On Zakharov's kernel and the interaction of non-collinear wavetrains in finite water depth

2009 ◽  
Vol 639 ◽  
pp. 433-442 ◽  
Author(s):  
MICHAEL STIASSNIE ◽  
ODIN GRAMSTAD
Keyword(s):  
Gravity Waves ◽  
Water Depth ◽  
Finite Depth ◽  
Mean Flow ◽  
Finite Water Depth ◽  
Physical Insight

The non-uniqueness of Zakharov's kernel T(ka, kb, ka, kb) for gravity waves in water of finite depth is resolved. This goal is achieved by the physical insight gained from the study of the induced mean flow generated by two interacting wavetrains.

scholarly journals Focusing wave group on a current of finite depth

2013 ◽  
Vol 13 (11) ◽  
pp. 2941-2949 ◽  
Author(s):  
D. Merkoune ◽  
J. Touboul ◽  
N. Abcha ◽  
D. Mouazé ◽  
A. Ezersky
Keyword(s):  
Numerical Simulations ◽  
Water Depth ◽  
Focal Point ◽  
Wave Train ◽  
Finite Depth ◽  
Freak Waves ◽  
Finite Water Depth ◽  
Wave Maker ◽  
A Current ◽  
Good Agreement

Abstract. Formation of freak waves resulting from the wave packets propagating in finite water depth on the background of a current is studied experimentally and numerically. In the experiment, the freak waves appear as a result of dispersion focusing of wave train excited by wave maker with modulated frequency. The space evolution of the frequency modulated train is studied in numerical simulations. We showed that in the water of finite depth, a distance of focusing increases and amplitude in the focal point decreases in comparison with infinite water depth. Experimental results are in good agreement with numerical simulations if wave breaking of surface waves does not occur.

Diffraction of sea waves by a slender body. Part 2. Water of finite depth

1990 ◽  
Vol 216 ◽  
pp. 133-160 ◽  
Author(s):  
J. A. P. Aranha ◽  
C. A. Martins
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Body Part ◽  
Finite Depth ◽  
Second Order ◽  
Slender Body ◽  
Sea Waves ◽  
Finite Water Depth

A uniformly valid theory (all wavelengths and angles of incidence) for the diffraction of sea waves by a slender body, correct to second order in the slenderness parameter, has been derived for the shallow-water limit. This theory is now extended to the finite water depth case, with the same results and accuracy.

scholarly journals Theoretical Studies of Convectively Forced Mesoscale Flows in Three Dimensions. Part II: Shear Flow with a Critical Level

2010 ◽  
Vol 67 (3) ◽  
pp. 694-712 ◽  
Author(s):  
Ji-Young Han ◽  
Jong-Jin Baik
Keyword(s):  
Shear Flow ◽  
Gravity Waves ◽  
Wind Direction ◽  
Critical Level ◽  
Deep Convection ◽  
Vertical Wind Shear ◽  
Finite Depth ◽  
Vertical Displacement ◽  
Two Dimensions ◽  
Three Dimensions

Abstract Convectively forced mesoscale flows in a shear flow with a critical level are theoretically investigated by obtaining analytic solutions for a hydrostatic, nonrotating, inviscid, Boussinesq airflow system. The response to surface pulse heating shows that near the center of the moving mode, the magnitude of the vertical velocity becomes constant after some time, whereas the magnitudes of the vertical displacement and perturbation horizontal velocity increase linearly with time. It is confirmed from the solutions obtained in present and previous studies that this result is valid regardless of the basic-state wind profile and dimension. The response to 3D finite-depth steady heating representing latent heating due to cumulus convection shows that, unlike in two dimensions, a low-level updraft that is necessary to sustain deep convection always occurs at the heating center regardless of the intensity of vertical wind shear and the heating depth. For deep heating across a critical level, little change occurs in the perturbation field below the critical level, although the heating top height increases. This is because downward-propagating gravity waves induced by the heating above, but not near, the critical level can hardly affect the flow response field below the critical level. When the basic-state wind backs with height, the vertex of V-shaped perturbations above the heating top points to a direction rotated a little clockwise from the basic-state wind direction. This is because the V-shaped perturbations above the heating top is induced by upward-propagating gravity waves that have passed through the layer below where the basic-state wind direction is clockwise relative to that above.

scholarly journals On strongly nonlinear gravity waves in a vertically sheared atmosphere

2020 ◽  
Vol 6 (1) ◽  
pp. 63-74
Author(s):  
Mark Schlutow ◽  
Georg S. Voelker
Keyword(s):  
Gravity Waves ◽  
Lower Layer ◽  
Vertical Shear ◽  
Horizontal Wind ◽  
Necessary Condition ◽  
Mean Flow ◽  
Individual Layer ◽  
Strongly Nonlinear ◽  
The Mean ◽  
The Stability

Abstract We investigate strongly nonlinear stationary gravity waves which experience refraction due to a thin vertical shear layer of horizontal background wind. The velocity amplitude of the waves is of the same order of magnitude as the background flow and hence the self-induced mean flow alters the modulation properties to leading order. In this theoretical study, we show that the stability of such a refracted wave depends on the classical modulation stability criterion for each individual layer, above and below the shearing. Additionally, the stability is conditioned by novel instability criteria providing bounds on the mean-flow horizontal wind and the amplitude of the wave. A necessary condition for instability is that the mean-flow horizontal wind in the upper layer is stronger than the wind in the lower layer.

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