scholarly journals The suppression of short waves by a train of long waves

1996 ◽  
Vol 315 ◽  
pp. 139-150 ◽  
Author(s):  
A. M. Balk

It is shown that a train of long waves can suppress a short-wave field due to four-wave resonance interactions. These interactions lead to the diffusion (in Fourier space) of the wave action of the short-wave field, so that the wave action is transported to the regions of higher wavenumbers, where it dissipates more effectively. The diffusion equation is derived.

Author(s):  
A. D. D. Craik

AbstractThe leading-order interaction of short gravity waves with a dominant long-wave swell is calculated by means of Zakharov's [7] spectral formulation. Results are obtained both for a discrete train of short waves and for a localised wave packet comprising a spectrum of short waves.The results for a discrete wavetrain agree with previous work of Longuet-Higgins & Stewart [5], and general agreement is found with parallel work of Grimshaw [4] which employed a very different wave-action approach.


1984 ◽  
Vol 139 ◽  
pp. 219-235 ◽  
Author(s):  
Chiang C. Mei ◽  
Chakib Benmoussa

Unidirectional and periodically modulated short waves on a horizontal or very nearly horizontal bottom are known to be accompanied by long waves which propagate together with the envelope of the short waves at their group velocity. However, for variable depth with a horizontal lengthscale which is not too great compared with the group length, long waves of another kind are further induced. If the variation of depth is only one-dimensional and localized in a finite region, then the additional long waves can radiate away from this region, in directions which differ from those of the short waves and their envelopes. There are also critical depths which define caustics for these new long waves but not for the short waves. Thus, while obliquely incident short waves can pass over a topography, these second-order long waves may be trapped on a ridge or away from a canyon.


A two-scale model of a wind-ruffled surface is developed which includes (1) modulation of the short waves by orbital straining in the long waves, (2) dissipation of short-wave energy by breaking, and (3) regeneration of the short-wave energy by the wind. For simplicity the long waves are at first assumed to be uniform. It is shown that the character of the surface is governed by the parameter Ω = (β/σγKA ), where β is the proportional rate of short-wave growth due to the wind, σ , K and A are the long-wave frequency wavenumber and amplitude, and γ = 2.08. When Ω < 1 the short waves break over only part of the long-wave surface. When Ω ≽ 1 they break everywhere. The mean-square steepness s 2 ¯ of the short waves is an increasing function of β/σ , but a decreasing function of the long-wave steepness AK . The phase angle between s 2 ¯ and the long-wave elevation η is an increasing function of Ω . The correlation between s 2 ¯ and η is largest when Ω ≪1, but tends to 0 as Ω → 1. The simple model is extended to the case when the long-wave amplitude A has a Rayleigh probability density. To take account of the ‘sheltering ’ effect of high waves we compute the case when any two successive waves have a bivariate Rayleigh density. The application of the model to laboratory and field data is discussed.


2016 ◽  
Vol 85 (4) ◽  
pp. 2827-2841 ◽  
Author(s):  
Hiu Ning Chan ◽  
Edwin Ding ◽  
David Jacob Kedziora ◽  
Roger Grimshaw ◽  
Kwok Wing Chow

2018 ◽  
Vol 3 (12) ◽  
Author(s):  
H. N. Chan ◽  
R. H. J. Grimshaw ◽  
K. W. Chow

The present paper continues the account of wireless investigations of the ionized regions of the upper atmosphere given in two previous papers. The results discussed in it consist chiefly of measurements of the equivalent heights of the ionized regions made simultaneously at two or three receiving stations with wave-lengths of the order of 100 metres. The frequency-change method of measuring the equivalent height was used throughout. 2. Extension of Equivalent Height Measurements to the Use of Short Waves . The experiments described previously were continued with shorter wave-lengths with two objects in view. In the first place it had been found that 400-metre waves penetrated the lower ionized region (E region) only on certain nights, and then only during the few hours before dawn. This result clearly showed that penetration of this region was most likely when the density of ionization was least. But, according to most theories of wireless propagation, a greater electronic density is required to reflect or refract short waves than is the case with long waves, so that it was anticipated that by reducing the wave-length below 400 metres it might be possible to penetrate E region over a longer period of time during the night than had been possible when 400-metre waves had been used. In this way it was hoped to make a more detailed study of the variation of the equivalent height of the upper region (F region) which had been found to reflect 400-metre waves on the occasion when they had penetrated the normal E region. Secondly, since it is known that the attenuation of the ground waves increases rapidly as the wave-length is reduced below, say, 400 metres, it was expected that, with the use of shorter waves, the ratio of the values of downcoming wave intensity and ground wave intensity would be much increased at all stations. Such an increase, it was expected, would make it possible to continue the measurements of equivalent heights, in general, a good deal further into the daylight hours. Such daylight measurements on longer waves had previously been found difficult, because of the relative weakness of the intensity of the downcoming waves as compared with that of the ground waves.


1988 ◽  
Vol 1 (21) ◽  
pp. 102 ◽  
Author(s):  
E.W. Bijker ◽  
C.A. De Bruyn

Tests have been performed on a vertical pile subject to current only and to a combination of current with normal waves and current with breaking waves. The scour around the pile produced by current only is decreased by normal short waves superimposed upon that current and increased when breaking waves are superimposed upon the current. After analysis of the velocity profiles in the undisturbed area upstream of the pile and next to the pile, the following explanation is found for this phenomenon. When normal short waves are superimposed upon a current, the bottom shear stress of the combination of current with waves is increased more in the undisturbed area than next to the pile in the scour area. This results in a decrease of the scour around the pile. Due to the large values of the orbital velocity under breaking waves this effect is reversed for the combination of a current with breaking and relatively long waves. This results in an increase of the scour around the pile.


1957 ◽  
Vol 24 (2) ◽  
pp. 240-244
Author(s):  
Julius Miklowitz ◽  
C. R. Nisewanger

Abstract Experimental results, obtained by employing an aerodynamic shock tube for rod excitation, are presented. Comparison of these results with the theoretical information presented in Part I is made. It is shown that the Mindlin-Herrmann theory, through its upper mode (radial), offers a good approximate representation of the moderately short waves that predominate at the later times at a random station of the rod. The very short waves of this same radial mode, however, govern the early disturbance, thus precluding the possibility of representing this portion of the disturbance, which the experiment shows to be composed of relatively long waves, by the longitudinal mode of the theory.


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