Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T09:23:46.907Z Has data issue: false hasContentIssue false
  • English
  • Français

Observation of surface wave patterns modified by sub-surface shear currents

Published online by Cambridge University Press:  25 June 2019

Benjamin K. Smeltzer Open the ORCID record for Benjamin K. Smeltzer [Opens in a new window] ,
Eirik Æsøy  and
Simen Å. Ellingsen Open the ORCID record for Simen Å. Ellingsen [Opens in a new window]
Benjamin K. Smeltzer
Affiliation:
Department of Energy and Process Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
Eirik Æsøy
Affiliation:
Department of Energy and Process Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
Simen Å. Ellingsen*
Affiliation:
Department of Energy and Process Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
*
†Email address for correspondence: simen.a.ellingsen@ntnu.no
Get access Rights & Permissions [Opens in a new window]

Abstract

We report experimental observations of two canonical surface wave patterns – ship waves and ring waves – skewed by sub-surface shear, thus confirming effects predicted by recent theory. Observed ring waves on a still surface with sub-surface shear current are strikingly asymmetric, an effect of strongly anisotropic wave dispersion. Ship waves for motion across a sub-surface current on a still surface exhibit striking asymmetry about the ship’s line of motion, and large differences in transverse wavelength for upstream versus downstream motion are demonstrated, all of which is in good agreement with theoretical predictions. Neither of these phenomena can occur on a depth-uniform current. A quantitative comparison of measured versus predicted average phase shift for a ring wave is grossly mispredicted by no-shear theory, but in good agreement with predictions for the measured shear current. A clear difference in wave frequency within the ring wave packet is observed in the upstream versus downstream direction for all shear flows, while wave dispersive behaviour is identical to that for quiescent water for propagation normal to the shear current, as expected. Peak values of the measured two-dimensional Fourier spectrum for ship waves are shown to agree well with the predicted criterion of stationary ship waves, with the exception of some cases where results are imperfect due to the limited wavenumber resolution, transient effects and/or experimental noise. Experiments were performed on controlled shear currents created in two different ways, with a curved mesh and beneath a blocked stagnant-surface flow. Velocity profiles were measured with particle image velocimetry, and surface waves with a synthetic schlieren method. Our observations lend strong empirical support to recent predictions that wave forces on vessels and structures can be greatly affected by shear in estuarine and tidal waters.

JFM classification

Geophysical and Geological Flows: Coastal engineering Waves/Free-surface Flows: Shear waves Waves/Free-surface Flows: Surface gravity waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 873 , 25 August 2019 , pp. 508 - 530
Check for updates
Copyright
© 2019 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

