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    #pragma once
    
    // [bl-turb.h]: boundary-layer turbulence statistics and budgets
    //
    // -------------------------------------------------------------------------------------------- //
    
    #include "wstgrid3d.h"
    
    //
    // *[Note]: we need gcz >= 2 for computation of production terms:
    //         _            _
    //        dU           dV
    // - w'w' -- ,  - w'w' --
    //        dz           dz
    //
    
    
    namespace nse
    {
    	// Friction velocity (get)
    	// -------------------------------------------------------------------------------------------- //
    	template< typename T >
    	T dynamic_velocity(T* U_z,
    		const T Umax, const T c_kinematic_viscosity, const wstGrid3d< T >& grid);
    	// -------------------------------------------------------------------------------------------- //
    
    	// Gradients
    	// -------------------------------------------------------------------------------------------- //
    	template< typename T >
    	void c_gradient_z(T* Grad,		// node: [W]
    		const T* const C,			// node: [C]
    
    		const nse_const3d::axisType axis, const wstGrid3d< T >& grid);	// [axisZ || axisYZ]
    
    	template< typename T >
    	void w_gradient_z(T* Grad,		// node: [C]
    		const T* const W,			// node: [W]
    
    		const nse_const3d::axisType axis, const wstGrid3d< T >& grid);	// [axisZ || axisYZ]
    	// -------------------------------------------------------------------------------------------- //
    
    	// Momentum eq. balance
    	// -------------------------------------------------------------------------------------------- //
    	template< typename T >
    	void momentum_eq(
    		T* momentum_balance,			// node: [W]
    		T* turbulent_momentum_flux,		// node: [W]
    		T* viscous_stress,				// node: [W]
    
    		const T* const uw_flux,			// node: [W]
    		const T* const U_grad,			// node: [W]
    		const T c_kinematic_viscosity, const wstGrid3d< T >& grid);
    	// -------------------------------------------------------------------------------------------- //
    
    	// TKE structure
    	// -------------------------------------------------------------------------------------------- //
    	template< typename T >
    	void TKE_structure(T* TKE,								// node: [C]
    		T* u_TKE, T* v_TKE, T* w_TKE,						// node: [C]
    		T* u_TKE_share, T* v_TKE_share, T* w_TKE_share,		// node: [C]
    
    		const T* const U2,		// node: [C]
    		const T* const V2,		// node: [C]
    		const T* const W2,		// node: [C]
    		const T* const U,		// node: [C]
    		const T* const V,		// node: [C]
    		const T* const W,		// node: [W]
    		const wstGrid3d< T >& grid);
    	// -------------------------------------------------------------------------------------------- //
    
    	// TKE anisotropy
    	// -------------------------------------------------------------------------------------------- //
    	template< typename T >
    	void TKE_anisotropy(
    		T* TKE_aniso_uu, T* TKE_aniso_vv, T* TKE_aniso_ww,	// node: [C]
    		T* TKE_aniso_uv, T* TKE_aniso_uw, T* TKE_aniso_vw,	// node: [C]
    
    		const T* const TKE,			// node: [C]
    		const T* const u_TKE,		// node: [C]
    		const T* const v_TKE,		// node: [C]
    		const T* const w_TKE,		// node: [C]
    		const T* const uv_flux,		// node: [C]
    		const T* const uw_flux,		// node: [W]
    		const T* const vw_flux,		// node: [W]
    		const wstGrid3d< T >& grid);
    	// -------------------------------------------------------------------------------------------- //
    
