Short Wave Groups Research Articles

On the interaction of small-scale oceanic internal waves with near-inertial waves

Ray theory is used to investigate the interaction of a short high-frequency progressive internal wave of infinitesimal amplitude with a long progressive near-inertial wave of arbitrary amplitude. Weak-interaction theory would, if applicable, predict that the largest changes in short-wave properties occur when the resonance condition c = cg is satisfied, where c is the phase velocity of the long wave and cg is the group velocity of the short wave. The present calculation confirms this prediction only when the long wave has exceedingly small amplitude (peak velocities of order 0.1 cm/s).However, when the background velocity has a realistic amplitude (e.g. oceanic values are of order 20 cm/s) the resonance condition fails to be relevant. For example, waves which initially have c = cg become trapped in low-shear regions and consequently experience very small changes in wavenumber. Other short waves, which initially have cg [Lt ] c and hence violate the resonance condition, exhibit large and permanent changes in vertical wavenumber.Remarkably, it is found that these permanent changes are much more likely to be decreases, rather than increases, in wavenumber. This can be explained as follows. Short waves which enter an inertial-wave packet experience both increases and decreases in wavenumber. However, at times when the wavenumber is relatively large, the group velocity is relatively small and the short wave is unlikely to escape from the inertial packet, whereas small wavenumber and large group velocity assist the escape of the short-wave group. Consequently the short waves that leave the inertial packet tend to have a smaller average wavenumber than those that enter. Thus the net effect of a near-inertial packet on a collection of short waves appears to be an increase in vertical wavelength and frequency.

Long waves induced by short-wave groups over an uneven bottom

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.

The dispersion of short wavelets in the presence of a dominant long wave

The characteristics are studied of short surface waves superimposed upon, and interacting with, a long, finite-amplitude dominant wave of frequency N . An asymptotic analysis allows the numerical investigation of Longuet-Higgins (1978) to be extended to higher superharmonic perturbations, and it is found that, although they are distorted by the underlying finite-amplitude wave, gravity wavelets continue to propagate freely provided the dominant wave does not break. Capillary waves can, however, be blocked by short, steep, non-breaking gravity waves, so that in a wind-wave tank at short fetch and high wind speed, freely travelling gravity-capillary waves can be erased by the successive dominant wave crests. A train or group of short gravity waves suffers modulations δ k in its local wave-number because of the straining of the long wave, and large modulations C δ k in its apparent frequency measured at a fixed point (where C is the long wave phase speed), largely because of the Doppler shifting produced by the dominant wave orbital velocity. The spectral signatures of a wave train are calculated by stationary phase and are found to have maxima at the upper wavenumber or frequency in the range. If an ensemble of short-wave groups is sampled at a given frequency f at a fixed point, the signal is derived from groups with a range of intrinsic frequencies δ, but is dominated by those at the long-wave crest for which f = δ + k.u 0 , where u 0 is the orbital velocity of the dominant wave. The apparent phase speed measured by a pair of such probes is the sum of the propagation speed c of the wavelet and the orbital velocity u 0 of the long wave. When f / N is large, the apparent phase speed approaches u 0 , independent of f . These results are consistent with measurements by Ramamonjiarisoa & Giovanangeli (1978) and others in which the apparent phase speed at high frequencies is found to be independent of the frequency — the measurements do not therefore imply a lack of dispersion of short gravity waves on the ocean surface.

Time impulse response and time frequency response of optical pupils.:Experimental confirmations and applications

Time impulse response and time frequency response of optical pupils.:Experimental confirmations and applications

Spatial observations of short internal waves in the Strait of Gibraltar

Several groups of short (periods of about 13 min) internal waves have been simultaneously recorded at two mooring stations in the Strait of Gibraltar. The variations and changes that occur to the waves while they are travelling west to east from one station to the other are described and discussed. The observations reveal that amplitudes may increase by factors from 2 to 6 over a distance of 3·7 km, corresponding to 3–4 wavelenghts. In addition to these oscillatory type waves, singular i.e. solitary type waves were also encountered which were, however, found to attenuate while, moving from one station to the other. The travelling speeds of the singular waves, observed on two days, were 1·6 ms −1 and 2·6 ms −1. The travelling speeds of the characteristic features of the oscillatory type wave groups ranged from 1·2 ms −1 to 2·2 ms −1. Preliminary measurements of the dynamics stability reveal Richardson numbers of the order of 5 during the occurrence of internal oscillations.