[zhxter]

Dear ngj,
Thank you for you advice on trying stokes second theory to simulate regular waves with large height.

The wave elevation for stokessecond theory in waves2Foam (stokesSecond.C) is as follows:

scalar stokesSecond::eta
(
const point& x,
const scalar& time
) const
{
scalar arg(omega_*time - (k_ & x) + phi_);

scalar eta = (
H_/2.0*Foam::cos(arg) // First order contribution.
// Second order contribution.
+ 1.0/16.0*K_*sqr(H_)
*(
3.0/Foam:ow(Foam::tanh(K_*h_),3.0)
- 1.0/Foam::tanh(K_*h_)
)
*Foam::cos(2.0*arg)
)*factor(time) // Hot-starting.
+ seaLevel_; // Adding sea level.

return eta;
}

However, I have some questions about the second order contribution presented above, which is different from the common stokes second oder theory. To my knowledge, the second order distribution is :

1.0/16.0*K_*sqr(H_)
*(
(2.0*Foam:ow(Foam::cosh(K_*h_),3.0)+Foam::cosh(K _*h_))/
Foam:ow(Foam::sinh(K_*h_),3.0)
)
*Foam::cos(2.0*arg)
Hope to receive your reply.

[ngj]

Good morning all,

@Xiantao: If you had plotted the two expressions on top of each other, you would have realised that they are identical. It should be possible to show analytically as well.

Kind regards,

Niels