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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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Turbulence Transitions in Kelvin–Helmholtz Instability “Tube” and “Knot” Dynamics: Vorticity, Helicity, and Twist Waves
We address the sources and dynamics of vorticity and helicity and their relations in transitions to turbulence arising due to Kelvin–Helmholtz instability (KHI) “Tube” and “Knot” (T&K) events. Such events are common in the atmosphere and oceans, and initial numerical simulations reveal that T&K dynamics significantly accelerate turbulence transitions and enhance KHI peak and mean energy dissipation rates. KHI T&K events arise where emerging KH billows exhibit varying wavelengths, phases, amplitudes, and/or discontinuities along their axes. As the KH billows intensify, these regions evolve roughly orthogonal billow cores and induced vortex tubes in close proximity. Their mutual advection as they intensify induces large-amplitude Kelvin vortex waves, or “twist waves”, that arise where locally uniform vortices are distorted by axial or radial advection. The twist waves propagate along, and fragment, the vortex tubes and billow cores, thus accounting for the emergence of helicity and the down-scale energy, enstrophy, and helicity fluxes within the turbulence inertial range. We describe the results of four direct numerical simulations (DNS) addressing KHI T&K dynamics in large and idealized small domains. The large-domain vorticity fields reveal the character and diversity of KHI T&K dynamics, the emergence of twist waves at larger and smaller scales, and their driving of turbulence transitions. Two small-domain DNS exhibit idealized KHI T&K events arising from KH billows that are mis-aligned and that exhibit phase variability along their axes. A third examines the interactions of two vortex tubes in close proximity. These reveal that twist waves drive the character and evolutions of the vorticity and helicity fields.
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- PAR ID:
- 10544452
- Publisher / Repository:
- PAR
- Date Published:
- Journal Name:
- Atmosphere
- Volume:
- 14
- Issue:
- 12
- ISSN:
- 2073-4433
- Page Range / eLocation ID:
- 1770
- 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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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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Accepted Manuscript
- Journal Article:
- https://doi.org/10.3390/atmos14121770