    	// TKE production
    	// -------------------------------------------------------------------------------------------- //
    	template< typename T >
    	void u_TKE_production(T* _u_TKE_production,		// node: [C]
    
    		const T* const UW_bottom,					// node: [W]
    		const T* const UW_top,						// node: [W]
    		const T* const U,							// node: [C]
    		const T* const W,							// node: [W]
    		const wstGrid3d< T >& grid);
    
    	template< typename T >
    	void v_TKE_production(T* _v_TKE_production,		// node: [C]
    
    		const T* const VW_bottom,					// node: [W]
    		const T* const VW_top,						// node: [W]
    		const T* const V,							// node: [C]
    		const T* const W,							// node: [W]
    		const wstGrid3d< T >& grid);
    
    	template< typename T >
    	void w_TKE_production(T* _w_TKE_production,		// node: [C]
    
    		const T* const W2_c,						// node: [C]
    		const T* const W2_w,						// node: [W]
    		const T* const W,							// node: [W]
    		const wstGrid3d< T >& grid);
    	// -------------------------------------------------------------------------------------------- //
    
    
    	// TKE transport
    	// -------------------------------------------------------------------------------------------- //
    	template< typename T >	// -1/2 * d[u'u'w']/dz
    	void u_TKE_transport(T* _u_TKE_transport,	// node: [C]
    
    		const T* const uu_w_flux,				// node: [W]
    		const wstGrid3d< T >& grid);
    
    	template< typename T >	// -1/2 * d[v'v'w']/dz
    	void v_TKE_transport(T* _v_TKE_transport,	// node: [C]
    
    		const T* const vv_w_flux,				// node: [W]
    		const wstGrid3d< T >& grid);
    
    	template< typename T >	// -1/2 * d[w'w'w']/dz
    	void w_TKE_transport(T* _w_TKE_transport,	// node: [C]
    
    		const T* const ww_w_flux,				// node: [C]
    		const wstGrid3d< T >& grid);
    	// -------------------------------------------------------------------------------------------- //
    
    	// TKE pressure work
    	// -------------------------------------------------------------------------------------------- //
    	template< typename T >	// - d[p'w']/dz
    	void w_TKE_pressure_work(T* _w_TKE_pressure_work,	// node: [C]
    
    		const T* const pw_flux,							// node: [W]
    		const wstGrid3d< T >& grid);
    	// -------------------------------------------------------------------------------------------- //
    
    	// TKE exchange
    	// -------------------------------------------------------------------------------------------- //
    	template< typename T >
    	void w_TKE_exchange(T* _w_TKE_energy_exchange,	// node: [C]
    		
    		const T* const PSww,						// node: [C]
    		const T* const Pressure,					// node: [C]
    		const T* const W,							// node: [W]
    		const wstGrid3d< T >& grid);
    	// -------------------------------------------------------------------------------------------- //
    
    	// TKE dissipation
    	// -------------------------------------------------------------------------------------------- //
    	template< typename T >
    	void u_TKE_dissipation(T* _u_TKE_dissipation,	// node: [C]
    
    		const T* const U_dissipation,				// node: [C]
    		const T* const U,							// node: [C]
    		const T c_kinematic_viscosity, const wstGrid3d< T >& grid);
    
    	template< typename T >
    	void v_TKE_dissipation(T* _v_TKE_dissipation,	// node: [C]
    
    		const T* const V_dissipation,				// node: [C]
    		const T* const V,							// node: [C]
    		const T c_kinematic_viscosity, const wstGrid3d< T >& grid);
    
    	template< typename T >
    	void w_TKE_dissipation(T* _w_TKE_dissipation,	// node: [C]
    
    		const T* const W_dissipation,				// node: [W]
    		const T* const W,							// node: [W]
    		const T c_kinematic_viscosity, const wstGrid3d< T >& grid);
    	// -------------------------------------------------------------------------------------------- //
    
    	// TKE iso dissipation
    	// -------------------------------------------------------------------------------------------- //
    	template< typename T >
    	void u_TKE_iso_dissipation(T* _u_TKE_iso_dissipation,	// node: [C]
    
    		const T* const U_iso_dissipation,					// node: [C]
    		const T* const U,									// node: [C]
    		const T c_kinematic_viscosity, const wstGrid3d< T >& grid);
    
    	template< typename T >
    	void v_TKE_iso_dissipation(T* _v_TKE_iso_dissipation,	// node: [C]
    
    		const T* const V_iso_dissipation,					// node: [C]
    		const T* const V,									// node: [C]
    		const T c_kinematic_viscosity, const wstGrid3d< T >& grid);
    
    	template< typename T >
    	void w_TKE_iso_dissipation(T* _w_TKE_iso_dissipation,	// node: [C]
    
    		const T* const W_iso_dissipation,					// node: [W]
    		const T* const W,									// node: [W]
    		const T c_kinematic_viscosity, const wstGrid3d< T >& grid);
    	// -------------------------------------------------------------------------------------------- //
    
