Skip to main content Accessibility help
×
Home
Hostname: page-component-59b7f5684b-vh8gq Total loading time: 0.932 Render date: 2022-09-24T18:05:16.468Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "displayNetworkTab": true, "displayNetworkMapGraph": false, "useSa": true } hasContentIssue true

A laboratory study of internal gravity waves incident upon slopes with varying surface roughness

Published online by Cambridge University Press:  20 May 2022

Yu-Hao He
Affiliation:
Center for Complex Flows and Soft Matter Research and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China Department of Physics, The Chinese University of Hong Kong, Hong Kong, PR China
Bu-Ying-Chao Cheng
Affiliation:
Department of Physics, The Chinese University of Hong Kong, Hong Kong, PR China
Ke-Qing Xia*
Affiliation:
Center for Complex Flows and Soft Matter Research and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China Department of Physics, The Chinese University of Hong Kong, Hong Kong, PR China Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Southern University of Science and Technology, Shenzhen 518055, PR China
*
Email address for correspondence: xiakq@sustech.edu.cn

Abstract

We report a laboratory study on the scattering, energy dissipation and mean flow induced by internal gravity waves incident upon slopes with varying surface roughness. The experiment was performed in a rectangular box filled with thermally stratified water. The roughness of the slope surface, $\lambda$, defined as the height of a roughness element over its base width, and the off-criticality $\gamma =(\alpha -\beta )/\beta$, with $\alpha$ and $\beta$ being the angles of the incident wave and the slope, are used as two control parameters. The distribution of energy dissipation in the direction normal to the slope is found to be more uniform in the rough surface cases. Counter-intuitively, both the maximum value in the dissipation profile and the total energy dissipation near the slope are reduced by surface roughness under most circumstances. The measured peak width (the full width at half-maximum of the peaks) of the dissipation profile is found to be broadened significantly in the rough surface cases. We also observed that there exists a non-zero optimal off-criticality ($\gamma =0.17$ for the present measurement resolution) for the normalized average dissipation and total dissipation, which may be due to the strongest wave energy near the slope at this $\gamma$. Unlike surface roughness, the off-criticality has a small effect on the distribution of energy dissipation. Moreover, surface roughness is also found to change the structure of the scattering-induced mean flow and enhance its strength. The present study provides new perspectives on how the surface roughness on topographic features influences energy dissipation.

