Foam::graph Foam::kShellIntegration
(
const complexVectorField& Ek,
const Kmesh& K
)
{
// evaluate the radial component of the spectra as an average
// over the shells of thickness dk
graph kShellMeanEk = kShellMean(Ek, K);
const scalarField& x = kShellMeanEk.x();
scalarField& y = *kShellMeanEk.begin()();
// now multiply by 4pi k^2 (the volume of each shell) to get the
// spectra E(k). int E(k) dk is now the total energy in a box
// of side 2pi
y *= sqr(x)*4.0*constant::mathematical::pi;
// now scale this to get the energy in a box of side l0
scalar l0(K.sizeOfBox()[0]*(scalar(K.nn()[0])/(scalar(K.nn()[0])-1.0)));
scalar factor = pow((l0/(2.0*constant::mathematical::pi)),3.0);
y *= factor;
// and divide by the number of points in the box, to give the
// energy density.
y /= scalar(K.size());
return kShellMeanEk;
}
Foam::graph Foam::kShellMean
(
const complexVectorField& Ek,
const Kmesh& K
)
{
const label tnp = Ek.size();
const label NoSubintervals = label
(
pow(scalar(tnp), 1.0/vector::dim)*pow(1.0/vector::dim, 0.5) - 0.5
);
scalarField k1D(NoSubintervals);
scalarField Ek1D(NoSubintervals);
scalarField EWeight(NoSubintervals);
scalar kmax = K.max()*pow(1.0/vector::dim,0.5);
scalar delta_k = kmax/(NoSubintervals);
forAll(Ek1D, a)
{
k1D[a] = (a + 1)*delta_k;
Ek1D[a] = 0.0;
EWeight[a] = 0;
}
graph calcEk
(
const volVectorField& U,
const Kmesh& K
)
{
return kShellIntegration
(
fft::forwardTransform
(
ReComplexField(U.internalField()),
K.nn()
),
K
);
}
