The reflection of short gravity waves on a non-uniform current

Smith, R. Jeffrey

doi:10.1017/s0305004100052002

Cited by 48 publications

(36 citation statements)

References 12 publications

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“…This characteristic feature of wave blocking has drawn the interest of oceanographers and coastal engineers alike for its ability to be used as signature patterns of underlying large-scale motion (e.g., fresh water plumes and internal waves) and for the navigational hazard it poses. Smith (1975), Peregrine (1976), andLavrenov (1998) analyzed refraction/reflection around a blocking region and obtained a uniformly valid linearized solution, including a short reflecting wave.…”

Section: V Shugan Et Al: An Analytical Model Of the Evolution Ofmentioning

confidence: 99%

An analytical model of the evolution of a Stokes wave and its two Benjamin–Feir sidebands on nonuniform unidirectional current

Shugan

Hwung

Yang

2015

Nonlin. Processes Geophys.

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Abstract. An analytical weakly nonlinear model of the Benjamin-Feir instability of a Stokes wave on nonuniform unidirectional current is presented. The model describes evolution of a Stokes wave and its two main sidebands propagating on a slowly varying steady current. In contrast to the models based on versions of the cubic Schrödinger equation, the current variations could be strong, which allows us to examine the blockage and consider substantial variations of the wave numbers and frequencies of interacting waves. The spatial scale of the current variation is assumed to have the same order as the spatial scale of the Benjamin-Feir (BF) instability. The model includes wave action conservation law and nonlinear dispersion relation for each of the wave's triad. The effect of nonuniform current, apart from linear transformation, is in the detuning of the resonant interactions, which strongly affects the nonlinear evolution of the system.The modulation instability of Stokes waves in nonuniform moving media has special properties. Interaction with countercurrent accelerates the growth of sideband modes on a short spatial scale. An increase in initial wave steepness intensifies the wave energy exchange accompanied by wave breaking dissipation, resulting in asymmetry of sideband modes and a frequency downshift with an energy transfer jump to the lower sideband mode, and depresses the higher sideband and carrier wave. Nonlinear waves may even overpass the blocking barrier produced by strong adverse current. The frequency downshift of the energy peak is permanent and the system does not revert to its initial state. We find reasonable correspondence between the results of model simulations and available experimental results for wave interaction with blocking opposing current. Large transient or freak waves with amplitude and steepness several times those of normal waves may form during temporal nonlinear focusing of the waves accompanied by energy income from sufficiently strong opposing current. We employ the model for the estimation of the maximum amplification of wave amplitudes as a function of opposing current value and compare the result obtained with recently published experimental results and modeling results obtained with the nonlinear Schrödinger equation.

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Section: V Shugan Et Al: An Analytical Model Of the Evolution Ofmentioning

confidence: 99%

An analytical model of the evolution of a Stokes wave and its two Benjamin–Feir sidebands on nonuniform unidirectional current

Shugan

Hwung

Yang

2015

Nonlin. Processes Geophys.

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“…the uniformly-valid approximation [e.g. Smith, 1975;Peregrine and Smith, 1979]. One encounters two difficulties associated with the matching of the far-field and near-field approximations:…”

Section: Matching Between Far-field and Near-field Approximationsmentioning

confidence: 99%

“…Smith, 1975;McKee, 1977;Stiassnie and Dagan, 1979;Shyu and Phillips, 1990;Trulsen and Mei, 1993]. However, these models do not handle dissipative effects for the waves in the vicinity of the blocking point where the wave amplitude varies rapidly.…”

Section: Introductionmentioning

confidence: 99%

A Model for Blocking of Periodic Waves

Suastika

Battjes

2009

Coastal Engineering Journal

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In this paper, we present a model for the amplitude evolution of periodic waves blocked by a counter current. The model consists of a WKB-solution for slowly varying waves far from the blocking point which is matched with a uniformly-valid approximation for the rapidly varying waves near the blocking point. Wave energy dissipation is taken into account both in the regions far from and near to the blocking point. The predicted pattern of wave amplitude evolution agrees well with observations.

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“…However, this conservation principle is based on ray theory approximations and fails close to the blocking point, which is a caustic in the ray theory. Smith [1975] and Peregrine [1976] obtained a uniformly valid linearized solution for the wave amplitude through the blocking region. They showed that around the blocking region the amplitude envelope is given by an Airy function, and away from the blocking region the wave field consists of an incident wave and a much shorter reflected wave.…”

Section: Introductionmentioning

confidence: 99%

Monochromatic and random wave breaking at blocking points

2002

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[1] In this paper we study the energy dissipation due to current-limited wave breaking in monochromatic and random waves with the help of experimental tests. The opposing currents are strong enough for wave blocking to occur. A modified bore model is used to simulate the dissipation rate in the monochromatic waves, and an empirical bulk dissipation formula for wave breaking in random waves is proposed. The effects of wave blocking on the dynamics of the wave field are also discussed. INDEX TERMS: 4546

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The reflection of short gravity waves on a non-uniform current

Abstract: A uniform asymptotic solution is obtained which describes the propagation near an isolated caustic of water waves on a slow irrotational current. Unlike earlier work there is no restriction to straight caustics or to steady currents.

Cited by 48 publications

References 12 publications

An analytical model of the evolution of a Stokes wave and its two Benjamin–Feir sidebands on nonuniform unidirectional current

An analytical model of the evolution of a Stokes wave and its two Benjamin–Feir sidebands on nonuniform unidirectional current

A Model for Blocking of Periodic Waves

Monochromatic and random wave breaking at blocking points

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