394 research outputs found
Numerical modeling of quasiplanar giant water waves
In this work we present a further analytical development and a numerical
implementation of the recently suggested theoretical model for highly nonlinear
potential long-crested water waves, where weak three-dimensional effects are
included as small corrections to exact two-dimensional equations written in the
conformal variables [V.P. Ruban, Phys. Rev. E 71, 055303(R) (2005)]. Numerical
experiments based on this theory describe the spontaneous formation of a single
weakly three-dimensional large-amplitude wave (alternatively called freak,
killer, rogue or giant wave) on the deep water.Comment: revtex4, 8 pages, 7 figure
Branch cuts of Stokes wave on deep water. Part I: Numerical solution and Pad\'e approximation
Complex analytical structure of Stokes wave for two-dimensional potential
flow of the ideal incompressible fluid with free surface and infinite depth is
analyzed. Stokes wave is the fully nonlinear periodic gravity wave propagating
with the constant velocity. Simulations with the quadruple and variable
precisions are performed to find Stokes wave with high accuracy and study the
Stokes wave approaching its limiting form with radians angle on the
crest. A conformal map is used which maps a free fluid surface of Stokes wave
into the real line with fluid domain mapped into the lower complex half-plane.
The Stokes wave is fully characterized by the complex singularities in the
upper complex half-plane. These singularities are addressed by rational
(Pad\'e) interpolation of Stokes wave in the complex plane. Convergence of
Pad\'e approximation to the density of complex poles with the increase of the
numerical precision and subsequent increase of the number of approximating
poles reveals that the only singularities of Stokes wave are branch points
connected by branch cuts. The converging densities are the jumps across the
branch cuts. There is one branch cut per horizontal spatial period of
Stokes wave. Each branch cut extends strictly vertically above the
corresponding crest of Stokes wave up to complex infinity. The lower end of
branch cut is the square-root branch point located at the distance from
the real line corresponding to the fluid surface in conformal variables. The
limiting Stokes wave emerges as the singularity reaches the fluid surface.
Tables of Pad\'e approximation for Stokes waves of different heights are
provided. These tables allow to recover the Stokes wave with the relative
accuracy of at least . The tables use from several poles to about
hundred poles for highly nonlinear Stokes wave with Comment: 38 pages, 9 figures, 4 tables, supplementary material
Free Surface in 2D Potential Flow: Singularities, Invariants and Virtual Fluid
We study a 2D potential flow of an ideal fluid with a free surface with
decaying conditions at infinity. By using the conformal variables approach, we
study a particular solution of Euler equations having a pair of square-root
branch points in the conformal plane, and find that the analytic continuation
of the fluid complex potential and conformal map define a flow in the entire
complex plane, excluding a vertical cut between the branch points. The expanded
domain is called the "virtual" fluid, and it contains a vortex sheet whose
dynamics is equivalent to the equations of motion posed at the free surface.
The equations of fluid motion are analytically continued to both sides of the
vertical branch cut (the vortex sheet), and additional time-invariants
associated with the topology of conformal plane and Kelvin's theorem for
virtual fluid are explored. We called them "winding" and virtual circulation.
This result can be generalized to a system of many cuts connecting many branch
points, and resulting in a pair of invariants for each pair of branch points.
We develop an asymptotic theory that shows how a solution originating from a
single vertical cut forms a singularity at the free surface in infinite time,
the rate of singularity approach is double-exponential, and supercedes the
previous result of the short branch cut theory with finite time singularity
formation. The present work offers a new look at fluid dynamics with free
surface by unifying the problem of motion of vortex sheets, and the problem of
2D water waves. A particularly interesting question that arises in this context
is whether instabilities of the virtual vortex sheet are related to breaking of
steep ocean waves when gravity effects are included
On the Quantum Kinetic Equation in Weak Turbulence
The quantum kinetic equation used in the study of weak turbulence is
reconsidered in the context of a theory with a generic quartic interaction. The
expectation value of the time derivative of the mode number operators is
computed in a perturbation expansion which places the large diagonal component
of the quartic term in the unperturbed Hamiltonian. Although one is not
perturbing around a free field theory, the calculation is easily tractable
owing to the fact that the unperturbed Hamiltonian can be written solely in
terms of the mode number operators.Comment: 12 pages, LATEX, no figures, to appear in Phys. Rev.
Studying the utilization techniques of ammonium hexafluorosilicate
The utilization techniques of ammonium hexafluorosilicate have been proposed and studied. Thermodynamic calculations of equilibrium gas phase compositions of topaz concentrate fluoridation reaction and reaction of (NH4)2SiF6 absorption by ammonium hydroxide were given. Experimental investigations in studying gas phase composition were carried out. The sublimation process of ammonium hexafluorosilicate as well as the process of its dissolving in ammonia water with silicon dioxide obtaining was studie
Topaz concentrate desiliconization with ammonium bifluoride
Fluoridizing agent for the process of topaz concentrate desiliconization has been selected, topaz thermodynamic potentials have been appraised, thermodynamic probabilities of fluorination reaction of topaz concentrate main constituents have been calculated. The results of studying the concentrate desiliconization process with ammonium bifluoride by the methods of thermogravimetry, RFA, microphotography are presente
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