    	// TKE heat flux
    	// -------------------------------------------------------------------------------------------- //
    	template< typename T >
    	void w_TKE_heat_flux(T* _w_TKE_heat_flux,	// node: [C]
    
    		const T* const Tw_flux,					// node: [W]
    		const T c_Richardson, const wstGrid3d< T >& grid);
    	// -------------------------------------------------------------------------------------------- //
    
    
    	// ui'uj' flux budget: production
    	// -------------------------------------------------------------------------------------------- //
    	template< typename T >
    	void uv_production_shearU(T* _uv_production_shearU,		// node: [C]
    
    		const T* const VW_bottom_uv,		// node: [~W-C]
    		const T* const VW_top_uv,			// node: [~W-C]
    		const T* const U,					// node: [C]
    		const T* const V,					// node: [C]
    		const T* const W,					// node: [W]
    		const wstGrid3d< T >& grid);
    
    	template< typename T >
    	void uv_production_shearV(T* _uv_production_shearV,		// node: [C]
    
    		const T* const UW_bottom_uv,		// node: [~W-C]
    		const T* const UW_top_uv,			// node: [~W-C]
    		const T* const U,					// node: [C]
    		const T* const V,					// node: [C]
    		const T* const W,					// node: [W]
    		const wstGrid3d< T >& grid);
    
    
    	template< typename T >
    	void uw_production_shearU(T* _uw_production_shearU,		// node: [W]
    
    		const T* const W2_u,				// node: [C]
    		const T* const W2_uw,				// node: [W]
    		const T* const U,					// node: [C]
    		const T* const W,					// node: [W]
    		const wstGrid3d< T >& grid);
    
    	template< typename T >
    	void uw_production_shearW(T* _uw_production_shearW,		// node: [W]
    
    		const T* const UW_bottom_uw,		// node: [~C-W]
    		const T* const UW_top_uw,			// node: [~C-W]
    		const T* const U,					// node: [C]
    		const T* const W,					// node: [W]
    		const wstGrid3d< T >& grid);
    
    
    	template< typename T >
    	void vw_production_shearV(T* _vw_production_shearV,		// node: [W]
    
    		const T* const W2_v,				// node: [C]
    		const T* const W2_vw,				// node: [W]
    		const T* const V,					// node: [C]
    		const T* const W,					// node: [W]
    		const wstGrid3d< T >& grid);
    
    	template< typename T >
    	void vw_production_shearW(T* _vw_production_shearW,		// node: [W]
    
    		const T* const VW_bottom_vw,		// node: [~C-W]
    		const T* const VW_top_vw,			// node: [~C-W]
    		const T* const V,					// node: [C]
    		const T* const W,					// node: [W]
    		const wstGrid3d< T >& grid);
    	// -------------------------------------------------------------------------------------------- //
    
    	// ui'uj' flux budget: transport
    	// -------------------------------------------------------------------------------------------- //
    	template< typename T >
    	void uv_transport(T* _uv_transport,		// node: [C]
    
    		const T* const uvw_flux,			// node: [W]
    		const wstGrid3d< T >& grid);
    
    	template< typename T >
    	void uw_transport(T* _uw_transport,		// node: [W]
    
    		const T* const uww_flux,			// node: [C]
    		const wstGrid3d< T >& grid);
    
    	template< typename T >
    	void vw_transport(T* _vw_transport,		// node: [W]
    
    		const T* const vww_flux,			// node: [C]
    		const wstGrid3d< T >& grid);
    	// -------------------------------------------------------------------------------------------- //
    
