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Solitary Water Wave

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Solitary Water Wave



27 Nov 2012 (Updated )

Solitary gravity wave solution of the free surface Euler equations

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Computes the steady irrotational surface solitary gravity wave solution of the Euler equations (homogeneous, incompressible and perfect fluids). The wave is defined by its Froude number Fr and the result is about fifteen digits accurate. The method works for all but the highest waves, i.e. for all amplitude/depth ratio less than 0.796.
SolitaryGravityWave(Fr,[],1); % plot results only
[zs,ws,fs,SWP] = SolitaryGravityWave(Fr); % output results at the surface and parameters
[zs,ws,fs,SWP,W,F,P,A] = SolitaryGravityWave(Fr,Z); % surface and bulk output
[zs,ws,fs,SWP,W,F,P,A] = SolitaryGravityWave(Fr,Z,1);

Fr : Froude number (must be a scalar).
Z : Complex abscissa where fields are desired inside the fluid (default Z = []).
      Z should be strictly below the surface, i.e., -1 <= imag(Z) < eta(real(Z))
      y = eta(x) being the equation of the free surface.
PF : Plot Flag. If PF=1 the final results are plotted, if PF~=1 nothing is plotted (default).

OUTPUT (dimensionless quantities):
zs : Complex abscissa at the surface, i.e., x + i*eta.
ws : Complex velocity at the surface, i.e., u - i*v.
fs : Complex potential at the surface, i.e., phi + i*psi.
SWP : Solitary Wave Parameters, i.e.
        SWP(1) = wave amplitude, max(eta)
        SWP(2) = wave mass
        SWP(3) = circulation
        SWP(4) = impulse
        SWP(5) = kinetic energy
        SWP(6) = potential energy
W : Complex velocity in the bulk at abscissas Z.
F : Complex potential in the bulk at abscissas Z.
P : Pressure in the bulk at abscissas Z.
A : Complex acceleration in the bulk at abscissas Z (A = dW / dt).


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This file inspired Solitary Capillary Gravity Wave.

MATLAB release MATLAB 7.14 (R2012a)
Other requirements The m-file should work with older versions, except perhaps for the graphic output (but this is a secondary feature here).
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15 Feb 2013 1.1

Added reference.

19 Feb 2013 1.2

Corrected link to the reference

05 Mar 2014 1.3

Added the file SolitaryGravityAmplitude.m for waves defined by amplitude instead of Froude number.

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