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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: p.f.linden@damtp.cam.ac.uk
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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

Bolster, D. T., Hang, A. & Linden, P. F. 2008 The front speed of intrusions into a continuously stratified medium. J. Fluid Mech. 594, 369–377.CrossRefGoogle Scholar
Cheong, H. B., Kuenen, J. J. P. & Linden, P. F. 2006 The front speed of intrusive gravity currents. J. Fluid Mech. 552, 1–11.Google Scholar
Dalziel, S. B. 2004 Digiflow Manual, 1st edn Dalziel Research Partners.Google Scholar
Dalziel, S. B., Hughes, G. O. & Sutherland, B. R. 2000 Whole-field density measurements by ‘synthetic schlieren’. Exp. Fluids 28, 322–335.Google Scholar
Economidou, M. & Hunt, G. R. 2009 Density stratified environments: the double-tank method. Exp. Fluids 46, 453–466.CrossRefGoogle Scholar
Flynn, M. R. & Linden, P. F. 2006 Intrusive gravity currents. J. Fluid Mech. 568, 193–202.CrossRefGoogle Scholar
Manins, P. C. 1976 Intrusion into a stratified fluid. J. Fluid Mech. 74, 547–560.Google Scholar
Maurer, B. D., Bolster, D. T. & Linden, P. F. 2010 Intrusive gravity currents between two stably stratified fluids. J. Fluid Mech. 647, 53–69.Google Scholar
Maxworthy, T., Leilich, J., Simpson, J. E. & Meiburg, E. H. 2002 The propagation of a gravity current into a linearly stratified fluid. J. Fluid Mech. 453, 371–394.CrossRefGoogle Scholar
McEwan, A. D. & Baines, P. G. 1974 Shear fronts and an experimental stratifed shear flow. J. Fluid Mech. 63, 257–272.CrossRefGoogle Scholar
Munroe, J. R., Voegeli, C., Sutherland, B. R., Birman, V. & Meiburg, E. H. 2009 Intrusive gravity currents from finite length locks in a uniformly stratified fluid. J. Fluid Mech. 635, 245–273.Google Scholar
Oster, G. 1965 Density gradients. Sci. Am. 213, 70–76.CrossRefGoogle Scholar
Rottman, J. W. & Simpson, J. E. 1983 Gravity currents produced by instantaneous release of a heavy fluid in a rectangular channel. J. Fluid Mech. 135, 95–110.CrossRefGoogle Scholar
Shin, J. O., Dalziel, S. B. & Linden, P. F. 2004 Gravity currents produced by lock exchange. J. Fluid Mech. 521, 1–34.Google Scholar
Sutherland, B. R., Flynn, M. R. & Dohan, K. 2004 Internal wave excitation from a collapsing mixed region. Deep-Sea Res. II 51 (25–26), 2889–2904.Google Scholar
Taylor, J. R.2008 Numerical simulations of the stratified oceanic bottom boundary layer. PhD thesis, University of California, San Diego.Google Scholar
Ungarish, M. 2005 Intrusive gravity currents in a stratified ambient: shallow-water theory and numerical results. J. Fluid Mech. 535, 287–323.CrossRefGoogle Scholar
Ungarish, M. 2011 Gravity currents and intrusions of stratified fluids into a stratified ambient. Environ. Fluid Mech. 12 (2), 115–132.Google Scholar
Ungarish, M. & Huppert, H. E. 2002 On gravity currents propagating at the base of a stratified ambient. J. Fluid Mech. 458, 283–301.CrossRefGoogle Scholar
Ungarish, M. & Huppert, H. E. 2006 Energy balances for propagating gravity currents: homogeneous and stratified ambients. J. Fluid Mech. 565, 363–380.Google Scholar
Wu, J. 1969 Mixed region collapse with internal wave generation in a density stratified medium. J. Fluid Mech. 35, 531–544.Google Scholar
Yih, C. S.1947 A study of the characteristics of gravity waves at a liquid interface. Master’s thesis, State University of Iowa.Google Scholar
Yih, C. S. 1965 Dynamics of Nonhomogeneous Fluids. Macmillan.Google Scholar

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