Type
JFM Papers
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Adrian, R.J. 1991 Particle-imaging techniques for experimental fluid mechanics. Annu. Rev. Fluid Mech. 23 (1), 261304.CrossRefGoogle Scholar
Alford, M.H. 2003 Redistribution of energy available for ocean mixing by long-range propagation of internal waves. Nature 423 (6936), 159162.CrossRefGoogle ScholarPubMed
Alford, M.H., et al. 2011 Energy flux and dissipation in Luzon Strait: two tales of two ridges. J. Phys. Oceanogr. 41 (11), 22112222.CrossRefGoogle Scholar
Alford, M.H. & Zhao, Z. 2007 Global patterns of low-mode internal-wave propagation. Part I: energy and energy flux. J. Phys. Oceanogr. 37 (7), 18291848.CrossRefGoogle Scholar
Arthur, R.S., Koseff, J.R. & Fringer, O.B. 2017 Local versus volume-integrated turbulence and mixing in breaking internal waves on slopes. J. Fluid Mech. 815, 169198.CrossRefGoogle Scholar
Aucan, J., Merrifield, M.A., Luther, D.S. & Flament, P. 2006 Tidal mixing events on the deep flanks of Kaena Ridge, Hawaii. J. Phys. Oceanogr. 36 (6), 12021219.CrossRefGoogle Scholar
Cacchione, D. & Wunsch, C. 1974 Experimental study of internal waves over a slope. J. Fluid Mech. 66 (2), 223239.CrossRefGoogle Scholar
Carter, G.S. & Gregg, M.C. 2006 Persistent near-diurnal internal waves observed above a site of $M_2$ barotropic-to-baroclinic conversion. J. Phys. Oceanogr. 36 (6), 11361147.CrossRefGoogle Scholar
Chalamalla, V.K., Gayen, B., Scotti, A. & Sarkar, S. 2013 Turbulence during the reflection of internal gravity waves at critical and near-critical slopes. J. Fluid Mech. 729, 4768.CrossRefGoogle Scholar
Eriksen, C.C. 1982 Observations of internal wave reflection off sloping bottoms. J. Geophys. Res. 87 (C1), 525538.CrossRefGoogle Scholar
Fortuin, J.M.H 1960 Theory and application of two supplementary methods of constructing density gradient columns. J. Polym. Sci. 44 (144), 505515.CrossRefGoogle Scholar
Gilbert, D. & Garrett, C. 1989 Implications for ocean mixing of internal wave scattering off irregular topography. J. Phys. Oceanogr. 19 (11), 17161729.2.0.CO;2>CrossRefGoogle Scholar
Gostiaux, L., Dauxois, T., Didelle, H., Sommeria, J. & Viboud, S. 2006 Quantitative laboratory observations of internal wave reflection on ascending slopes. Phys. Fluids 18 (5), 056602.CrossRefGoogle Scholar
Grisouard, N. 2010 Réflexions non-linéaires d'ondes de gravité internes. PhD thesis, Université de Grenoble.Google Scholar
Hall, R.A., Huthnance, J.M. & Williams, R.G. 2013 Internal wave reflection on shelf slopes with depth-varying stratification. J. Phys. Oceanogr. 43 (2), 248258.CrossRefGoogle Scholar
Hurley, D.G. & Keady, G 1997 The generation of internal waves by vibrating elliptic cylinders. Part 2. Approximate viscous solution. J. Fluid Mech. 351, 119138.CrossRefGoogle Scholar
Ivey, G.N. & Nokes, R.I. 1989 Vertical mixing due to the breaking of critical internal waves on sloping boundaries. J. Fluid Mech. 204, 479500.CrossRefGoogle Scholar
Ivey, G.N., Winters, K.B. & De Silva, I.P.D. 2000 Turbulent mixing in a sloping benthic boundary layer energized by internal waves. J. Fluid Mech. 418, 5976.CrossRefGoogle Scholar
Johnston, T.M.S., Rudnick, D.L., Carter, G.S., Todd, R.E. & Cole, S.T. 2011 Internal tidal beams and mixing near Monterey Bay. J. Geophys. Res.: Oceans 116, C03017.Google Scholar
Kataoka, T. & Akylas, T.R. 2020 Viscous reflection of internal waves from a slope. Phys. Rev. Fluids 5 (1), 014803.CrossRefGoogle Scholar
Kell, G.S. 1975 Density, thermal expansivity, and compressibility of liquid water from $0\,^{\circ }$ to $150\,^{\circ }{\rm C}$: correlations and tables for atmospheric pressure and saturation reviewed and expressed on 1968 temperature scale. J. Chem. Engng Data 20 (1), 97105.CrossRefGoogle Scholar
