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On the interaction of an internal wavepacket with its induced mean flow and the role of streaming

Published online by Cambridge University Press:  18 January 2018

Boyu Fan ,
T. Kataoka Open the ORCID record for T. Kataoka [Opens in a new window]  and
T. R. Akylas
Boyu Fan
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
T. Kataoka
Affiliation:
Department of Mechanical Engineering, Graduate School of Engineering, Kobe University, Rokkodai, Nada, Kobe 657-8501, Japan
T. R. Akylas*
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: [email protected]
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Abstract

The coupled nonlinear interaction of three-dimensional gravity–inertia internal wavepackets, in the form of beams with nearly monochromatic profile, with their induced mean flow is discussed. Unlike general three-dimensional wavepackets, such modulated nearly monochromatic beams are not susceptible to modulation instability from their inviscid, purely modulation-induced mean flow. However, streaming – the induced mean flow associated with the production of mean potential vorticity via the combined action of dissipation and nonlinearity – can cause cross-beam bending, transverse broadening and increased along-beam decay of the beam profile, in qualitative agreement with earlier laboratory experiments. For wavepackets with general three-dimensional modulations, by contrast, streaming does arise, but plays a less prominent role in the interaction dynamics.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Internal waves
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 838 , 10 March 2018 , R1
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Copyright
© 2018 Cambridge University Press 

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