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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Multi‐Scale Kelvin‐Helmholtz Instability Dynamics Observed by PMC Turbo on 12 July 2018: 2. DNS Modeling of KHI Dynamics and PMC Responses
Kjellstrand et al. (2022),
- Award ID(s):
- 2032678
- NSF-PAR ID:
- 10372834
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Journal of Geophysical Research: Atmospheres
- Volume:
- 127
- Issue:
- 18
- ISSN:
- 2169-897X
- 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 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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Abstract A companion paper by Hecht et al. (2020,
https://doi.org/10.1002/2014JD021833 ) describes high‐resolution observations in the hydroxyl (OH) airglow layer of interactions among adjacent Kelvin‐Helmholtz instabilities (KHI). The interactions in this case were apparently induced by gravity waves propagating nearly orthogonally to the KHI orientations, became strong as Kelvin‐Helmholtz (KH) billows achieved large amplitudes, and included features named “tubes” and “knots” in early laboratory KHI studies. A numerical modeling study approximating the KHI environment and revealing the dynamics of knots and tubes is described here. These features arise where KH billows are misaligned along their axes or where two billows must merge with one. They bear a close resemblance to the observed instability dynamics and suggest that they are likely to occur wherever KHI formation is modulated by variable wind shears, stability, or larger‐scale motions. Small‐scale features typical of those in turbulence develop in association with the formation of the knots and tubes earlier and more rapidly than those accompanying individual billows, supporting an earlier conjecture that tubes and knots are commonly major sources of intense turbulent dissipation accompanying KHI events in the atmosphere. -
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.more » « less
