关于nutkAtmRoughWallFunction中nutw公式的疑问

LuoS

文件来源：atmosphericModels/derivedFvPatchFields/nutkAtmRoughWallFunction
头文件描述：

Description
    This boundary condition provides a turbulent kinematic viscosity for
    atmospheric velocity profiles.  It is desinged to be used in conjunction
    with the atmBoundaryLayerInletVelocity boundary condition.  The values
    are calculated using:

        \f[
            U = frac{U_f}{K} ln(\frac{z + z_0}{z_0})
        \f]

    where

    \vartable
        U_f | frictional velocity
        K   | Von Karman's constant
        z_0 | surface roughness length
        z   | vertical co-ordinate
    \endvartable

程序代码：

tmp<scalarField> nutkAtmRoughWallFunctionFvPatchScalarField::calcNut() const
{
    const label patchi = patch().index();

    const turbulenceModel& turbModel = db().lookupObject<turbulenceModel>
    (
        IOobject::groupName
        (
            turbulenceModel::propertiesName,
            internalField().group()
        )
    );
    const scalarField& y = turbModel.y()[patchi];
    const tmp<volScalarField> tk = turbModel.k();
    const volScalarField& k = tk();
    const tmp<scalarField> tnuw = turbModel.nu(patchi);
    const scalarField& nuw = tnuw();

    const scalar Cmu25 = pow025(Cmu_);

    tmp<scalarField> tnutw(new scalarField(*this));
    scalarField& nutw = tnutw.ref();

    forAll(nutw, facei)
    {
        label celli = patch().faceCells()[facei];

        scalar uStar = Cmu25*sqrt(k[celli]);
        scalar yPlus = uStar*y[facei]/nuw[facei];

        scalar Edash = (y[facei] + z0_[facei])/z0_[facei];

        nutw[facei] =
            nuw[facei]*(yPlus*kappa_/log(max(Edash, 1+1e-4)) - 1);

        if (debug)
        {
            Info<< "yPlus = " << yPlus
                << ", Edash = " << Edash
                << ", nutw = " << nutw[facei]
                << endl;
        }
    }

    return tnutw;
}

疑问：头文件描述中并未展示公式的来源，故无从得知该壁面函数的推导过程，更无法获知该壁面函数的适用条件。
求教：哪位大神知道这个壁面函数的来源吗？
备注：OpenFOAM初学，扒扒公式。

LuoS

《A Thorough Description Of How Wall Functions Are Implemented In OpenFOAM》一文2.6节描述了nutWallFunction，nutAtmRoughWallFunction中nutw公式与之相同，其他量有改变，我再看看。

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关于nutkAtmRoughWallFunction中nutw公式的疑问