    	// ui'uj' flux budget: pressure-strain correlations: 2 * p' * S'ij, i != j
    	// -------------------------------------------------------------------------------------------- //
    	template< typename T >
    	void uw_pressure_strain(
    		T* P2Suw_turb,		// node: [W]
    		T* P2Suw_turb_c,	// node: [C] (shifting [W] -> [C])
    
    		const T* const P2Suw,		// node: [W]
    		const T* const Pressure,	// node: [C]
    		const T* const U,			// node: [C]
    		const wstGrid3d< T >& grid);
    
    	template< typename T >
    	void vw_pressure_strain(
    		T* P2Svw_turb,		// node: [W]
    		T* P2Svw_turb_c,	// node: [C] (shifting [W] -> [C])
    
    		const T* const P2Svw,		// node: [C]
    		const T* const Pressure,	// node: [C]
    		const T* const V,			// node: [C]
    		const wstGrid3d< T >& grid);
    	// -------------------------------------------------------------------------------------------- //
    
    	// ui'uj' flux budget: pressure work
    	// -------------------------------------------------------------------------------------------- //
    	template< typename T >
    	void uw_pressure_work(T* _uw_pressure_work,		// node: [W]
    
    		const T* const pu_flux,						// node: [C]
    		const wstGrid3d< T >& grid);
    
    	template< typename T >
    	void vw_pressure_work(T* _vw_pressure_work,		// node: [W]
    
    		const T* const pv_flux,						// node: [C]
    		const wstGrid3d< T >& grid);
    	// -------------------------------------------------------------------------------------------- //
    
    	// ui'uj' flux budget: dissipation
    	// -------------------------------------------------------------------------------------------- //
    	template< typename T >
    	void uv_dissipation(T* _uv_dissipation,		// node: [C]
    
    		const T* const UV_dissipation,			// node: [C]
    		const T* const U,						// node: [C]
    		const T* const V,						// node: [C]
    		const T c_kinematic_viscosity,
    		const wstGrid3d< T >& grid);
    
    	template< typename T >
    	void uw_dissipation(T* _uw_dissipation,		// node: [W]
    
    		const T* const UW_dissipation,			// node: [W]
    		const T* const U,						// node: [C]
    		const T* const W,						// node: [W]
    		const T c_kinematic_viscosity,
    		const wstGrid3d< T >& grid);
    
    	template< typename T >
    	void vw_dissipation(T* _vw_dissipation,		// node: [W]
    
    		const T* const VW_dissipation,			// node: [W]
    		const T* const V,						// node: [C]
    		const T* const W,						// node: [W]
    		const T c_kinematic_viscosity,
    		const wstGrid3d< T >& grid);
    	// -------------------------------------------------------------------------------------------- //
    
    	// ui'uj' flux budget: iso dissipation
    	// -------------------------------------------------------------------------------------------- //
    	template< typename T >
    	void uv_iso_dissipation(T* _uv_iso_dissipation,		// node: [C]
    
    		const T* const UV_iso_dissipation,				// node: [C]
    		const T* const U,								// node: [C]
    		const T* const V,								// node: [C]
    		const T c_kinematic_viscosity,
    		const wstGrid3d< T >& grid);
    
    	template< typename T >
    	void uw_iso_dissipation(T* _uw_iso_dissipation,		// node: [W]
    
    		const T* const UW_iso_dissipation,				// node: [W]
    		const T* const U,								// node: [C]
    		const T* const W,								// node: [W]
    		const T c_kinematic_viscosity,
    		const wstGrid3d< T >& grid);
    
    	template< typename T >
    	void vw_iso_dissipation(T* _vw_iso_dissipation,		// node: [W]
    
    		const T* const VW_iso_dissipation,				// node: [W]
    		const T* const V,								// node: [C]
    		const T* const W,								// node: [W]
    		const T c_kinematic_viscosity,
    		const wstGrid3d< T >& grid);
    	// -------------------------------------------------------------------------------------------- //
    