Akselsen, A. H. & Ellingsen, S. Å. 2018 Weakly non-linear transient waves on a shear current: ring waves and skewed Langmuir rolls. J. Fluid Mech. 863, 114–149.Google Scholar
Alpers, W. & Hühnerfuss, H. 1989 The damping of ocean waves by surface films: a new look at an old problem. J. Geophys. Res. 94, 6251–6265.Google Scholar
Belcher, S. E., Grant, A. L. M., Hanley, K. E., Fox-Kemper, B., Van Roekel, L., Sullivan, P. P., Large, W. G., Brown, A., Hines, A., Calvert, D. et al. 2012 A global perspective on Langmuir turbulence in the ocean surface boundary layer. Geophys. Res. Lett. 39, L18605.Google Scholar
Campana, J., Terrill, E. J. & de Paolo, T. 2016 The development of an inversion technique to extract vertical current profiles from x-band radar observations. J. Atmos. Ocean. Technol. 33, 2015–2028.Google Scholar
Cauchy, A.-L. 1827 Théorie de la propagation des ondes à la surface d’un fluide pesant d’une profondeur indéfinie. Mém. Présentés par Divers Savants Acad. Sci. Inst. Fr. 1, 3–123.Google Scholar
Caplier, C., Rousseaux, G., Calluaud, D. & Laurent, D. 2015 The effects of river counter-currents on ship wakes: an experimental approach. In Proceedings of International Conference SHF and AICPN: Hydrodynamics and Simulation Applied to Inland Waterway and Port Approaches. SHF (Société Hydrotechnique de France).Google Scholar
Dalrymple, R. A.1973 Water wave models and wave forces with shear currents. Tech. Rep. 20. Coastal and Oceanographic Engineering Laboratory, Uni. Florida.Google Scholar
Darmon, A., Benzaquen, M. & Raphaël, E. 2014 Kelvin wake pattern at large Froude numbers. J. Fluid Mech. 738, R3.Google Scholar
Dunn, W. & Tavoularis, S. 2007 The use of curved screens for generating uniform shear at low Reynolds numbers. Exp. Fluids 42, 281–290.Google Scholar
Elias, E. P. L., Gelfenbaum, G. & van der Westhuysen, A. J. 2012 Validation of a coupled wave-flow model in a high-energy setting: the mouth of the Columbia River. J. Geophys. Res. 117, C09011.Google Scholar
Ellingsen, S. Å. 2014a Ship waves in the presence of uniform vorticity. J. Fluid Mech. 742, R2.Google Scholar
Ellingsen, S. Å. 2014b Initial surface disturbance on a shear current: the Cauchy–Poisson problem with a twist. Phys. Fluids 26, 082104.Google Scholar
Ellingsen, S. Å. 2016 Oblique waves on a vertically sheared current are rotational. Eur. J. Mech (B/Fluids) 56, 156–160.Google Scholar
Ellingsen, S. Å. & Li, Y. 2017 Approximate dispersion relations for waves on arbitrary shear flows. J. Geophys. Res.: Oceans 122, 9889–9905.Google Scholar
Faltinsen, O. M. 2005 Hydrodynamics of High-Speed Marine Vehicles. Cambridge University Press.Google Scholar
Fienup, J. R. 1982 Phase retrieval algorithms: a comparison. Appl. Opt. 21, 2758–2769.Google Scholar
Harper, J. F. & Dixon, J. N. 1974 The leading edge of a surface film on contaminated flowing water. In Proceedings of 5th Australasian Conference on Hydraulics and Fluid Mechanics, pp. 499–505. University of Canterbury.Google Scholar
Johnson, R. S. 1990 Ring waves on the surface of shear flows: a linear and nonlinear theory. J. Fluid Mech. 215, 145–160.Google Scholar
Khusnutdinova, K. R. & Zhang, X. 2016 Long ring waves in a stratified fluid over a shear flow. J. Fluid Mech. 794, 14–44.Google Scholar
Kumar, N., Voulgaris, G. & Warner, J. C. 2011 Implementation and modification of a three-dimensional radiation stress formulation for surf zone and rip-current applications. Ocean Mod. 47, 1097–1117.Google Scholar
Lee, C.-H. 1995 WAMIT Theory Manual. Massachusetts Institute of Technology, Department of Ocean Engineering.Google Scholar
Li, Y. & Ellingsen, S. Å. 2016 Ship waves on uniform shear current at finite depth: wave resistance and critical velocity. J. Fluid Mech. 791, 539–567.Google Scholar
Li, Y. & Ellingsen, S. Å. 2019 A framework for modelling linear surface waves on shear currents in slowly varying waters. J. Geophys. Res.: Oceans 124, 2527–2545.Google Scholar
Li, Y., Smeltzer, B. K. & Ellingsen, S. Å. 2018 Transient wave resistance upon a real shear current. Eur. J. Mech. (B/Fluids) 73, 180–192.Google Scholar
Lund, B., Graber, H. C., Tamura, H., Collins, C. O. & Varlamov, S. M. 2015 A new technique for the retrieval of near-surface vertical current shear from marine X-band radar images. J. Geophys. Res.: Oceans 120, 8466–8496.Google Scholar
Moisy, F., Rabaud, M. & Salsac, K. 2009 A synthetic Schlieren method for the measurement of the topography of a liquid interface. Exp. Fluids 36, 1021–1036.Google Scholar
Noblesse, F., He, J., Zhu, Y., Hong, L., Zhang, C., Zhu, R. & Yang, C. 2014 Why can ship wakes appear narrower than Kelvin’s angle? Eur. J. Mech. (B/Fluids) 46, 164–171.Google Scholar
Paterson, E. G., Wilson, R. V. & Stern, F. 2003 General-Purpose Parallel Unsteady RANS Ship Hydrodynamics Code: CFDSHIP-IOWA. Iowa Institute of Hydraulic Research.Google Scholar
Peregrine, D. H. 1976 Interaction of water waves and currents. Adv. Appl. Mech. 16, 9–117.Google Scholar
Pethiagoda, R., McCue, S. W. & Moroney, T. J. 2014 What is the apparent angle of a Kelvin ship wave pattern? J. Fluid Mech. 758, 468–485.Google Scholar
Poisson, S.-D. 1818 Mémoire sur la théorie des ondes. Mem. Prés. divers Savants Acad. Roy. Sci. Inst. 1, 70–186.Google Scholar
Rabaud, M. & Moisy, F. 2013 Ship wakes: Kelvin or Mach angle? Phys. Rev. Lett. 110, 214503.Google Scholar
Scott, J. C. 1982 Flow beneath a stagnant film on water: the Reynolds ridge. J. Fluid Mech. 116, 283–296.Google Scholar
Shrira, V. I. 1993 Surface waves on shear currents: solution of the boundary-value problem. J. Fluid Mech. 252, 565–584.Google Scholar
Smeltzer, B. K. & Ellingsen, S. Å. 2017 Surface waves on arbitrary vertically-sheared currents. Phys. Fluids 29, 047102.Google Scholar
Stewart, R. J. & Joy, J. W. 1974 HF radio measurements of surface currents. Deep Sea Res. Ocean. Abstracts 21, 1039–1049.Google Scholar
Thomson, S. W. 1887 On ship waves. Proc. Inst. Mech. Engrs 38, 409–434.Google Scholar
Wehausen, J. W. & Laitone, E. V. 1960 Surface waves. In Fluid Dynamics III (ed. Flügge, S.), Encyclopedia of Physics, vol. IX, pp. 446–778. Springer.Google Scholar
Willert, C., Stasicki, B., Klinner, J. & Moessner, S. 2010 Pulsed operation of high-power light emitting diodes for imaging flow velocimetry. Meas. Sci. Technol. 21, 075402.Google Scholar
Zippel, S. & Thomson, J. 2017 Surface wave breaking over sheared currents: observations from the mouth of the Columbia River. J. Geophys. Res.: Oceans 122, 3311–3328.Google Scholar

Smeltzer et al. supplementary movie

Examples of measured ship waves and ring waves.
Download Smeltzer et al. supplementary movie(Video)
Video 2 MB