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Teresa L. Palmer
,
David C. Fritts
, and
Øyvind Andreassen

Abstract

A companion paper by Fritts et al. employed a nonlinear, compressible, spectral collocation code to examine the effects of secondary instability on the evolution of Kelvin–Helmholtz billows in stratified shear flows at intermediate Reynolds numbers. The purpose of this paper is to examine the structure, sources, evolution, and energetics of the secondary instability itself. It is found that this instability comprises counterrotating vortices aligned largely along the two-dimensional velocity field (with spanwise wavenumber), with initial instability occurring in the stably stratified braids between adjacent billows and thereafter in the billow cores as maximum KH amplitudes are achieved. The more energetic secondary instabilities are confined to the billows, where the major sources of instability energy are buoyancy and shear due to negative stratification and the solenoidal generation of negative spanwise vorticity within the billow cores. Strain also represents a significant source of streamwise eddy vorticity, with the dominant contribution due to vertical shear within the KH billow acting on vertical eddy vorticity. The authors find that the instability contributes significant fluxes of heat and momentum that act to stabilize the billow structures and advance the restratification at later times. The instability structure within the billows is closely related to that observed in breaking gravity waves and can be viewed as arising due to convective and inertials instability of the evolving two-dimensional flow.

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David C. Fritts
,
Teresa L. Palmer
,
Øyvind Andreassen
, and
Ivar Lie

Abstract

The authors use a nonlinear, compressible, spectral collocation code to examine the evolution and secondary instability of Kelvin–Helmholtz billows in stratified shear flows at intermediate Reynolds numbers. Two-dimensional results exhibit structure consistent with previous numerical studies and suggest dissipation via diffusive transports within the billow cores. Results obtained permitting three-dimensional structures show, in contrast, that secondary instability results in a series of counter-rotating vortices that occupy the outer portions of the billow structures, are oriented in the plane of two-dimensional motion, largely along the two-dimensional velocity field, and contribute substantially to mixing and homogenization of the billow cores at later times. Examination of the flow structure leading to secondary instability also suggests an alternative explanation of the nature of this instability in stratified flows to that offered previously. Comparison of the two-dimensional and spanwise-averaged three-dimensional results reveals that secondary instability contributes large fluxes of momentum and potential temperature, and advances somewhat the restoration of a stratified mean state, but also suggests that secondary instability does not strongly affect the initial two-dimensional evolution for the parameters considered. Though representative of Kelvin–Helmholtz evolutions only under a limited range of flow conditions, our results imply an important role for secondary instability and an inability of two-dimensional studies to describe the dynamics, transports, and mixing in cases where it occurs. The structure, evolution, sources, and energetics of the secondary instability observed in our simulations are the subject of a companion paper by Palmer et al.

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David C. Fritts
,
James F. Garten
, and
Øyvind Andreassen

Abstract

In a previous study the authors used a nonlinear, compressible, spectral collocation numerical model to examine the evolution of a breaking gravity wave in two and three dimensions. The present paper extends that effort to examine the implications of higher resolution and smaller dissipation for wave and instability evolutions, transports, and energetics in shear flows aligned with and having a component transverse to the direction of wave propagation. A component of mean shear transverse to the direction of wave propagation (denoted as a skew shear) results in the alignment of instability structures with the background shear flow rather than in the direction of wave propagation. This alignment leads to asymmetric instability structures and less rapid instability growth relative to the parallel shear flow. Slower instability evolution due to a skew shear has several implications for wave breakdown, including a delayed state of maximum instability, a larger wave amplitude prior to and throughout wave breaking, larger wave fluxes of energy and momentum, and more vigorous instability and small-scale energetics. The spectral evolutions of the motion fields exhibit the development of isotropy and the approach toward a spectrum having inertial character at smaller scales of motion due to instability within the breaking wave.

