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Intrusion-generated waves in a linearly stratified fluid

Published online by Cambridge University Press:  04 July 2014

Benjamin D. Maurer  and
P. F. Linden
Benjamin D. Maurer
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK
P. F. Linden*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK
*
†Email address for correspondence: [email protected]
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Abstract

We present an experimental and numerical study of the upstream internal wavefield in a channel generated by constant density intrusions propagating into a linearly stratified ambient fluid during the initial phase of translation. Using synthetic schlieren imaging and two-dimensional direct numerical simulations, we quantify this wave motion within the ambient stratified fluid ahead of the advancing front. We show that the height of the neutral buoyancy surface in the ambient fluid determines the vertical modal response with the predominant waves being mode 2 for intrusions near the mid-depth of the channel and mode 1 waves being produced by intrusions nearer the top or bottom of the domain. All higher vertical modes travel slower than the intrusion and so do not appear upstream ahead of the intrusion front. We find the energy flux into this upstream wavefield to be approximately constant, and to be between 10 and 30 % of the rate of available potential energy transfer into the flow.

JFM classification

Geophysical and Geological Flows: Gravity currents Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Stratified flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 752 , 10 August 2014 , pp. 282 - 295
Copyright
© 2014 Cambridge University Press 

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References

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Maurer and Linden supplementary movie

A movie of a laboratory experiment of an intrusion at hN = 0.1H. In the upper frame, the intrusions is imaged via the squared buoyancy frequency perturbation field ΔN2 < -0.9N, and the front position is demarcated with a vertical white line. In the lower frame, the mode strength of the horizontal perturbation velocity component û' is shown for individual modes. Though the data is noisy, a strong mode-1 signal is evident, decreasing monotonically upstream of the front.

Download Maurer and Linden supplementary movie(Video)
Video 31 MB

Maurer and Linden supplementary movie

A movie of a laboratory experiment of an intrusion at hN = 0.3H. In the upper frame, the intrusions is imaged via the squared buoyancy frequency perturbation field ΔN2 < -0.9N, and the front position is demarcated with a vertical white line. In the lower frame, the mode strength of the horizontal perturbation velocity component û' is shown for individual modes. Though the data is noisy, both mode-1 and mode-2 signals are evident, decreasing monotonically upstream of the front.

Download Maurer and Linden supplementary movie(Video)
Video 30.3 MB

Maurer and Linden supplementary movie

A movie of a laboratory experiment of an intrusion at hN = 0.5H. In the upper frame, the intrusions is imaged via the squared buoyancy frequency perturbation field ΔN2 < -0.9N, and the front position is demarcated with a vertical white line. In the lower frame, the mode strength of the horizontal perturbation velocity component û' is shown for individual modes. Though the data is noisy, a stronger mode-2 signal is evident, decreasing monotonically upstream of the front.

Download Maurer and Linden supplementary movie(Video)
Video 30.3 MB

Maurer and Linden supplementary movie

A movie of a numerical simulation of an intrusion at hN = 0.1H.In the upper frame, the intrusions is imaged as a passive tracer concentration > 0.95, and the front position is demarcated with a vertical white line. In the lower frame, the mode strength of the horizontal perturbation velocity component û' is shown for individual modes. A strong mode-1 signal is evident, decreasing monotonically upstream of the front.

Download Maurer and Linden supplementary movie(Video)
Video 36 MB

Maurer and Linden supplementary movie

A movie of a numerical simulation of an intrusion at hN = 0.3H. In the upper frame, the intrusions is imaged as a passive tracer concentration > 0.95, and the front position is demarcated with a vertical white line. In the lower frame, the mode strength of the horizontal perturbation velocity component û' is shown for individual modes. Both mode-1 and mode-2 signals are evident, decreasing monotonically upstream of the front.

Download Maurer and Linden supplementary movie(Video)
Video 36 MB

Maurer and Linden supplementary movie

A movie of a numerical simulation of an intrusion at hN = 0.5H. In the upper frame, the intrusions is imaged as a passive tracer concentration > 0.95, and the front position is demarcated with a vertical white line. In the lower frame, the mode strength of the horizontal perturbation velocity component û' is shown for individual modes. A strong mode-2 signal is evident, decreasing monotonically upstream of the front.

Download Maurer and Linden supplementary movie(Video)
Video 36 MB