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Abstract A companion paper by Fritts et al. reviews extensive evidence for Kelvin–Helmholtz instability (KHI) “tube” and “knot” (T&K) dynamics at multiple altitudes in the atmosphere and in the oceans that reveal these dynamics to be widespread. A second companion paper by Fritts and Wang reveals KHI T&K events at larger and smaller scales to arise on multiple highly stratified sheets in a direct numerical simulation (DNS) of idealized, multiscale gravity wave–fine structure interactions. These studies reveal the diverse environments in which KHI T&K dynamics arise and suggest their potentially ubiquitous occurrence throughout the atmosphere and oceans. This paper describes a DNS of multiple KHI evolutions in wide and narrow domains enabling and excluding T&K dynamics. These DNSs employ common initial conditions but are performed for decreasing Reynolds numbers (Re) to explore whether T&K dynamics enable enhanced KHI-induced turbulence where it would be weaker or not otherwise occur. The major results are that KHI T&K dynamics extend elevated turbulence intensities and energy dissipation ratesεto smaller Re. We expect these results to have important implications for improving parameterizations of KHI-induced turbulence in the atmosphere and oceans. Significance StatementTurbulence due to small-scale shear flows plays important roles in the structure and variability of the atmosphere and oceans extending to large spatial and temporal scales. New modeling reveals that enhanced turbulence accompanies Kelvin–Helmholtz instabilities (KHIs) that arise on unstable shear layers and exhibit what were initially described as “tubes” and “knots” (T&K) when they were first observed in early laboratory experiments. We perform new modeling to explore two further aspects of these dynamics: 1) can KHI T&K dynamics increase turbulence intensities compared to KHI without T&K dynamics for the same initial fields and 2) can KHI T&K dynamics enable elevated turbulence and energy dissipation extending to more viscous flows? We show here that the answer to both questions is yes. 

Abstract 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. Significance StatementAtmospheric 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. 

Abstract Gravity waves (GWs) and their associated multi‐scale dynamics are known to play fundamental roles in energy and momentum transport and deposition processes throughout the atmosphere. We describe an initial machine learning model—the Compressible Atmosphere Model Network (CAM‐Net). CAM‐Net is trained on high‐resolution simulations by the state‐of‐the‐art model Complex Geometry Compressible Atmosphere Model (CGCAM). Two initial applications to a Kelvin‐Helmholtz instability source and mountain wave generation, propagation, breaking, and Secondary GW (SGW) generation in two wind environments are described here. Results show that CAM‐Net can capture the key 2‐D dynamics modeled by CGCAM with high precision. Spectral characteristics of primary and SGWs estimated by CAM‐Net agree well with those from CGCAM. Our results show that CAM‐Net can achieve a several order‐of‐magnitude acceleration relative to CGCAM without sacrificing accuracy and suggests a potential for machine learning to enable efficient and accurate descriptions of primary and secondary GWs in global atmospheric models. 

Abstract 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. 

Abstract Fritts, Wang, Lund, and Thorpe (2022,https://doi.org/10.1017/jfm.2021.1085) and Fritts, Wang, Thorpe, and Lund (2022,https://doi.org/10.1017/jfm.2021.1086) described a 3‐dimensional direct numerical simulation of interacting Kelvin‐Helmholtz instability (KHI) billows and resulting tube and knot (T&K) dynamics that arise at a stratified shear layer defined by an idealized, large‐amplitude inertia‐gravity wave. Using similar initial conditions, we performed a high‐resolution compressible simulation to explore the emission of GWs by these dynamics. The simulation confirms that such shear can induce strong KHI with large horizontal scales and billow depths that readily emit GWs having high frequencies, small horizontal wavelengths, and large vertical group velocities. The density‐weighted amplitudes of GWs reveal “fishbone” structures in vertical cross sections above and below the KHI source. Our results reveal that KHI, and their associated T&K dynamics, may be an important additional source of high‐frequency, small‐scale GWs at higher altitudes. 

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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. 

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.