Klymak, J.M., Moum, J.N., Nash, J.D., Kunze, E., Girton, J.B., Carter, G.S., Lee, C.M., Sanford, T.B. & Gregg, M.C. 2006 An estimate of tidal energy lost to turbulence at the Hawaiian Ridge. J. Phys. Oceanogr. 36 (6), 11481164.CrossRefGoogle Scholar
Klymak, J.M., Pinkel, R. & Rainville, L. 2008 Direct breaking of the internal tide near topography: Kaena Ridge, Hawaii. J. Phys. Oceanogr. 38 (2), 380399.CrossRefGoogle Scholar
Kunze, E. & Llewellyn Smith, S.G. 2004 The role of small-scale topography in turbulent mixing of the global ocean. Oceanography 17 (1), 5564.CrossRefGoogle Scholar
Kunze, E., MacKay, C., McPhee-Shaw, E.E., Morrice, K., Girton, J.B. & Terker, S.R. 2012 Turbulent mixing and exchange with interior waters on sloping boundaries. J. Phys. Oceanogr. 42 (6), 910927.CrossRefGoogle Scholar
Lamb, K.G. 2014 Internal wave breaking and dissipation mechanisms on the continental slope/shelf. Annu. Rev. Fluid Mech. 46 (1), 231254.CrossRefGoogle Scholar
Ledwell, J.R., Montgomery, E.T., Polzin, K.L., St. Laurent, L.C., Schmitt, R.W. & Toole, J.M. 2000 Evidence for enhanced mixing over rough topography in the Abyssal Ocean. Nature 403 (6766), 179182.CrossRefGoogle ScholarPubMed
Lee, C.M., Sanford, T.B., Kunze, E., Nash, J.D., Merrifield, M.A. & Holloway, P.E. 2006 Internal tides and turbulence along the 3000-m isobath of the Hawaiian Ridge. J. Phys. Oceanogr. 36 (6), 11651183.CrossRefGoogle Scholar
Legg, S 2004 Internal tides generated on a corrugated continental slope. Part I: cross-slope barotropic forcing. J. Phys. Oceanogr. 34 (1), 156173.2.0.CO;2>CrossRefGoogle Scholar
Legg, S. 2014 Scattering of low-mode internal waves at finite isolated topography. J. Phys. Oceanogr. 44 (1), 359383.CrossRefGoogle Scholar
Legg, S. & Adcroft, A. 2003 Internal wave breaking at concave and convex continental slopes. J. Phys. Oceanogr. 33 (11), 22242246.2.0.CO;2>CrossRefGoogle Scholar
Levine, M.D. & Boyd, T.J. 2006 Tidally forced internal waves and overturns observed on a slope: results from home. J. Phys. Oceanogr. 36 (6), 11841201.CrossRefGoogle Scholar
Lighthill, J. 1978 Waves in Fluids. Cambridge University Press.Google Scholar
Longuet-Higgins, M.S. 1969 On the reflexion of wave characteristics from rough surfaces. J. Fluid Mech. 37 (2), 231250.CrossRefGoogle Scholar
Martini, K., Alford, M., Kunze, E., Kelly, S. & Nash, J. 2011 Observations of internal tides on the Oregon continental slope. J. Phys. Oceanogr. 41 (9), 17721794.CrossRefGoogle Scholar
Mied, R.P. & Dugan, J.P. 1976 Internal wave reflexion from a sinusoidally corrugated surface. J. Fluid Mech. 76 (2), 259272.CrossRefGoogle Scholar
Müller, P. & Liu, X.B. 2000 a Scattering of internal waves at finite topography in two dimensions. Part I: theory and case studies. J. Phys. Oceanogr. 30 (3), 532549.2.0.CO;2>CrossRefGoogle Scholar
Müller, P. & Liu, X.B. 2000 b Scattering of internal waves at finite topography in two dimensions. Part II: spectral calculations and boundary mixing. J. Phys. Oceanogr. 30 (3), 550563.2.0.CO;2>CrossRefGoogle Scholar
Munk, W. & Wunsch, C. 1998 Abyssal recipes II: energetics of tidal and wind mixing. Deep-Sea Res. (I) 45 (12), 19772010.CrossRefGoogle Scholar
Nakamura, T. & Awaji, T. 2009 Scattering of internal waves with frequency change over rough topography. J. Phys. Oceanogr. 39 (7), 15741594.CrossRefGoogle Scholar
Nash, J., Alford, M., Kunze, E., Martini, K. & Kelley, S. 2007 Hotspots of deep ocean mixing on the Oregon continental slope. Geophys. Res. Lett. 34 (1), L01605.CrossRefGoogle Scholar
