×

The breaking of interfacial waves at a submerged bathymetric ridge. (English) Zbl 1183.76023

Summary: The breaking of periodic progressive two-layer interfacial waves at a Gaussian ridge is investigated through laboratory experiments. Length scales of the incident wave and topography are used to parameterize when and how breaking occurs. Qualitative observations suggest both shear and convection play a role in the instability of waves breaking at the ridge. Simultaneous particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) measurements are used to calculate high resolution, two-dimensional velocity and density fields from which the local gradient Richardson number \(Ri_{g}\) is calculated. The transition to breaking occurred when \(0.2 \leq Ri_{g} \leq 0.4\). In these wave-ridge breaking events, the destabilizing effects of waves steepening in shallow layers may be responsible for breaking at higher \(Ri_{g}\) than for similar waves breaking through shear instability in deep water (Troy & Koseff, J. Fluid Mech., vol. 543, 2005b, p. 107). Due to the effects of unsteadiness, nonlinear shoaling and flow separation, the canonical \(Ri_{g} > 0.25\) is not sufficient to predict the stability of interfacial waves. A simple model is developed to estimate \(Ri_{g}\) in waves between finite depth layers using scales of the incident wave scale and topography. The observed breaking transition corresponds with a constant estimated value of \(Ri_{g}\) from the model, suggesting that interfacial shear plays an important role in initial wave instability. For wave amplitudes above the initial breaking transition, convective breaking events are also observed.

MSC:

76-05 Experimental work for problems pertaining to fluid mechanics
76D33 Waves for incompressible viscous fluids
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] DOI: 10.1175/1520-0485(2003)033<2093:SAGOTA>2.0.CO;2
[2] DOI: 10.1029/JC074i028p06975
[3] DOI: 10.1017/S0022112061000305 · Zbl 0101.43002
[4] DOI: 10.1007/s10652-008-9055-x
[5] DOI: 10.1029/1999JC900037
[6] DOI: 10.1063/1.2931693 · Zbl 1182.76119
[7] DOI: 10.1063/1.2162033 · Zbl 1185.76484
[8] DOI: 10.1126/science.276.5320.1831
[9] DOI: 10.1017/S0022112074000164
[10] DOI: 10.1063/1.858055
[11] DOI: 10.1175/1520-0485(1997)027<1181:SRAMBR>2.0.CO;2
[12] DOI: 10.1038/35003164
[13] Boegman, Limnol. Oceanogr. 50 pp 1620– (2005)
[14] DOI: 10.1061/(ASCE)0733-9399(2003)129:10(1189)
[15] DOI: 10.1029/2007JC004411
[16] DOI: 10.1175/1520-0485(1996)026<2286:AMWIIN>2.0.CO;2
[17] DOI: 10.1017/S002211200000286X · Zbl 0963.76505
[18] DOI: 10.1017/S0022112006000061 · Zbl 1156.76350
[19] DOI: 10.1017/S0022112085003081
[20] DOI: 10.1007/s00348-005-0016-6
[21] DOI: 10.1175/1520-0485(1996)026<0005:IOIWWA>2.0.CO;2
[22] DOI: 10.1017/S0022112000008788 · Zbl 0955.76516
[23] DOI: 10.1017/S0022112089001849
[24] DOI: 10.1017/S0022112088001636
[25] DOI: 10.1063/1.2335963
[26] DOI: 10.1175/1520-0485(2002)032<1779:NEOTBO>2.0.CO;2
[27] DOI: 10.1017/S0022112061000317 · Zbl 0104.20704
[28] DOI: 10.1063/1.2221863
[29] DOI: 10.1017/S0022112079002585 · Zbl 0426.76021
[30] DOI: 10.1007/978-3-540-36906-6_3
[31] DOI: 10.1146/annurev.fluid.38.050304.092129 · Zbl 1098.76018
[32] DOI: 10.1017/S0022112005006798 · Zbl 1081.76516
[33] DOI: 10.1017/S0022112086002823
[34] DOI: 10.1007/s00348-004-0909-9
[35] DOI: 10.1017/S0022112092002660
[36] DOI: 10.1029/96JC03160
[37] DOI: 10.1017/S0022112072001065 · Zbl 0239.76112
[38] Thorpe, Phys. Processes Lakes Oceans, Coast. Estuar. Stud. 54 pp 441– (1998)
[39] DOI: 10.1017/S0022112000008648 · Zbl 0979.76013
[40] DOI: 10.1017/S0022112087001228 · Zbl 0633.76024
[41] DOI: 10.1017/S0022112078000518 · Zbl 0379.76016
[42] DOI: 10.1017/S0022112008004898 · Zbl 1156.76313
[43] DOI: 10.1017/S0022112003006189 · Zbl 1063.76013
[44] DOI: 10.1016/0377-0265(93)90038-9
[45] DOI: 10.1073/pnas.70.8.2379
[46] DOI: 10.1017/S0022112002001556 · Zbl 1152.76312
[47] DOI: 10.1016/j.ijheatfluidflow.2005.10.003
[48] DOI: 10.1007/s00348-006-0233-7
[49] DOI: 10.1175/JPO2900.1
[50] Nagashima, J. Oceanogr. 27 pp 1– (1971)
[51] DOI: 10.1016/0012-821X(96)00129-X
[52] DOI: 10.1126/science.276.5309.93
[53] Dean, River Edge (1984)
[54] Phillips, The Dynamics of the Upper Ocean (1966) · Zbl 0193.56902
[55] DOI: 10.1007/s003480000260
[56] DOI: 10.1146/annurev.fluid.35.101101.161144 · Zbl 1041.76024
[57] DOI: 10.1088/0957-0233/18/3/001
[58] DOI: 10.1017/S0022112003005007 · Zbl 1063.76559
[59] DOI: 10.1007/s003480000263
[60] DOI: 10.1017/S002211209800250X · Zbl 0941.76524
[61] DOI: 10.1007/s00348-008-0496-2
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.