Equations of the second order potentials in a bounded solid space-bulk and surface waves

1995 ◽  
Vol 186 (4) ◽  
pp. 561-566 ◽  
Author(s):  
Z.W. Qian
Keyword(s):  
Surface Waves ◽  
Second Order ◽  
Solid Space

Subharmonic resonance of short internal standing waves by progressive surface waves

1996 ◽  
Vol 321 ◽  
pp. 217-233 ◽  
Author(s):  
D. F. Hill ◽  
M. A. Foda
Keyword(s):  
Surface Wave ◽  
Internal Wave ◽  
Surface Waves ◽  
Internal Waves ◽  
Growth Rates ◽  
Evolution Equations ◽  
Standing Waves ◽  
Second Order ◽  
Inviscid Limit ◽  
Initial Growth

Experimental evidence and a theoretical formulation describing the interaction between a progressive surface wave and a nearly standing subharmonic internal wave in a two-layer system are presented. Laboratory investigations into the dynamics of an interface between water and a fluidized sediment bed reveal that progressive surface waves can excite short standing waves at this interface. The corresponding theoretical analysis is second order and specifically considers the case where the internal wave, composed of two oppositely travelling harmonics, is much shorter than the surface wave. Furthermore, the analysis is limited to the case where the internal waves are small, so that only the initial growth is described. Approximate solution to the nonlinear boundary value problem is facilitated through a perturbation expansion in surface wave steepness. When certain resonance conditions are imposed, quadratic interactions between any two of the harmonics are in phase with the third, yielding a resonant triad. At the second order, evolution equations are derived for the internal wave amplitudes. Solution of these equations in the inviscid limit reveals that, at this order, the growth rates for the internal waves are purely imaginary. The introduction of viscosity into the analysis has the effect of modifying the evolution equations so that the growth rates are complex. As a result, the amplitudes of the internal waves are found to grow exponentially in time. Physically, the viscosity has the effect of adjusting the phase of the pressure so that there is net work done on the internal waves. The growth rates are, in addition, shown to be functions of the density ratio of the two fluids, the fluid layer depths, and the surface wave conditions.

scholarly journals An improved Lagrangian model for the time evolution of nonlinear surface waves

2019 ◽  
Vol 876 ◽  
pp. 527-552 ◽  
Author(s):  
Charles-Antoine Guérin ◽  
Nicolas Desmars ◽  
Stéphan T. Grilli ◽  
Guillaume Ducrozet ◽  
Yves Perignon ◽  
...  
Keyword(s):  
Surface Waves ◽  
Time Evolution ◽  
Forecast Accuracy ◽  
Second Order ◽  
Stokes Drift ◽  
Irregular Waves ◽  
Lagrangian Model ◽  
Simple Method ◽  
Lagrangian Models ◽  
Wave Forecast

Accurate real-time simulations and forecasting of phase-revolved ocean surface waves require nonlinear effects, both geometrical and kinematic, to be accurately represented. For this purpose, wave models based on a Lagrangian steepness expansion have proved particularly efficient, as compared to those based on Eulerian expansions, as they feature higher-order nonlinearities at a reduced numerical cost. However, while they can accurately model the instantaneous nonlinear wave shape, Lagrangian models developed to date cannot accurately predict the time evolution of even simple periodic waves. Here, we propose a novel and simple method to perform a Lagrangian expansion of surface waves to second order in wave steepness, based on the dynamical system relating particle locations and the Eulerian velocity field. We show that a simple redefinition of reference particles allows us to correct the time evolution of surface waves, through a modified nonlinear dispersion relationship. The resulting expressions of free surface particle locations can then be made numerically efficient by only retaining the most significant contributions to second-order terms, i.e. Stokes drift and mean vertical level. This results in a hybrid model, referred to as the ‘improved choppy wave model’ (ICWM) (with respect to Nouguier et al.’s J. Geophys. Res., vol. 114, 2009, p. C09012), whose performance is numerically assessed for long-crested waves, both periodic and irregular. To do so, ICWM results are compared to those of models based on a high-order spectral method and classical second-order Lagrangian expansions. For irregular waves, two generic types of narrow- and broad-banded wave spectra are considered, for which ICWM is shown to significantly improve wave forecast accuracy as compared to other Lagrangian models; hence, ICWM is well suited to providing accurate and efficient short-term ocean wave forecast (e.g. over a few peak periods). This aspect will be the object of future work.

scholarly journals A non-linear second-order stochastic model of ocean surface waves

2001 ◽  
Vol 24 (5) ◽  
pp. 409-415 ◽  
Author(s):  
Maminirina Joelson ◽  
Alfred Ramamonjiarisoa
Keyword(s):  
Stochastic Model ◽  
Surface Waves ◽  
Ocean Surface ◽  
Second Order ◽  
Ocean Surface Waves ◽  
Non Linear

scholarly journals Wave Ogives as Second-Order Effects in the Creep of Large Ice Masses

1979 ◽  
Vol 24 (90) ◽  
pp. 509-510
Author(s):  
F. M. Williams
Keyword(s):  
Steady State ◽  
Surface Waves ◽  
Mathematical Analysis ◽  
Second Order ◽  
Order Effects ◽  
Ice Shelves ◽  
Steady State Motion ◽  
Second Order Effects

AbstractThis paper presents a mathematical analysis of the steady-state motion of a large ice mass. The purpose of the study is to determine the parameters which govern the motion of the ice and to establish the relationships between these parameters and the observable features of the motion. The study considers both land-based glaciers and floating ice shelves as different cases of the same problem. The particular features of the motion which are considered in this study are the surface waves or ogives which appear on both glaciers and ice shelves.

An experimental study of the pressure variations in standing water waves

1951 ◽  
Vol 206 (1086) ◽  
pp. 424-435 ◽  
Keyword(s):  
Experimental Study ◽  
Surface Waves ◽  
Standing Wave ◽  
Water Waves ◽  
Wave Length ◽  
Second Order ◽  
First Order ◽  
Standing Water ◽  
Plane Barrier ◽  
Progressive Waves

Although the first-order pressure variations in surface waves on water are known to decrease exponentially downwards, it has recently been shown theoretically that in a standing wave there should be some second-order terms which are unattenuated with depth. The present paper describes experiments which verify the existence of pressure variations of this type in waves of period 0·45 to 0·50 sec. When the motion consists of two progressive waves of equal wave-length travelling in opposite directions, the amplitude of the unattenuated pressure variations is found to be proportional to the product of the wave amplitudes. This property is used to determine the coefficient of reflexion from a sloping plane barrier.

SECOND ORDER HARMONIC SURFACE WAVES GENERATED BY ONE FUNDAMENTAL WAVE

1979 ◽  
Vol 40 (C7) ◽  
pp. C7-607-C7-608
Author(s):  
A. Shivarova ◽  
T. Stoychev
Keyword(s):  
Surface Waves ◽  
Second Order ◽  
Fundamental Wave
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