    	// ui'uj' flux budget: buoyancy
    	// -------------------------------------------------------------------------------------------- //
    	template< typename T >
    	void uw_buoyancy(T* _uw_buoyancy,	// node: [W]
    
    		const T* const CU_uw,			// node: [W]
    		const T* const C,				// node: [C]
    		const T* const U,				// node: [C]
    		const T c_Richardson, const wstGrid3d< T >& grid);
    
    	template< typename T >
    	void vw_buoyancy(T* _vw_buoyancy,	// node: [W]
    
    		const T* const CV_vw,			// node: [W]
    		const T* const C,				// node: [C]
    		const T* const V,				// node: [C]
    		const T c_Richardson, const wstGrid3d< T >& grid);
    	// -------------------------------------------------------------------------------------------- //
    }
    
    
    // Friction velocity (get)
    // -------------------------------------------------------------------------------------------- //
    template< typename T >
    T nse::dynamic_velocity(T* U_z,
    	const T Umax, const T c_kinematic_viscosity, const wstGrid3d< T >& grid)
    {
    	T u_bottom = (T)0, u_top = (T)0;
    
    	if (grid.mpi_com.rank_z == 0)
    		u_bottom = sqrt((T) 2.0 * c_kinematic_viscosity *
    		fabs(U_z[grid.gcz] + (T) 0.5 * Umax) * (T) 2.0 * grid.dzmi[grid.gcz]);
    
    	if (grid.mpi_com.rank_z == grid.mpi_com.size_z - 1)
    		u_top = sqrt((T) 2.0 * c_kinematic_viscosity *
    		fabs((T) 0.5 * Umax - U_z[grid.nz - grid.gcz - 1]) * (T) 2.0 * grid.dzpi[grid.nz - grid.gcz - 1]);
    
    	mpi_allreduce(&u_bottom, &u_top, MPI_MAX, grid.mpi_com.comm);
    
    	return (T) 0.5 * (u_bottom + u_top);
    }
    // -------------------------------------------------------------------------------------------- //
    
    // Gradients
    // -------------------------------------------------------------------------------------------- //
    template< typename T >
    void nse::c_gradient_z(
    	T* Grad,					// node: [W]
    
    	const T* const C,			// node: [C]
    	const nse_const3d::axisType axis, const wstGrid3d< T >& grid)
    	//  __
    	//  dC
    	//  --
    	//	dz
    	//
    	// [C] average has to be known at all [C] nodes and ghost nodes: (k + 1/2), (k - 1/2)
    {
    	if (axis == nse_const3d::axisZ) {
    
    		int k;
    #pragma omp parallel for private(k) shared(Grad)
    		for (k = grid.gcz; k <= grid.nz - grid.gcz; k++) {	// all [W] nodes
    			Grad[k] = (C[k] - C[k - 1]) * (T) 2.0 * grid.dzmi[k];
    		}
    		return;
    	}
    	if (axis == nse_const3d::axisYZ) {
    
    		int j, k, idx;
    #pragma omp parallel for private(j, k, idx) shared(Grad)
    		for (j = grid.gcy; j < grid.ny - grid.gcy; j++)
    			for (k = grid.gcz; k <= grid.nz - grid.gcz; k++) {	// all [W] nodes
    				idx = j * grid.nz + k;
    				Grad[idx] = (C[idx] - C[idx - 1]) * (T) 2.0 * grid.dzmi[k];
    			}
    		return;
    	}
    }
    // -------------------------------------------------------------------------------------------- //
    
    template< typename T >
    void nse::w_gradient_z(
    	T* Grad,					// node: [C]
    
    	const T* const W,			// node: [W]
    	const nse_const3d::axisType axis, const wstGrid3d< T >& grid)
    	//  __
    	//  dW
    	//  --
    	//	dz
    	//
    	// [W] average has to be known at all [W] nodes, including walls
    {
    	if (axis == nse_const3d::axisZ) {
    
