Three‐dimensional evolution of Kelvin‐Helmholtz billows in stratified compressible flow

Palmer, Teresa Lynne; Fritts, David C.; Andreassen, Øyvind; Lie, Ivar

doi:10.1029/94gl01714

Cited by 29 publications

(22 citation statements)

References 29 publications

(13 reference statements)

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“…For sufficiently inviscid flows, these motions undergo a transition to 3D structure similar to that found in breaking gravity waves, with more recent numerical simulations again consistent with the predictions of linear stability theory (Klaassen and Peltier, 1985;Palmer et al, 1994Palmer et al, , 1996Caulfield and Peltier, 1994;Scinocca, 1995;Fritts et al, 1996b; see also Hill et al, 1999, in this issue). Thus, the initial transitions from laminar, quasi-two-dimensional (2D) to 3D flows are now reasonably understood in sheared and stratified fluids.…”

Section: Introductionsupporting

confidence: 66%

The vorticity dynamics of instability and turbulence in a breaking internal gravity wave

2014

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We perform a three-dimensional simulation of a breaking internal gravity wave in a stratified, compressible, and sheared fluid to investigate the vorticity dynamics accompanying the transition from laminar to turbulent flow. Baroclinic sources contribute preferentially to eddy vorticity generation during the initial convective instability of the wave field, yielding counter-rotating vortices aligned with the external shear flow. These vortices enhance the spanwise vorticity of the shear flow via stretching and distort the spanwise vorticity via advective tilting. The resulting vortex sheets undergo a dynamical (Kelvin-Helmholtz) instability which rolls the vortex sheets into tubes which link, in turn, with the original streamwise convective rolls to produce a collection of intertwined vortex loops. Following the formation of discrete vortex loops, the most important interactions are the self-interactions of single vortex tubes and the mutual interactions of adjacent vortex tubes in close proximity. The initial formation of vortex tubes from the roll-up of localized vortex sheets imposes axial vorticity variations having both axisymmetric and azimuthal wavenumber two components. Axisymmetric variations excite axisymmetric twist waves, or Kelvin vortex waves, which propagate along the tubes, drive axial flows, and deplete and fragment the tubes. Azimuthal wavenumber two variations excite m = 2 twist waves on the vortex tubes which amplify and unravel single vortex tubes into pairs of intertwined helical tubes. Other interactions, judged less fundamental to the turbulence cascade, include reconnection among tube fragments, mutual stretching of orthogonal tubes in close proximity, excitation of azimuthal wavenumber one twist waves, and the continual roll-up of weaker vortex sheets throughout the evolution. Collectively, these vortex interactions result in a rapid cascade of energy and enstrophy toward smaller scales of motion.

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Section: Introductionsupporting

confidence: 66%

The vorticity dynamics of instability and turbulence in a breaking internal gravity wave

2014

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“…Laboratory experiments (Miles 1961;Thorpe 1973a;DaSilva et al 1996) have shown that the transition to turbulence is via the development of 2D Kelvin-Helmholtz (KH) billows that become unstable and eventually breakdown into 3D turbulence. Low Reynolds direct numerical simulations have provided additional insight into the evolution of stratified shear layer turbulence; these include the work of Smyth and Moum (2000), Smyth et al (2001), Joseph et al (2004), Palmer et al (1994Palmer et al ( , 1996, and Werne andFritts (1999, 2000).…”

Section: Discussionmentioning

confidence: 99%

Velocity and Temperature Structure Functions in the Upper Troposphere and Lower Stratosphere from High-Resolution Aircraft Measurements

Wróblewski

Coté

Hacker

et al. 2010

Journal of the Atmospheric Sciences

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High-resolution measurements obtained from NOAA ''best'' atmospheric turbulence (BAT) probes mounted on an EGRETT high-altitude research aircraft were used to characterize turbulence in the upper troposphere and lower stratosphere at scales from 2 m to 20 km, focusing on three-dimensional behavior in the sub-kilometer-scale range. Data were analyzed for 129 separate level flight segments representing 41 h of flight time and 12 600 km of wind-relative flight distances. The majority of flights occurred near the tropopause layer of the winter subtropical jet stream in the Southern Hemisphere. Second-order structure functions for velocity and temperature were analyzed for the separate level-flight segments, individually and in various ensembles. A 3D scaling range was observed at scales less than about 100 m, with power-law exponents for the structure functions of the velocity component in the flight direction varying mostly between 0.4 and 0.75 for the separate flight segments, but close to 2 /3 for the ensemble-averaged curves for all levels and for various subensembles. Structure functions in the 3D scaling range were decoupled from those at scales greater than 10 km, with the large-scale structure functions showing less variation than those at smaller scales. Weakly anisotropic behavior was observed in the 3D range, with structure parameters for the lateral and vertical velocities on the same order as those in the flight direction but deviating from the expected isotropic value. Anisotropy was correlated with turbulence intensity, with greater anisotropy associated with weaker turbulence.

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“…A best guess here might be that a needed Re turb allowing secondary instability and turbulence for Ri ~0.20 in Event 2 is Re turb ~500 or greater (also depending on Ri ), implying a maximum ν turb / ν ~5. This is because KHI secondary instabilities are increasingly suppressed as Ri increases and Re decreases ([ Klaassen and Peltier , ; Palmer et al ., , ]; also see Figure ). These estimates seem roughly consistent given that we should expect stronger background turbulence when the underlying GW and instability dynamics are more energetic.…”

Section: Discussionmentioning

confidence: 99%

Quantifying Kelvin‐Helmholtz instability dynamics observed in noctilucent clouds: 2. Modeling and interpretation of observations

et al. 2014

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A companion paper describes high-resolution, ground-based imaging of apparent Kelvin-Helmholtz instabilities (KHI) observed in noctilucent clouds (NLCs) near the polar summer mesopause. Here we employ direct numerical simulations of KHI at Richardson numbers from Ri = 0.05 to 0.20 and relatively high Reynolds numbers to illustrate the dependence of KHI and secondary instabilities on these quantities and interpret and quantify the KHI events described by Baumgarten and Fritts (2014). We conclude that one event triggered by small-scale gravity waves provides clear evidence of strong KHI initiated at Ri~0.05-0.10. Events arising in a more uniform shear environment exhibit KHI and small-scale dynamics that compare reasonably well with modeled KHI initiated at Ri~0.20. Our application of numerical modeling in quantifying KHI dynamics observed in NLCs suggests that characteristics of KHI, and perhaps other small-scale dynamics, that are defined well in NLC displays can be used to quantify the dynamics and spatial scales of such events with high confidence. Specifically, our comparisons of KHI observations and modeling appear to indicate a "turbulent" viscosity~5-40 times the true kinematic viscosity at the NLC altitude. This offers an alternative, or an augmentation, to more traditional radar, lidar, and/or airglow measurements employed for such studies of small-scale dynamics at coarser spatial scales during polar summer.

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Three‐dimensional evolution of Kelvin‐Helmholtz billows in stratified compressible flow

Cited by 29 publications

References 29 publications

The vorticity dynamics of instability and turbulence in a breaking internal gravity wave

The vorticity dynamics of instability and turbulence in a breaking internal gravity wave

Velocity and Temperature Structure Functions in the Upper Troposphere and Lower Stratosphere from High-Resolution Aircraft Measurements

Quantifying Kelvin‐Helmholtz instability dynamics observed in noctilucent clouds: 2. Modeling and interpretation of observations

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