scholarly journals The formation of strip-like vortex motion by surface gravity waves

2021 ◽  
Vol 2056 (1) ◽  
pp. 012033
Author(s):  
A V Poplevin ◽  
S V Filatov ◽  
A A Levchenko

Abstract We studied experimentally the generation of vortex flow by non-collinear gravity waves with a frequency of 2.34 Hz. The vortices formed on the water surface have the form of stripes, the width L=π/(2k sin θ) of which is determined by the wave vector k and the angle between them, and the length is determined by the size of the system. We demonstrate that the measured dependence Ω(t) can be described within the recently developed model that considers the Eulerian contribution to the generated vortex flow and the effect of surface contamination.

Author(s):  
John A. Adam

This chapter deals with the underlying mathematics of surface gravity waves, defined as gravity waves observed on an air–sea interface of the ocean. Surface gravity waves, or surface waves, differ from internal waves, gravity waves that occur within the body of the water (such as between parts of different densities). Examples of gravity waves are wind-generated waves on the water surface, as well tsunamis and ocean tides. Wind-generated gravity waves on the free surface of the Earth's seas, oceans, ponds, and lakes have a period of between 0.3 and 30 seconds. The chapter first describes the basic fluid equations before discussing the dispersion relations, with a particular focus on deep water waves, shallow water waves, and wavepackets. It also considers ship waves and how dispersion affects the wave pattern produced by a moving object, along with long and short waves.


2012 ◽  
Vol 42 (5) ◽  
pp. 725-747 ◽  
Author(s):  
Hidenori Aiki ◽  
Richard J. Greatbatch

Abstract The residual effect of surface gravity waves on mean flows in the upper ocean is investigated using thickness-weighted mean (TWM) theory applied in a vertically Lagrangian and horizontally Eulerian coordinate system. Depth-dependent equations for the conservation of volume, momentum, and energy are derived. These equations allow for (i) finite amplitude fluid motions, (ii) the horizontal divergence of currents, and (iii) a concise treatment of both kinematic and viscous boundary conditions at the sea surface. Under the assumptions of steady and monochromatic waves and a uniform turbulent viscosity, the TWM momentum equations are used to illustrate the pressure- and viscosity-induced momentum fluxes through the surface, which are implicit in previous studies of the wave-induced modification of the classical Ekman spiral problem. The TWM approach clarifies, in particular, the surface momentum flux associated with the so-called virtual wave stress of Longuet-Higgins. Overall, the TWM framework can be regarded as an alternative to the three-dimensional Lagrangian mean framework of Pierson. Moreover, the TWM framework can be used to include the residual effect of surface waves in large-scale circulation models. In specific models that carry the TWM velocity appropriate for advecting tracers as their velocity variable, the turbulent viscosity term should be modified so that the viscosity acts only on the Eulerian mean velocity.


Author(s):  
Sudebi Bhattacharyya ◽  
K. P. Das

AbstractThe effect of randomness on the stability of deep water surface gravity waves in the presence of a thin thermocline is studied. A previously derived fourth order nonlinear evolution equation is used to find a spectral transport equation for a narrow band of surface gravity wave trains. This equation is used to study the stability of an initially homogeneous Lorentz shape of spectrum to small long wave-length perturbations for a range of spectral widths. The growth rate of the instability is found to decrease with the increase of spectral widths. It is found that the fourth order term in the evolution equation produces a decrease in the growth rate of the instability. There is stability if the spectral width exceeds a certain critical value. For a vanishing bandwidth the deterministic growth rate of the instability is recovered. Graphs have been plotted showing the variations of the growth rate of the instability against the wavenumber of the perturbation for some different values of spectral width, thermocline depth, angle of perturbation and wave steepness.


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