    		int k;
    #pragma omp parallel for private(k) shared(Grad)
    		for (k = grid.gcz; k < grid.nz - grid.gcz; k++) {
    			Grad[k] = (W[k + 1] - W[k]) * grid.dzi[k];
    		}
    		return;
    	}
    	if (axis == nse_const3d::axisYZ) {
    
    		int j, k, idx;
    #pragma omp parallel for private(j, k, idx) shared(Grad)
    		for (j = grid.gcy; j < grid.ny - grid.gcy; j++)
    			for (k = grid.gcz; k < grid.nz - grid.gcz; k++) {
    				idx = j * grid.nz + k;
    				Grad[idx] = (W[idx + 1] - W[idx]) * grid.dzi[k];
    			}
    		return;
    	}
    }
    // -------------------------------------------------------------------------------------------- //
    
    // Momentum eq. balance
    // -------------------------------------------------------------------------------------------- //
    template< typename T >
    void nse::momentum_eq(
    	T* momentum_balance,			// node: [W]
    	T* turbulent_momentum_flux,		// node: [W]
    	T* viscous_stress,				// node: [W]
    
    	const T* const uw_flux,			// node: [W]
    	const T* const U_grad,			// node: [W]
    	const T c_kinematic_viscosity, const wstGrid3d< T >& grid)
    	// integrated [U] averaged momentum equation
    	//               _
    	//    ____   1  dU
    	//	- u'w' + -- -- = (u*)^2 
    	//			 Re dz
    	//    (1)      (2)
    	// (1) - turbulent momentum flux
    	// (2) - viscous stress
    	// terms are defined at [UW] nodes (averaged in [W] nodes)
    	//
    	// [u'w', dU/dz] have to be known at all [W] nodes, including walls
    {
    	int k;
    #pragma omp parallel for private(k) shared(momentum_balance, \
    	turbulent_momentum_flux, viscous_stress)
    	for (k = grid.gcz; k <= grid.nz - grid.gcz; k++) { // all [W] nodes
    		turbulent_momentum_flux[k] = -uw_flux[k];
    		viscous_stress[k] = c_kinematic_viscosity * U_grad[k];
    
    		momentum_balance[k] = turbulent_momentum_flux[k] + viscous_stress[k];
    	}
    }
    // -------------------------------------------------------------------------------------------- //
    
    // TKE structure
    // -------------------------------------------------------------------------------------------- //
    template< typename T >
    void nse::TKE_structure(
    	T* TKE,												// node: [C]
    	T* u_TKE, T* v_TKE, T* w_TKE,						// node: [C]
    	T* u_TKE_share, T* v_TKE_share, T* w_TKE_share,		// node: [C]
    	
    	const T* const U2,		// node: [C]
    	const T* const V2,		// node: [C]
    	const T* const W2,		// node: [C]
    	const T* const U,		// node: [C]
    	const T* const V,		// node: [C]
    	const T* const W,		// node: [W]
    	const wstGrid3d< T >& grid)
    	//
    	// 1/2*u'[i]*u'[i]
    	//
    	// [W] average has to be known at all [W] nodes, including walls
    {
    	int k;
    #pragma omp parallel for private(k) shared(TKE, u_TKE, v_TKE, w_TKE, \
    	u_TKE_share, v_TKE_share, w_TKE_share)
    	for (k = grid.gcz; k < grid.nz - grid.gcz; k++) {
    		u_TKE[k] = (T)0.5 * (U2[k] - U[k] * U[k]);
    		v_TKE[k] = (T)0.5 * (V2[k] - V[k] * V[k]);
    		w_TKE[k] = (T)0.5 * (W2[k] - W[k] * W[k + 1]);
    
    		TKE[k] = u_TKE[k] + v_TKE[k] + w_TKE[k];
    
    		u_TKE_share[k] = u_TKE[k] / TKE[k];
    		v_TKE_share[k] = v_TKE[k] / TKE[k];
    		w_TKE_share[k] = w_TKE[k] / TKE[k];
    	}
    }
    // -------------------------------------------------------------------------------------------- //
    
