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SUMMARY:Vortex waves in deep water: Lagrange approach - Anatoly Abrashkin 
 (Higher School of Economics\, Moscow)
DTSTART:20170810T160000Z
DTEND:20170810T170000Z
UID:TALK75381@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:A lecture consists of two parts. The first one deals with a th
 eory of weakly nonlinear vortex waves. The vorticity is set in the series 
 expansion in the small parameter of wave steepness. Each term of this row 
 is an arbitrary function of the vertical Lagrange coordinate. We study dif
 ferent types of the waves: the stationary waves on shear flow\, the standi
 ng vortex waves and the spatial vortex waves in the low vorticity fluid. T
 he perturbation theory up to the third order is analyzed. The nonlinear Sc
 hr&ouml\;dinger (NLS) equation describing weakly nonlinear wave packets in
  an infinity-depth fluid with non-uniform vorticity is obtained. The vorti
 city is assumed to be an arbitrary function of both Lagrangian coordinates
  and quadratic in the small parameter proportional to the wave&rsquo\;s st
 eepness. The effects of vorticity are manifested in a shift of the wavenum
 ber of the carrier wave and a changing of the coefficient in nonlinear ter
 m of the NLS equation. The modulated Gouyon waves are studied. There is a 
 special case of the vortex waves for which the resulting non-linearity in 
 the NLS equation vanishes. The Gerstner wave belongs among them. The secon
 d part of the lecture presents the theory of strongly nonlinear waves. A v
 ortex model of a rogue wave formation at the background of uniform waves i
 s proposed. It based on an exact analytical solution of equations of 2D hy
 drodynamics of an ideal incompressible fluid. A unique feature of flows of
  this class is the dependence of complex coordinate of liquid particle&rsq
 uo\;s motion on two functions that may be arbitrary to a large extent. As 
 a consequence the model may be used for the analysis of different forms of
  surface pressure as well as of liquid vorticity\, i.e. when taking into a
 ccount both these factors of air flow impact on the surface waves simultan
 eously. A process of formation of a rogue wave in the field of the Gerstne
 r wave is studied. The physical parameters of the rogue wave and feasibili
 ty of the proposed scenario are disc.
LOCATION:Seminar Room 1\, Newton Institute
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