scholarly journals The modulation of short gravity waves by long waves or currents

1988 ◽  
Vol 29 (4) ◽  
pp. 410-429 ◽  
Author(s):  
R. Grimshaw
Keyword(s):  
Gravity Waves ◽  
Finite Amplitude ◽  
Basic Flow ◽  
Long Waves ◽  
Water Current ◽  
Kinematic Equation ◽  
Local Dispersion ◽  
Short Waves ◽  
First Case ◽  
A Current

AbstractThe modulation of short gravity waves by long waves or currents is described for the situation when the flow is irrotational and when the short waves are described by linearised equations. Two cases are distinguished depending on whether the basic flow can be characterised as a deep-water current, or a shallow-water current. In both cases the basic flow has a current which has finite amplitude, while in the first case the free surface slope of the basic flow can be finite, but in the second case is small. The modulation equations are the local dispersion relation of the short waves, the kinematic equation for conservation of wave crests and the wave action equation. The results incorporate and extend the earlier work of Longuet-Higgins and Stewart [10, 11].

scholarly journals EROSION AROUND A PILE DUE TO CURRENT AND BREAKING WAVES

1988 ◽  
Vol 1 (21) ◽  
pp. 102 ◽  
Author(s):  
E.W. Bijker ◽  
C.A. De Bruyn
Keyword(s):  
Shear Stress ◽  
Breaking Waves ◽  
Velocity Profiles ◽  
Long Waves ◽  
Orbital Velocity ◽  
Bottom Shear Stress ◽  
Normal Waves ◽  
Short Waves ◽  
A Current

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.

scholarly journals On the mass and momentum transfer between short gravity waves and larger-scale motions

1971 ◽  
Vol 50 (1) ◽  
pp. 189-205 ◽  
Author(s):  
K. Hasselmann
Keyword(s):  
Mass Transfer ◽  
Gravity Waves ◽  
Cross Sections ◽  
Residual Energy ◽  
Long Waves ◽  
Mean Flow ◽  
Surface Mass ◽  
Short Waves ◽  
Surface Mass Transfer ◽  
Order Of Magnitude

Interactions between short gravity waves and larger-scale flows are investigated in the two-scale approximation. The effect of the wave field on the mean flow is described by an interaction stress tensor and a surface mass transfer. The results are applied to Phillips’ and Longuet-Higgins’ model of short waves breaking on the crests of long carrier waves. It is found that the work done on the long waves by the interaction stresses (corresponding to Longuet-Higgins’ ‘maser’ mechanism of wave generation) is almost exactly balanced by the loss of potential energy arising from the mass transfer. The residual energy transfer leads to attenuation of the long waves, independent of their propagation direction relative to the short waves. Damping factors are estimated from the upwind–downwind ratios of radar backscatter cross-sections. It is found that interactions with waves shorter than 35cm yield attenuation rates about an order of magnitude smaller than the observed growth rates due to the wind.

scholarly journals CHANGES IN HEIGHT OP SHORT WAVES ON LONG WAVES

1978 ◽  
Vol 1 (16) ◽  
pp. 22
Author(s):  
Michio Sato ◽  
Kazuo Nakamura
Keyword(s):  
Experimental Study ◽  
Exact Solution ◽  
Gravity Waves ◽  
Approximate Expression ◽  
Long Waves ◽  
Experimental Results ◽  
Wave Flume ◽  
Short Waves

In this paper we describe an experimental study on changes in height of short gravity waves on long waves. Experiments were conducted by making mechanically generated long waves superpose on mechanically generated short waves in a wave flume of 30m long and lm wide. Exact solution by Longuet-Higgins and Stewart explained our experimental results, but approximate expression a'= a,(l+P) which is widely accepted seemed to be inadequate to explain our results.

An instability of internal gravity waves

1972 ◽  
Vol 52 (2) ◽  
pp. 393-399 ◽  
Author(s):  
Ronald Smith
Keyword(s):  
Surface Wave ◽  
Internal Wave ◽  
Surface Waves ◽  
Gravity Waves ◽  
Internal Gravity Waves ◽  
Long Waves ◽  
Wave Number ◽  
Short Waves

When water is slightly stratified, internal gravity waves are considerably shorter than surface waves of comparable frequency. Here, this fact is exploited in demonstrating that an internal wave is unstable when it forms part of a resonant triad with a surface wave and another internal wave whose wave number is approximately equal to that of the original internal wave. It is suggested that in a system where there are two classes of waves of comparable frequencies but greatly differing wavelengths the short waves may be expected to generate long waves by this mechanism.

Steep gravity waves in water of arbitrary uniform depth

1977 ◽  
Vol 286 (1335) ◽  
pp. 183-230 ◽  
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Water Waves ◽  
Perturbation Parameter ◽  
Intermediate Energy ◽  
Finite Amplitude ◽  
Wave Profile ◽  
Accurate Calculation ◽  
Theoretical Developments ◽  
Deep Water Waves

Modern applications of water-wave studies, as well as some recent theoretical developments, have shown the need for a systematic and accurate calculation of the characteristics of steady, progressive gravity waves of finite amplitude in water of arbitrary uniform depth. In this paper the speed, momentum, energy and other integral properties are calculated accurately by means of series expansions in terms of a perturbation parameter whose range is known precisely and encompasses waves from the lowest to the highest possible. The series are extended to high order and summed with Padé approximants. For any given wavelength and depth it is found that the highest wave is not the fastest. Moreover the energy, momentum and their fluxes are found to be greatest for waves lower than the highest. This confirms and extends the results found previously for solitary and deep-water waves. By calculating the profile of deep-water waves we show that the profile of the almost-steepest wave, which has a sharp curvature at the crest, intersects that of a slightly less-steep wave near the crest and hence is lower over most of the wavelength. An integration along the wave profile cross-checks the Padé-approximant results and confirms the intermediate energy maximum. Values of the speed, energy and other integral properties are tabulated in the appendix for the complete range of wave steepnesses and for various ratios of depth to wavelength, from deep to very shallow water.

