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ABSTRACT: Nonlinear corrections to the frequencies of surface and subsurface waves are obtained in calculations of the third order of smallness in dimensionless amplitude. It is found that the corrections are of a resonance character; that is, they indefinitely grow at certain values of physical quantities, going out of an asymptotic limit. Under resonance conditions, the nonlinear correction to the frequency of waves on the free surface may change sign and so both increase and decrease the frequency. At the interface, the nonlinear correction to the frequency is everywhere negative except in the neighborhood of the resonance point. Therefore, it decreases the frequencies of the waves as a rule. No preview · Article · Jun 2015 · Technical Physics

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ABSTRACT: Analytical expressions for the decay rates of surface (on the free boundary) and internal (on the interface) waves in a twolayer fluid are derived in the small kinematic viscosity asymptotics. The internal wave decay rates are found to be approximately two orders smaller than those of the surface waves, which is attributable to the difference in their frequencies, all other factors being the same. The decay rates depend on the kinematic viscosities of both media but, when the viscosity of one of the media is small, they are chiefly determined by the viscosity of the other medium, which allows one to use the model of the contact between viscous and inviscid media. The frequencies of the capillary surface and internal waves in the capillary counterpart of the “dead water” effect considerably differ in value which has an effect on the large difference in the decay rates. No preview · Article · Nov 2014 · Fluid Dynamics

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ABSTRACT: Eight nonlinear resonances may arise in a twolayer liquid with a free surface, as follows from asymptotic calculations of the second order of smallness. Two of them involve waves generated by either surface, and six mixed resonances involve waves generated by different surfaces. Of these six resonances, two are degenerate and the remaining four are secondary combination resonances. However, not all of them are observed in practice. In the mixed combination resonances, interaction arises only between surface waves provided that the internal wave (which does not change its parameters but is necessary for the resonance to occur) has a catalytic influence. No preview · Article · Sep 2014 · Technical Physics

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ABSTRACT: The influence of a solid bottom on the “dead water” effect for gravitational and fluctuation waves (having the same dispersion law), as well as capillary waves, is calculated in a linear statement. It is found that the presence of a solid bottom aggravates the dead water effect. No preview · Article · Nov 2012 · Technical Physics

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ABSTRACT: It is shown that the capillary analogue of the deadwater effect strongly depends on an external electrostatic field: in the presence of the field, the number of nonlinear resonance situations increases sharply. The field increases the wave amplitudes and excites both degenerate and secondary combination resonances, which are not observed without the field. No preview · Article · Jun 2012 · Technical Physics

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ABSTRACT: The nonlinear capillary wave motion in a twolayer liquid with a free surface is analytically investigated accurate to the second order of smallness in ratio of the wave amplitude to the layer thickness. The layers differ in physicochemical properties. A capillary analogue to the “dead water” effect is observed in the system in both linear and quadratic approximations. In the absence of an electric charge at the interfaces, internal nonlinear resonance interaction between capillary waves is also absent regardless of the place of their origination. When there is a charge at the interlayer boundary, capillary waves resonantly interact with each other. No preview · Article · Nov 2011 · Technical Physics

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ABSTRACT: Regularities of the nonlinear gravitational wave motion in a twolayer densitystratified fluid are investigated for a finite
thickness of the upper, lighter, layer. The characteristics of the nonlinear internal resonant interaction of the gravity
waves generated by the free surface of the upper layer and the medium interface are considered. It is shown that in secondorder
calculations both degenerate (twowave) and secondary combined (threewave) resonant interactions may be realized. No preview · Article · Oct 2010 · Fluid Dynamics

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ABSTRACT: In terms of a linear mathematical model of a capillarygravitational flow in a twolayer liquid with a finitethickness upper
layer, it is shown analytically that an analogue of the dead water phenomenon exists in the domain of capillary waves, which
was previously observed only in gravitational waves. This phenomenon shows up as an exponential increase in the capillary
wave amplitude at the interface with the surface tension coefficient at the interface tending to zero. It is found that an
external electric field displaces this phenomenon toward the range of finite surface tension coefficients. No preview · Article · Jul 2010 · Technical Physics