scalar cnoidalFirst::ddxPd
(
const point & x,
const scalar & time,
const vector & unitVector
) const
{
scalar Z(returnZ(x));
scalar arg(argument(x,time));
scalar snn(0.0), cnn(0.0), dnn(0.0);
gsl_sf_elljac_e( arg, m_, &snn, &cnn, &dnn);
scalar ddxPd(0);
ddxPd = rhoWater_ * Foam::mag(g_)
* (
eta_x(snn, cnn, dnn) + 1.0 / 2.0 * Foam::pow(h_, 2.0) * (1 - Foam::pow((Z + h_) / h_, 2.0)) * eta_xxx(snn, cnn, dnn)
);
ddxPd *= factor(time);
// Info << "ddxPd still isn't implemented. Need to think about the gradient on arbitrary directed mesh with arbitrary wave number vector! and arbitrary g-direction!!!" << endl;
return ddxPd;
}
vector stokesFirstStanding::U
(
const point& x,
const scalar& time
) const
{
scalar Z(returnZ(x));
scalar Uhorz = PI_*H_/period_ *
Foam::cosh(K_*(Z + h_))/Foam::sinh(K_*h_) *
Foam::cos(omega_*time - (k_ & x) + phi_)
- PI_*H_/period_ *
Foam::cosh(K_*(Z + h_))/Foam::sinh(K_*h_) *
Foam::cos(omega_*time + (k_ & x) + phi_);
Uhorz *= factor(time);
scalar Uvert = - PI_*H_/period_ *
Foam::sinh(K_*(Z + h_))/Foam::sinh(K_*h_) *
Foam::sin(omega_*time - (k_ & x) + phi_)
- PI_*H_/period_ *
Foam::sinh(K_*(Z + h_))/Foam::sinh(K_*h_) *
Foam::sin(omega_*time + (k_ & x) + phi_);
Uvert *= factor(time);
// Note "-" because of "g" working in the opposite direction
return Uhorz*k_/K_ - Uvert*direction_;
}
vector cnoidalFirst::U
(
const point & x,
const scalar & time
) const
{
scalar Z(returnZ(x));
scalar arg(argument(x, time));
scalar snn(0.0), cnn(0.0), dnn(0.0);
gsl_sf_elljac_e( arg, m_, &snn, &cnn, &dnn);
scalar etaVal = eta(x,time);
scalar Uhorz = celerity_
* (
etaVal / h_
- Foam::pow(etaVal / h_, 2.0)
+ 1.0 / 2.0 *
(
1.0 / 3.0
- Foam::pow((Z + h_) / h_, 2.0)
)
* h_ * eta_xx(snn, cnn, dnn)
);
Uhorz *= factor(time);
scalar Uvert = - celerity_ * (Z + h_)
* (
eta_x(snn, cnn, dnn) / h_ * (1 - 2.0 * etaVal / h_)
+ 1.0 / 6.0 * h_ * eta_xxx(snn, cnn, dnn)
* (1 - Foam::pow((Z + h_) / h_, 2.0))
);
Uvert *= factor(time);
return Uhorz * propagationDirection_ - Uvert * direction_; // Note "-" because of "g" working in the opposite direction
}
scalar stokesFirstStanding::ddxPd
(
const point& x,
const scalar& time,
const vector& unitVector
) const
{
scalar Z(returnZ(x));
scalar arg1(omega_*time - (k_ & x) + phi_);
scalar arg2(omega_*time + (k_ & x) + phi_);
scalar ddxPd(0);
ddxPd = (
rhoWater_*mag(g_)*K_*H_/2.0*Foam::cosh(K_*(Z + h_))
/Foam::cosh(K_*h_)*Foam::sin(arg1)
- rhoWater_*mag(g_)*K_*H_/2.0*Foam::cosh(K_*(Z + h_))
/Foam::cosh(K_*h_)*Foam::sin(arg2)
)*factor(time);
return ddxPd;
}