On resonant over-reflexion of internal gravity waves from a Helmholtz velocity profile

1979 ◽  
Vol 90 (1) ◽  
pp. 161-178 ◽  
Author(s):  
R. H. J. Grimshaw
Keyword(s):  
Velocity Profile ◽  
Gravity Waves ◽  
Second Harmonic ◽  
Phase Speed ◽  
Internal Gravity Waves ◽  
Finite Amplitude ◽  
Weakly Nonlinear ◽  
Velocity Discontinuity ◽  
Interface Displacement ◽  
Boussinesq Fluid

A Helmholtz velocity profile with velocity discontinuity 2U is embedded in an infinite continuously stratified Boussinesq fluid with constant Brunt—Väisälä frequency N. Linear theory shows that this system can support resonant over-reflexion, i.e. the existence of neutral modes consisting of outgoing internal gravity waves, whenever the horizontal wavenumber is less than N/2½U. This paper examines the weakly nonlinear theory of these modes. An equation governing the evolution of the amplitude of the interface displacement is derived. The time scale for this evolution is α−2, where α is a measure of the magnitude of the interface displacement, which is excited by an incident wave of magnitude O(α3). It is shown that the mode which is symmetrical with respect to the interface (and has a horizontal phase speed equal to the mean of the basic velocity discontinuity) remains neutral, with a finite amplitude wave on the interface. However, the other modes, which are not symmetrical with respect to the interface, become unstable owing to the self-interaction of the primary mode with its second harmonic. The interface displacement develops a singularity in a finite time.

Approach to dyspnoea in pregnancy in the COVID-19 era

2020 ◽  
Vol 19 (4) ◽  
pp. 230-234
Author(s):  
Anita Banerjee ◽  
◽  
Lindsay A Arrandale ◽  
Srividhya Sankaran ◽  
Guy W Glover ◽  
...  
Keyword(s):  
Decision Making ◽  
Pregnant Women ◽  
Correct Diagnosis ◽  
Case Series ◽  
Differential Diagnoses ◽  
Shared Decision ◽  
First Case ◽  
Compromise Design ◽  
A Current ◽  
In Pregnancy

Importance: Dyspnoea and hypoxia in pregnant women during the COVID-19 pandemic may be due to causes other than SARS Co-V-2 infection which should not be ignored. Shared decision-making regarding early delivery is paramount. Objective: To highlight and discuss the differential diagnoses of dyspnoea and hypoxia in pregnant women and to discuss the risks versus benefit of delivery for maternal compromise. Design, setting and participants: Case series of two pregnant women who presented with dyspnoea and hypoxia during the COVID-19 pandemic. Results: Two pregnant women presented with dyspnoea and hypoxia. The first case had COVID-19 infection in the 3rd trimester. The second case had an exacerbation of asthma without concurrent COVID-19. Only the first case required intubation and delivery. Both recovered and were discharged home. Conclusion and relevance: Our two cases highlight the importance of making the correct diagnosis and timely decision-making to consider if delivery for maternal compromise is warranted. Whilst COVID-19 is a current healthcare concern other differential diagnoses must still be considered when pregnant women present with dyspnoea and hypoxia.

Scattering of an eddy advected by a current towards a topographic obstacle

2000 ◽  
Vol 402 ◽  
pp. 211-223 ◽  
Author(s):  
MELVIN E. STERN
Keyword(s):  
Dipole Moment ◽  
Constant Velocity ◽  
Grazing Incidence ◽  
Plane Motion ◽  
Basic Flow ◽  
Homogeneous Fluid ◽  
Azimuthal Mode ◽  
Main Effect ◽  
A Current ◽  
Stratified Model

Contour dynamics is used to compute the two-dimensional (f-plane) motion of an initially circularly symmetric barotropic eddy with piecewise-uniform vorticity as it is advected around a circular obstacle by a uniform upstream current. For grazing incidence of this ‘shielded’ eddy (compensating positive and negative vorticity) the main effect of the vortex images (inside the obstacle) is to change the speed of those particles in the outer portion of the eddy that are closest to the obstacle; a lesser velocity is induced on the oppositely signed vortices near the eddy centre. The result is a systematic separation of the centroids of the ± vortices in the eddy, and the eddy emerges far downstream with an invariant dipole moment (m = 1 azimuthal mode). This causes the eddy to move with a constant velocity V normal to the uniform basic flow. The ratio of the numerically computed V to the accompanying far-field dipole moment agrees with a previous analytical theory for a completely isolated eddy subjected to a small-amplitude m = 1 initial disturbance. The scattering effect might be realizable in a rotating homogeneous fluid by translating a cylinder relative to an otherwise stationary eddy. Application to a density-stratified model is suggested.

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