    // TKE anisotropy
    // -------------------------------------------------------------------------------------------- //
    template< typename T >
    void nse::TKE_anisotropy(
    	T* TKE_aniso_uu, T* TKE_aniso_vv, T* TKE_aniso_ww,		// node: [C]
    	T* TKE_aniso_uv, T* TKE_aniso_uw, T* TKE_aniso_vw,		// node: [C]
    
    	const T* const TKE,		// node: [C]
    	const T* const u_TKE,	// node: [C]
    	const T* const v_TKE,	// node: [C]
    	const T* const w_TKE,	// node: [C]
    	const T* const uv_flux,	// node: [C]
    	const T* const uw_flux,	// node: [W]
    	const T* const vw_flux,	// node: [W]
    
    	const wstGrid3d< T >& grid)
    	//
    	// TKE anisotropy symmetric zero-trace tensor:
    	// [(u(i)u(j)) / (u(k)u(k))] - 1/3 * delta(i,j)
    	//
    	// [u'w', v'w'] fluxes have to be known at all [W] nodes, including walls
    {
    	int k;
    #pragma omp parallel for private(k) shared(TKE_aniso_uu, TKE_aniso_vv, TKE_aniso_ww, \
    	TKE_aniso_uv, TKE_aniso_uw, TKE_aniso_vw)
    	for (k = grid.gcz; k < grid.nz - grid.gcz; k++) {
    
    		TKE_aniso_uu[k] = (u_TKE[k] / TKE[k]) - ((T)1.0 / (T)3.0);
    		TKE_aniso_vv[k] = (v_TKE[k] / TKE[k]) - ((T)1.0 / (T)3.0);
    		TKE_aniso_ww[k] = (w_TKE[k] / TKE[k]) - ((T)1.0 / (T)3.0);
    
    		TKE_aniso_uv[k] = (uv_flux[k] / ((T)2.0*TKE[k]));
    		TKE_aniso_uw[k] = ((uw_flux[k] + uw_flux[k + 1]) / ((T)4.0*TKE[k]));
    		TKE_aniso_vw[k] = ((vw_flux[k] + vw_flux[k + 1]) / ((T)4.0*TKE[k]));
    	}
    }
    // -------------------------------------------------------------------------------------------- //
    
    // TKE production
    // -------------------------------------------------------------------------------------------- //
    template< typename T >
    void nse::u_TKE_production(
    	T* _u_TKE_production,		// node: [C]
    
    	const T* const UW_bottom,	// node: [W]
    	const T* const UW_top,		// node: [W]
    	const T* const U,			// node: [C]
    	const T* const W,			// node: [W]
    	const wstGrid3d< T >& grid)
    	//
    	// [U] component of T.K.E. equation defined at [C] node via interpolation
    	//            _
    	//    ____   dU
    	//	- u'w' * -- 
    	//			 dz
    	// [W] average has to be known at all [W] nodes, including walls
    	// [U] average has to be known at all [C] nodes and ghost nodes: (k + 1/2), (k - 1/2)
    {
    	int k;
    #pragma omp parallel for private(k) shared(_u_TKE_production)
    	for (k = grid.gcz; k < grid.nz - grid.gcz; k++) {
    		_u_TKE_production[k] = -(T) 0.5 * (
    			// discretization is based on ADV. form //
    			// correct for SKEW.form (checked) //
    			(UW_bottom[k] - U[k] * W[k]) * (U[k] - U[k - 1]) * grid.dzi[k] +
    			(UW_top[k] - U[k] * W[k + 1]) * (U[k + 1] - U[k]) * grid.dzi[k]);
    	}
    }
    
    template< typename T >
    void nse::v_TKE_production(
    	T* _v_TKE_production,		// node: [C]
    
