NDLI: On the nonnormal–nonlinear interaction mechanism between counter-propagating Rossby waves

Content Provider	Springer Nature Link
Author	Tamarin, Talia Heifetz, Eyal Umurhan, Orkan M. Yellin, Ron
Copyright Year	2015
Abstract	The counter-propagating Rossby wave perspective to shear flow instability is extended here to the weakly nonlinear phase. The nonlinear action at a distance interaction mechanism between a pair of waves is identified and separated from the linear one. In the former, the streamwise velocity converges the far-field vorticity anomaly of the opposed wave, whereas in the latter, the cross-stream velocity advects the far-field mean vorticity. A truncated analytical model of two vorticity interfaces shows that higher harmonics generated by the nonlinear interaction act as a forcing on the nonnormal linear dynamics. Furthermore, an intrinsic positive feedback toward small-scale enstrophy results from the fact that higher harmonic pair of waves are generated in anti-phase configuration which is favored for nonnormal growth. Near marginal stability, the waves preserve their structure and numerical simulations of the weakly nonlinear interaction show wave saturation into finite amplitudes, in good agreement both with the fixed point solution of the truncated model, as well as with its corresponding weakly nonlinear Ginzburg–Landau amplitude equation.
Starting Page	205
Ending Page	224
Page Count	20
File Format	PDF
ISSN	09354964
Journal	Theoretical and Computational Fluid Dynamics
Volume Number	29
Issue Number	3
e-ISSN	14322250
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2015-04-18
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Counter-propagating Rossby waves Linear nonnormal and nonlinear interactions Geophysical fluid dynamics Engineering Fluid Dynamics Classical Continuum Physics Computational Science and Engineering
Content Type	Text
Resource Type	Article
Subject	Fluid Flow and Transfer Processes Condensed Matter Physics Computational Mechanics

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