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J. K. Andersen
,
Liss M. Andreassen
,
Emily H. Baker
,
Thomas J. Ballinger
,
Logan T. Berner
,
Germar H. Bernhard
,
Uma S. Bhatt
,
Jarle W. Bjerke
,
Jason E. Box
,
L. Britt
,
R. Brown
,
David Burgess
,
John Cappelen
,
Hanne H. Christiansen
,
B. Decharme
,
C. Derksen
,
D. S. Drozdov
,
Howard E. Epstein
,
L. M. Farquharson
,
Sinead L. Farrell
,
Robert S. Fausto
,
Xavier Fettweis
,
Vitali E. Fioletov
,
Bruce C. Forbes
,
Gerald V. Frost
,
Sebastian Gerland
,
Scott J. Goetz
,
Jens-Uwe Grooß
,
Edward Hanna
,
Inger Hanssen-Bauer
,
Stefan Hendricks
,
Iolanda Ialongo
,
K. Isaksen
,
Bjørn Johnsen
,
L. Kaleschke
,
A. L. Kholodov
,
Seong-Joong Kim
,
Jack Kohler
,
Zachary Labe
,
Carol Ladd
,
Kaisa Lakkala
,
Mark J. Lara
,
Bryant Loomis
,
Bartłomiej Luks
,
K. Luojus
,
Matthew J. Macander
,
G. V. Malkova
,
Kenneth D. Mankoff
,
Gloria L. Manney
,
J. M. Marsh
,
Walt Meier
,
Twila A. Moon
,
Thomas Mote
,
L. Mudryk
,
F. J. Mueter
,
Rolf Müller
,
K. E. Nyland
,
Shad O’Neel
,
James E. Overland
,
Don Perovich
,
Gareth K. Phoenix
,
Martha K. Raynolds
,
C. H. Reijmer
,
Robert Ricker
,
Vladimir E. Romanovsky
,
E. A. G. Schuur
,
Martin Sharp
,
Nikolai I. Shiklomanov
,
C. J. P. P. Smeets
,
Sharon L. Smith
,
Dimitri A. Streletskiy
,
Marco Tedesco
,
Richard L. Thoman
,
J. T. Thorson
,
X. Tian-Kunze
,
Mary-Louise Timmermans
,
Hans Tømmervik
,
Mark Tschudi
,
Dirk van As
,
R. S. W. van de Wal
,
Donald A. Walker
,
John E. Walsh
,
Muyin Wang
,
Melinda Webster
,
Øyvind Winton
,
Gabriel J. Wolken
,
K. Wood
,
Bert Wouters
, and
S. Zador
Free access
Richard L. Thoman
,
Matthew L. Druckenmiller
,
Twila A. Moon
,
L. M. Andreassen
,
E. Baker
,
Thomas J. Ballinger
,
Logan T. Berner
,
Germar H. Bernhard
,
Uma S. Bhatt
,
Jarle W. Bjerke
,
L.N. Boisvert
,
Jason E. Box
,
B. Brettschneider
,
D. Burgess
,
Amy H. Butler
,
John Cappelen
,
Hanne H. Christiansen
,
B. Decharme
,
C. Derksen
,
Dmitry Divine
,
D. S. Drozdov
,
Chereque A. Elias
,
Howard E. Epstein
,
Sinead L. Farrell
,
Robert S. Fausto
,
Xavier Fettweis
,
Vitali E. Fioletov
,
Bruce C. Forbes
,
Gerald V. Frost
,
Sebastian Gerland
,
Scott J. Goetz
,
Jens-Uwe Grooß
,
Christian Haas
,
Edward Hanna
,
-Bauer Inger Hanssen
,
M. M. P. D. Heijmans
,
Stefan Hendricks
,
Iolanda Ialongo
,
K. Isaksen
,
C. D. Jensen
,
Bjørn Johnsen
,
L. Kaleschke
,
A. L. Kholodov
,
Seong-Joong Kim
,
J. Kohler
,
Niels J. Korsgaard
,
Zachary Labe
,
Kaisa Lakkala
,
Mark J. Lara
,
Simon H. Lee
,
Bryant Loomis
,
B. Luks
,
K. Luojus
,
Matthew J. Macander
,
R. Í Magnússon
,
G. V. Malkova
,
Kenneth D. Mankoff
,
Gloria L. Manney
,
Walter N. Meier
,
Thomas Mote
,
Lawrence Mudryk
,
Rolf Müller
,
K. E. Nyland
,
James E. Overland
,
F. Pálsson
,
T. Park
,
C. L. Parker
,
Don Perovich
,
Alek Petty
,
Gareth K. Phoenix
,
J. E. Pinzon
,
Robert Ricker
,
Vladimir E. Romanovsky
,
S. P. Serbin
,
G. Sheffield
,
Nikolai I. Shiklomanov
,
Sharon L. Smith
,
K. M. Stafford
,
A. Steer
,
Dimitri A. Streletskiy
,
Tove Svendby
,
Marco Tedesco
,
L. Thomson
,
T. Thorsteinsson
,
X. Tian-Kunze
,
Mary-Louise Timmermans
,
Hans Tømmervik
,
Mark Tschudi
,
C. J. Tucker
,
Donald A. Walker
,
John E. Walsh
,
Muyin Wang
,
Melinda Webster
,
A. Wehrlé
,
Øyvind Winton
,
G. Wolken
,
K. Wood
,
B. Wouters
, and
D. Yang
Free access