award ID(s):
- 1758293
- NSF-PAR ID:
- 10124870
- Publisher / Repository:
- American Meteorological Society
- Date Published:
- Journal Name:
- Journal of Atmospheric and Oceanic Technology
- Volume:
- 36
- Issue:
- 11
- ISSN:
- 0739-0572
- Page Range / eLocation ID:
- p. 2247-2255
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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We perform a direct numerical simulation (DNS) of interacting Kelvin–Helmholtz instabilities (KHI) that arise at a stratified shear layer where KH billow cores are misaligned or exhibit varying phases along their axes. Significant evidence of these dynamics in early laboratory shear-flow studies by Thorpe (Geophys. Astrophys. Fluid Dyn., vol. 34, 1985, pp. 175–199) and Thorpe (J. Geophys. Res., vol. 92, 1987, pp. 5231–5248), in observations of KH billow misalignments in tropospheric clouds (Thorpe, Q. J. R. Meteorol. Soc., vol. 128, 2002, pp. 1529–1542) and in recent direct observations of such events in airglow and polar mesospheric cloud imaging in the upper mesosphere reveals that these dynamics are common. More importantly, the laboratory and mesospheric observations suggest that these dynamics lead to more rapid and more intense instabilities and turbulence than secondary convective instabilities in billow cores and secondary KHI in stratified braids between and around adjacent billows. To date, however, no simulations exploring the dynamics and energetics of interacting KH billows (apart from pairing) have been performed. Our DNS performed for Richardson number Ri = 0.10 and Reynolds number Re = 5000 demonstrates that KHI tubes and knots (i) comprise strong and complex vortex interactions accompanying misaligned KH billows, (ii) accelerate the transition to turbulence relative to secondary instabilities of individual KH billows, (iii) yield significantly stronger turbulence than secondary KHI in billow braids and secondary convective instabilities in KHI billow cores and (iv) expand the suite of secondary instabilities previously recognized to contribute to KHI dynamics and breakdown to turbulence in realistic geophysical environments.more » « less
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Abstract Multiple recent observations in the mesosphere have revealed large-scale Kelvin–Helmholtz instabilities (KHI) exhibiting diverse spatial features and temporal evolutions. The first event reported by Hecht et al. exhibited multiple features resembling those seen to arise in early laboratory shear-flow studies described as “tube” and “knot” (T&K) dynamics by Thorpe. The potential importance of T&K dynamics in the atmosphere, and in the oceans and other stratified and sheared fluids, is due to their accelerated turbulence transitions and elevated energy dissipation rates relative to KHI turbulence transitions occurring in their absence. Motivated by these studies, we survey recent observational evidence of multiscale Kelvin–Helmholtz instabilities throughout the atmosphere, many features of which closely resemble T&K dynamics observed in the laboratory and idealized initial modeling. These efforts will guide further modeling assessing the potential importance of these T&K dynamics in turbulence generation, energy dissipation, and mixing throughout the atmosphere and other fluids. We expect these dynamics to have implications for parameterizing mixing and transport in stratified shear flows in the atmosphere and oceans that have not been considered to date. Companion papers describe results of a multiscale gravity wave direct numerical simulation (DNS) that serendipitously exhibits a number of KHI T&K events and an idealized multiscale DNS of KHI T&K dynamics without gravity wave influences.
Significance Statement Kelvin–Helmholtz instabilities (KHI) occur throughout the atmosphere and induce turbulence and mixing that need to be represented in weather prediction and other models of the atmosphere and oceans. This paper documents recent atmospheric evidence for widespread, more intense, features of KHI dynamics that arise where KH billows are initially discontinuous, misaligned, or varying along their axes. These features initiate strong local vortex interactions described as “tubes” and “knots” in early laboratory experiments, suggested by, but not recognized in, earlier atmospheric and oceanic profiling, and only recently confirmed in newer, high-resolution atmospheric imaging and idealized modeling to date.
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