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Title: Multi-scale dynamics of Kelvin–Helmholtz instabilities. Part 1. Secondary instabilities and the dynamics of tubes and knots
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
Award ID(s):
2128443
NSF-PAR ID:
10348818
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Journal of Fluid Mechanics
Volume:
941
ISSN:
0022-1120
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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  1. 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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  2. Fritts et al. (J. Fluid Mech., vol. xx, 2022, xx) describe a direct numerical simulation of interacting Kelvin–Helmholtz instability (KHI) billows arising due to initial billow cores that exhibit variable phases along their axes. Such KHI exhibit strong ‘tube and knot’ dynamics identified in early laboratory studies by Thorpe ( Geophys. Astrophys. Fluid Dyn. , vol. 34, 1985, pp. 175–199). Thorpe ( Q.J.R. Meteorol. Soc. , vol. 128, 2002, pp. 1529–1542) noted that these dynamics may be prevalent in the atmosphere, and they were recently identified in atmospheric observations at high altitudes. Tube and knot dynamics were found by Fritts et al. ( J. Fluid. Mech. , 2022) to drive stronger and faster turbulence transitions than secondary instabilities of individual KH billows. Results presented here reveal that KHI tube and knot dynamics also yield energy dissipation rates $\sim$ 2–4 times larger as turbulence arises and that remain $\sim$ 2–3 times larger to later stages of the flow evolution, compared with those of secondary convective instabilities (CI) and secondary KHI accompanying KH billows without tube and knot influences. Elevated energy dissipation rates occur due to turbulence transitions by tube and knot dynamics arising on much larger scales than secondary CI and KHI where initial KH billows are misaligned. Tube and knot dynamics also excite large-scale Kelvin ‘twist waves’ that cause vortex tube and billow core fragmentation, more energetic cascades of similar interactions to smaller scales and account for the strongest energy dissipation events accompanying such KH billow evolutions. 
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  3. 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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  4. Abstract

    Kjellstrand et al. (2022),https://10.1029/2021JD036232describes the evolution and dynamics of a strong, large‐scale Kelvin‐Helmholtz instability (KHI) event observed in polar mesospheric clouds (PMCs) on 12 July 2018 by high‐resolution imagers aboard the PMC Turbulence (PMC Turbo) stratospheric long‐duration balloon experiment. The imaging provides evidence of KH billow interactions and instabilities that are strongly influenced by gravity waves at larger scales. Specific features include initially separated regions of KHI, secondary convective and KH instabilities of individual billows, and “tubes” and “knots” that arise where billow cores are mis‐aligned or discontinuous along their axes. This study describes a direct numerical simulation of KH billow interactions in a periodic domain seeded with random initial noise that enables excitation of multiple KH billows exhibiting variable phase structures that capture multiple features of the observed KHI dynamics. Variable KH billow phases along their axes yield initial vortex tubes having diagonal alignments that link adjacent, but mis‐aligned, billow cores. Weak initial vortex tubes and billow cores having nearly orthogonal alignments amplify, interact strongly, and drive intense vortex knots at these sites. These vortex tube and knot (T&K) dynamics excite “twist waves” that unravel the initial vortex tubes, and drive increasingly strong vortex interactions and a cascade of energy and enstrophy to successively smaller scales in the turbulence inertial range. The implications of T&K dynamics are much more rapid and intense breakdown and decay of the KH billows, and significantly enhanced energy dissipation rates, where these interactions occur.

     
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  5. Abstract

    A very high spatial resolution (25 m pixel at 90 km altitude) OH airglow imager was installed at the Andes Lidar Observatory on Cerro Pachón, Chile, in February 2016. This instrument was collocated with a Na wind‐temperature lidar. On 1 March 2016, the lidar data showed that the atmosphere was dynamically unstable before 0100 UT and thus conducive to the formation of Kelvin‐Helmholtz instabilities (KHIs). The imager revealed the presence of a KHI and an apparent atmospheric gravity wave (AGW) propagating approximately perpendicular to the plane of primary KHI motions. The AGW appears to have induced modulations of the shear layer leading to misalignments of the emerging KHI billows. These enabled strong KHI billow interactions, as they achieved large amplitudes and a rapid transition to turbulence thereafter. The interactions manifested themselves as vortex tube and knot features that were earlier identified in laboratory studies, as discussed in Thorpe (1987,https://doi.org/10.1029/JC092iC05p05231; 2002,https://doi.org/10.1002/qj.200212858307) and inferred to be widespread in the atmosphere based on features seen in tropospheric clouds but which have never been identified in previous upper atmospheric observations. This study presents the first high‐resolution airglow imaging observation of these KHI interaction dynamics that drive rapid transitions to turbulence and suggest the potential importance of these dynamics in the mesosphere and at other altitudes. A companion paper (Fritts et al., 2020,https://doi.org/10.1029/2020JD033412) modeling these dynamics confirms that the vortex tubes and knots yield more rapid and significantly enhanced turbulence relative to the internal instabilities of individual KHI billows.

     
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