Topic
Waves and shallow water
About: Waves and shallow water is a research topic. Over the lifetime, 5833 publications have been published within this topic receiving 108413 citations.
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TL;DR: In this article, the second-order currents and changes in mean surface level which are caused by gravity waves of non-uniform amplitude are investigated, and the effects are interpreted in terms of the radiation stresses in the waves.
Abstract: This paper studies the second-order currents and changes in mean surface level which are caused by gravity waves of non-uniform amplitude. The effects are interpreted in terms of the radiation stresses in the waves.The first example is of wave groups propagated in water of uniform mean depth. The problem is solved first by a perturbation analysis. In two special cases the second-order currents are found to be proportional simply to the square of the local wave amplitude: (a) when the lengths of the groups are large compared to the mean depth, and (b) when the groups are all of equal length. Then the surface is found to be depressed under a high group of waves and the mass-transport is relatively negative there. In case (a) the result can be simply related to the radiation stresses, which tend to expel fluid from beneath the higher waves.The second example considered is the propagation of waves of steady amplitude in water of gradually varying depth. Assuming no loss of energy by friction or reflexion, the wave amplitude must vary horizontally, to maintain the flux of energy constant; it is shown that this produces a negative tilt in the mean surface level as the depth diminishes. However, if the wave height is limited by breaking, the tilt is positive. The results are in agreement with some observations by Fairchild.Lastly, the propagation of groups of waves from deep to shallow water is studied. As the mean depth decreases, so the response of the fluid to the radiation stresses tends to increase. The long waves thus generated may be reflected as free waves, and so account for the 'surf beats’ observed by Munk and Tucker.Generalle speaking, the changes in mean sea level produced by ocean waves are comparable with those due to horizontal wind stress. It may be necessary to allow for the wave stresses in calculating wind stress coefficients.
959 citations
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TL;DR: In this paper, the authors used known results on the radiation stress associated with gravity waves, and showed that the total lateral thrust exerted by incoming waves on the beach and in the nearshore zone is rigorously shown to equal (E 0/4) sin 2θ 0 per unit distance parallel to the coastline, where E denotes the energy density of the waves in deep water and θ denotes the waves' angle of incidence.
Abstract: By using known results on the radiation stress associated with gravity waves, the total lateral thrust exerted by incoming waves on the beach and in the nearshore zone is rigorously shown to equal (E0/4) sin 2θ0 per unit distance parallel to the coastline, where E0 denotes the energy density of the waves in deep water and θ0 denotes the waves' angle of incidence. The local stress exerted on the surf zone in steady conditions is shown to be given by (D/c) sin θ per unit area, where D is the local rate of energy dissipation and c is the phase velocity. These relations are independent of the manner of the energy dissipation, but, because breaker height is related to local depth in shallow water, it is argued that ordinarily most of the dissipation is due to wave breaking, not to bottom friction. Under these conditions the local mean longshore stress in the surf zone will be given by (5/4)ρumax2 s sin θ, where ρ is the density, umax is the maximum orbital velocity in the waves, s is the local beach slope, and θ is the angle of incidence. It is further shown that, if the friction coefficient C on the bottom is assumed constant and if horizontal mixing is neglected, the mean longshore component of velocity is given by (5π/8)(s/C) umax sin θ. This value is proportional to the longshore component of the orbital velocity. When the horizontal mixing is taken into account, the longshore currents observed in field observations and laboratory experiments are consistent with a friction coefficient of about 0.010.
832 citations
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TL;DR: In this paper, a new form of the Boussinesq equations applicable to irregular wave propagation on a slowly varying bathymetry from deep to shallow water is introduced, which incorporate excellent linear dispersion characteristics, and are formulated and solved in two horizontal dimensions.
783 citations
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TL;DR: In this paper, various types of carbonate platforms change in response to variations in sedimentation, subsidence or sea level rise, and may form distinctive evolutionary sequences, and the relatively few models presented appear to accommodate most geological examples, some of which contain major reservoir facies.
Abstract: Various types of carbonate platforms are characterized by distinctive profiles, facies, and evolutionary sequences. Ramps may be homoclinal or distally steepened, and may have fringing or barrier shoal-water complexes of ooid-pellet sands or skeletal banks. Homoclinal ramps pass seaward into deeper water without major break in slope, and lack deep-water breccias. Distally steepened ramps may be low energy, and characterized by widespread, shallow, subwave-base mud blankets, or high energy with coastal beach/dune complexes and widespread skeletal sand blankets. Slope facies may contain abundant breccias of slope-derived clasts. Rimmed shelves have relatively flat tops, and marked break in slopes at the high energy, shallow-shelf edge where they pass into deep water. Such shelves may be aggraded with peritidal facies extending over much of the shelf, or incipiently drowned, depending on magnitude of sea level fluctuations. They may be accretionary, or bypass types that include gullied slope, escarpment, and high-relief erosional forms. Intrashelf basins occur on some shelves, controlling distribution of reservoir and source beds. Isolated platforms are surrounded by deeper water and may be located on rifted continental margins, or on submarine volcanoes. Most have high-relief rimmed margins. Platforms that have been subjected to rapid sea level rise may be incipiently drowned, and characterized by raised rims, elevated patch or pinnacle reefs, and widespread subwave-base carbonate or fine clastic blankets. Completely drowned shelves develop where the shelf is submerged to subphotic depths, terminating shallow water deposition, and commonly resulting in blanketing of the shelf by deeper water facies. Some margins show extensive down-to-basin faulting that is contemporaneous with carbonate deposition, or associated with thick prograding clastic sequences. The various types of platforms change in response to variations in sedimentation, subsidence or sea level rise, and may form distinctive evolutionary sequences. The relatively few models presented appear to accommodate most geological examples, some of which contain major reservoir facies.
699 citations
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01 Jan 2003TL;DR: In this article, some remarkable features of stratified flow are discussed, including linear and nonlinear instability of strongly stratified flows with strong stratification Rotating shallow water theory Linear and weakly nonlinear theory of dispersive waves with geophysical examples Simplified equations for the dynamics of strongly-strained flow The stratified quasi-geostrophic equations as a singular limit of the rotating Boussinesq equations.
Abstract: Introduction Some remarkable features of stratified flow Linear and nonlinear instability of stratified flows with strong stratification Rotating shallow water theory Linear and weakly nonlinear theory of dispersive waves with geophysical examples Simplified equations for the dynamics of strongly stratified flow The stratified quasi-geostrophic equations as a singular limit of the rotating Boussinesq equations Introduction to averaging over fast waves for geophysical flows Waves and PDEs for the equatorial atmosphere and ocean Bibliography.
675 citations