Nonlinear interfacial wave formation in three dimensions

Grue, John

doi:10.1017/jfm.2015.42

Cited by 15 publications

(10 citation statements)

References 33 publications

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“…However, the choice of an oscillating topography has also proven to be of use in the study of strongly nonlinear interfacial waves. For instance, Grue (2015) recently confirmed findings on the onset of wave train formation observed in experimental measurements by Maxworthy (1979) with a three-dimensional two-layer, fully dispersive and strongly nonlinear interfacial wave model with a time-varying bottom topography.…”

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confidence: 68%

Limiting amplitudes of fully nonlinear interfacial tides and solitons

Aguiar‐González

Gerkema

2016

Nonlin. Processes Geophys.

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Abstract. A new two-fluid layer model consisting of forced rotation-modified Boussinesq equations is derived for studying tidally generated fully nonlinear, weakly nonhydrostatic dispersive interfacial waves. This set is a generalization of the Choi-Camassa equations, extended here with forcing terms and Coriolis effects. The forcing is represented by a horizontally oscillating sill, mimicking a barotropic tidal flow over topography. Solitons are generated by a disintegration of the interfacial tide. Because of strong nonlinearity, solitons may attain a limiting table-shaped form, in accordance with soliton theory. In addition, we use a quasi-linear version of the model (i.e. including barotropic advection but linear in the baroclinic fields) to investigate the role of the initial stages of the internal tide prior to its nonlinear disintegration. Numerical solutions reveal that the internal tide then reaches a limiting amplitude under increasing barotropic forcing. In the fully nonlinear regime, numerical experiments suggest that this limiting amplitude in the underlying internal tide extends to the nonlinear case in that internal solitons formed by a disintegration of the internal tide may not reach their table-shaped form with increased forcing, but appear limited well below that state.

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confidence: 68%

Limiting amplitudes of fully nonlinear interfacial tides and solitons

Aguiar‐González

Gerkema

2016

Nonlin. Processes Geophys.

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“…In particular, large-amplitude internal waves in the Strait of Gibraltar have been modelled by Vlasenko et al (2009) and Sannino et al (2014). Tidal generation of internal waves in the Celtic Sea has been modelled by Vlasenko et al (2013Vlasenko et al ( , 2014 and Grue (2015). We note that the waves generated in the Strait of Gibraltar are nearly annular (see figure 1), as are the waves generated near a sea mountain in the Celtic Sea (see Vlasenko et al (2014, figure A1)).…”

Section: Introductionmentioning

confidence: 99%

Long ring waves in a stratified fluid over a shear flow

Хуснутдинова

Zhang

2016

J. Fluid Mech.

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Oceanic waves registered by satellite observations often have curvilinear fronts and propagate over various currents. In this paper we study long linear and weakly nonlinear ring waves in a stratified fluid in the presence of a depth-dependent horizontal shear flow. It is shown that, despite the clashing geometries of the waves and the shear flow, there exists a linear modal decomposition (different from the known decomposition in Cartesian geometry), which can be used to describe distortion of the wavefronts of surface and internal waves, and systematically derive a 2+1-dimensional cylindrical Korteweg-de Vries-type equation for the amplitudes of the waves. The general theory is applied to the case of the waves in a two-layer fluid with a piecewise-constant current, with an emphasis on the effect of the shear flow on the geometry of the wavefronts. The distortion of the wavefronts is described by the singular solution (envelope of the general solution) of the nonlinear first-order differential equation, constituting generalisation of the dispersion relation in this curvilinear geometry. There exists a striking difference in the shapes of the wavefronts of surface and interfacial waves propagating over the same shear flow.

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“…Two-dimensional calculations have shown that (see Grue 25 ) the quadratic approximation provides a very accurate evaluation of solitary waves of amplitude even comparable to the upper (thinner) layer depth. Further, the additions from the cubic terms are much smaller than those from the leading two terms in the successive approximations.…”

Section: A Interfacial Motionmentioning

confidence: 99%

“…24 Mathematically, we extend an interfacial method in three dimensions, accounting for a body moving in the upper (thin) layer of the two-layer fluid. The method has previously included a geometry in the lower layer, 25 and presently, a new version of the set of relations is obtained. New expressions for the nonlinear time-dependent force on the moving ship are derived.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dead water resistance at subcritical speed

Grue

2015

Physics of Fluids

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The dead water resistance F1=12CdwρSU2 (ρ fluid density, U ship speed, S wetted body surface, Cdw resistance coefficient) on a ship moving at subcritical speed along the upper layer of a two-layer fluid is calculated by a strongly nonlinear method assuming potential flow in each layer. The ship dimensions correspond to those of the Polar ship Fram. The ship draught, b0, is varied in the range 0.25h0–0.9h0 (h0 the upper layer depth). The calculations show that Cdw/(b0/h0)2 depends on the Froude number only, in the range close to critical speed, Fr = U/c0 ∼ 0.875–1.125 (c0 the linear internal long wave speed), irrespective of the ship draught. The function Cdw/(b0/h0)2 attains a maximum at subcritical Froude number depending on the draught. Maximum Cdw/(b0/h0)2 becomes 0.15 for Fr = 0.76, b0/h0 = 0.9, and 0.16 for Fr = 0.74, b0/h0 = 1, where the latter extrapolated value of the dead water resistance coefficient is about 60 times higher than the frictional drag coefficient and relevant for the historical dead water observations. The nonlinear Cdw significantly exceeds linear theory (Fr < 0.85). The ship generated waves have a wave height comparable to the upper layer depth. Calculations of three-dimensional wave patterns at critical speed compare well to available laboratory experiments. Upstream solitary waves are generated in a wave tank of finite width, when the layer depths differ, causing an oscillation of the force. In a wide ocean, a very wide wave system develops at critical speed. The force approaches a constant value for increasing time.

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Nonlinear interfacial wave formation in three dimensions

Cited by 15 publications

References 33 publications

Limiting amplitudes of fully nonlinear interfacial tides and solitons

Limiting amplitudes of fully nonlinear interfacial tides and solitons

Long ring waves in a stratified fluid over a shear flow

Nonlinear dead water resistance at subcritical speed

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