Nash, J., Kunze, E., Toole, J. & Schmitt, R. 2004 Internal tide reflection and turbulent mixing on the continental slope. J. Phys. Oceanogr. 34 (5), 11171134.2.0.CO;2>CrossRefGoogle Scholar
Nazarian, R.H. & Legg, S. 2017 a Internal wave scattering in continental slope canyons, part 1: theory and development of a ray tracing algorithm. Ocean Model. 118, 115.CrossRefGoogle Scholar
Nazarian, R.H. & Legg, S. 2017 b Internal wave scattering in continental slope canyons, part 2: a comparison of ray tracing and numerical simulations. Ocean Model. 118, 1630.CrossRefGoogle Scholar
Nikurashin, M. & Legg, S. 2011 A mechanism for local dissipation of internal tides generated at rough topography. J. Phys. Oceanogr. 41 (2), 378395.CrossRefGoogle Scholar
Pope, S.B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Ray, R. & Mitchum, G. 1996 Surface manifestation of internal tides generated near Hawaii. Geophys. Res. Lett. 23 (16), 21012104.CrossRefGoogle Scholar
Rodenborn, B., Kiefer, D., Zhang, H.P. & Swinney, H.L. 2011 Harmonic generation by reflecting internal waves. Phys. Fluids 23 (2), 026601.CrossRefGoogle Scholar
Sarkar, S. & Scotti, A. 2017 From topographic internal gravity waves to turbulence. Annu. Rev. Fluid Mech. 49, 195220.CrossRefGoogle Scholar
Scotti, A. 2011 Inviscid critical and near-critical reflection of internal waves in the time domain. J. Fluid Mech. 674, 464488.CrossRefGoogle Scholar
St. Laurent, L. & Garrett, C. 2002 The role of internal tides in mixing the deep ocean. J. Phys. Oceanogr. 32 (10), 28822899.2.0.CO;2>CrossRefGoogle Scholar
Sutherland, B.R. 2010 Internal Gravity Waves. Cambridge University Press.CrossRefGoogle Scholar
Sutherland, B.R., Dalziel, S.B., Hughes, G.O. & Linden, P.F. 1999 Visualization and measurement of internal waves by ‘synthetic schlieren’. Part 1. Vertically oscillating cylinder. J. Fluid Mech. 390, 93126.CrossRefGoogle Scholar
Taylor, J.R. 1993 Turbulence and mixing in the boundary layer generated by shoaling internal waves. Dyn. Atmos. Oceans 19 (1–4), 233258.CrossRefGoogle Scholar
Thorpe, S.A. 2001 Internal wave reflection and scatter from sloping rough topography. J. Phys. Oceanogr. 31 (2), 537553.2.0.CO;2>CrossRefGoogle Scholar
Thorpe, S.A. & Haines, A.P. 1987 On the reflection of a train of finite-amplitude internal waves from a uniform slope. J. Fluid Mech. 178, 279302.CrossRefGoogle Scholar
Tokgoz, S., Elsinga, G.E., Delfos, R. & Westerweel, J. 2012 Spatial resolution and dissipation rate estimation in Taylor–Couette flow for tomographic PIV. Exp. Fluids 53 (3), 561583.CrossRefGoogle Scholar
Wunsch, C. & Ferrari, R. 2004 Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech. 36 (1), 281314.CrossRefGoogle Scholar
Xia, K.-Q., Sun, C. & Zhou, S.Q. 2003 Particle image velocimetry measurement of the velocity field in turbulent thermal convection. Phys. Rev. E 68 (6), 066303.CrossRefGoogle ScholarPubMed
Zhang, H.P., King, B. & Swinney, H.L. 2007 Experimental study of internal gravity waves generated by supercritical topography. Phys. Fluids 19 (9), 096602.CrossRefGoogle Scholar
Zhao, Z., Alford, M. & Mackinnon, J. 2010 Long-range propagation of the semi-diurnal internal tide from the Hawaiian Ridge. J. Phys. Oceanogr. 40 (4), 713736.CrossRefGoogle Scholar

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

A laboratory study of internal gravity waves incident upon slopes with varying surface roughness
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

A laboratory study of internal gravity waves incident upon slopes with varying surface roughness
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

A laboratory study of internal gravity waves incident upon slopes with varying surface roughness
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *