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A companion paper by Fritts et al. reviews evidence for Kelvin–Helmholtz instability (KHI) “tube” and “knot” (T&K) dynamics that appear to be widespread throughout the atmosphere. Here we describe the results of an idealized direct numerical simulation of multiscale gravity wave dynamics that reveals multiple larger- and smaller-scale KHI T&K events. The results enable assessments of the environments in which these dynamics arise and their competition with concurrent gravity wave breaking in driving turbulence and energy dissipation. A larger-scale event is diagnosed in detail and reveals diverse and intense T&K dynamics driving more intense turbulence than occurs due to gravity wave breaking in the same environment. Smaller-scale events reveal that KHI T&K dynamics readily extend to weaker, smaller-scale, and increasingly viscous shear flows. Our results suggest that KHI T&K dynamics should be widespread, perhaps ubiquitous, wherever superposed gravity waves induce intensifying shear layers, because such layers are virtually always present. A second companion paper demonstrates that KHI T&K dynamics exhibit elevated turbulence generation and energy dissipation rates extending to smaller Reynolds numbers for relevant KHI scales wherever they arise. These dynamics are suggested to be significant sources of turbulence and mixing throughout the atmosphere that are currently ignored or underrepresented in turbulence parameterizations in regional and global models.

Atmospheric observations reveal that Kelvin–Helmholtz instabilities (KHI) often exhibit complex interactions described as “tube” and “knot” (T&K) dynamics in the presence of larger-scale gravity waves (GWs). These dynamics may prove to make significant contributions to energy dissipation and mixing that are not presently accounted for in large-scale modeling and weather prediction. We explore here the occurrence of KHI T&K dynamics in an idealized model that describes their behavior and character arising at larger and smaller scales due to superposed, large-amplitude GWs. The results reveal that KHI T&K dynamics arise at larger and smaller scales, and that their turbulence intensities can be comparable to those of the GWs.

 

We present modeling results of tube and knot (T&K) dynamics accompanying thermospheric Kelvin Helmholtz Instabilities (KHI) in an event captured by the 2018 Super Soaker campaign (R. L. Mesquita et al., 2020,https://doi.org/10.1029/2020JA027972). Chemical tracers released by a rocketsonde on 26 January 2018 showed coherent KHI in the lower thermosphere that rapidly deteriorated within 45–90 s. Using wind and temperature data from the event, we conducted high resolution direct numerical simulations (DNS) employing both wide and narrow spanwise domains to facilitate (wide domain case) and prohibit (narrow domain case) the axial deformation of KH billows that allows tubes and knots to form. KHI T&K dynamics are shown to produce accelerated instability evolution consistent with the observations, achieving peak dissipation rates nearly two times larger and 1.8 buoyancy periods faster than axially uniform KHI generated by the same initial conditions. Rapidly evolving twist waves are revealed to drive the transition to turbulence; their evolution precludes the formation of secondary convective instabilities and secondary KHI seen to dominate the turbulence evolution in artificially constrained laboratory and simulation environments. T&K dynamics extract more kinetic energy from the background environment and yield greater irreversible energy exchange and entropy production, yet they do so with weaker mixing efficiency due to greater energy dissipation. The results suggest that enhanced mixing from thermospheric KHI T&K events could account for the discrepancy between modeled and observed mixing in the lower thermosphere (Garcia et al., 2014,https://doi.org/10.1002/2013JD021208; Liu, 2021,https://doi.org/10.1029/2020GL091474) and merits further study.

 

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. 

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. 

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. 

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.

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.

 

Abstract A companion paper by Lund et al. (2020) employed a compressible model to describe the evolution of mountain waves arising due to increasing flow with time over the Southern Andes, their breaking, secondary gravity waves and acoustic waves arising from these dynamics, and their local responses. This paper describes the mountain wave, secondary gravity wave, and acoustic wave vertical fluxes of horizontal momentum, and the local and large-scale three-dimensional responses to gravity breaking and wave/mean-flow interactions accompanying this event. Mountain wave and secondary gravity wave momentum fluxes and deposition vary strongly in space and time due to variable large-scale winds and spatially-localized mountain wave and secondary gravity wave responses. Mountain wave instabilities accompanying breaking induce strong, local, largely-zonal forcing. Secondary gravity waves arising from mountain wave breaking also interact strongly with large-scale winds at altitudes above ~80km. Together, these mountain wave and secondary gravity wave interactions reveal systematic gravity-wave/mean-flow interactions having implications for both mean and tidal forcing and feedbacks. Acoustic waves likewise achieve large momentum fluxes, but typically imply significant responses only at much higher altitudes.