    	const T* const VW_bottom,	// node: [W]
    	const T* const VW_top,		// node: [W]
    	const T* const V,			// node: [C]
    	const T* const W,			// node: [W]
    	const wstGrid3d< T >& grid)
    	//
    	// [V] component of T.K.E. equation defined at [C] node via interpolation
    	//            _
    	//    ____   dV
    	//	- v'w' * -- 
    	//			 dz
    	// [W] average has to be known at all [W] nodes, including walls
    	// [V] average has to be known at all [C] nodes and ghost nodes: (k + 1/2), (k - 1/2)
    {
    	int k;
    #pragma omp parallel for private(k) shared(_v_TKE_production)
    	for (k = grid.gcz; k < grid.nz - grid.gcz; k++) {
    		_v_TKE_production[k] = -(T) 0.5 * (
    			// discretization is based on ADV. form //
    			// correct for SKEW.form (checked) //
    			(VW_bottom[k] - V[k] * W[k]) * (V[k] - V[k - 1]) * grid.dzi[k] +
    			(VW_top[k] - V[k] * W[k + 1]) * (V[k + 1] - V[k]) * grid.dzi[k]);
    	}
    }
    template< typename T >
    void nse::w_TKE_production(
    	T* _w_TKE_production,		// node: [C]
    
    	const T* const W2_c,		// node: [C]
    	const T* const W2_w,		// node: [W]
    	const T* const W,			// node: [W]
    	const wstGrid3d< T >& grid)
    	//
    	// [W] component of T.K.E. equation defined at [C] node via interpolation
    	//            _
    	//    ____   dW
    	//	- w'w' * -- 
    	//			 dz
    	// [W] average has to be known at all [W] nodes, including walls
    {
    	T* w_production;
    	int buf_id = memStx::get_buf(&w_production, grid.nz);
    
    	int k;
    
    	// computing at [W] nodes:
    #pragma omp parallel for private(k) shared(w_production)
    	for (k = grid.gcz; k < grid.nz - grid.gcz; k++) {
    		w_production[k] = -(
    			(W2_w[k] + W2_c[k] - W[k] * W[k] - W[k] * W[k + 1]) * (W[k + 1] - W[k]) * grid.dzmih[k] +
    			(W2_w[k] + W2_c[k - 1] - W[k] * W[k] - W[k] * W[k - 1]) * (W[k] - W[k - 1]) * grid.dzmih[k]);
    	}
    
    	// setting boundary conditions:
    	w_dirichlet_bc_z(w_production, (T)0, (T)0, grid);
    
    	// interpolation [W]->[C]:
    #pragma omp parallel for private(k) shared(_w_TKE_production, w_production)
    	for (k = grid.gcz; k < grid.nz - grid.gcz; k++) {
    		_w_TKE_production[k] =
    			(T) 0.5 * (w_production[k] + w_production[k + 1]);
    	}
    
    	memStx::free_buf(buf_id);
    }
    // -------------------------------------------------------------------------------------------- //
    
    // TKE transport
    // -------------------------------------------------------------------------------------------- //
    template< typename T >
    void nse::u_TKE_transport(
    	T* _u_TKE_transport,		// node: [C]
    
    	const T* const uu_w_flux,	// node: [W]
    	const wstGrid3d< T >& grid)
    	// [U] transport term of T.K.E. equation defined at [C] node via interpolation
    	//       _____________________
    	//      d[(1/2) * (u')^2 * w'] 
    	//	-  ------------------------ 
    	//				dz
    	// [u'u'w'] flux has to be known at all [W] nodes, including walls
    {
    	int k;
    #pragma omp parallel for private(k) shared(_u_TKE_transport)
    	for (k = grid.gcz; k < grid.nz - grid.gcz; k++) {
    		_u_TKE_transport[k] = -(T) 0.5 *
    			(uu_w_flux[k + 1] - uu_w_flux[k]) * grid.dzi[k];
    	}
    }
    // -------------------------------------------------------------------------------------------- //
    
    template< typename T >
    void nse::v_TKE_transport(
    	T* _v_TKE_transport,		// node: [C]
    
    	const T* const vv_w_flux,	// node: [W]
    	const wstGrid3d< T >& grid)
    	// [V] transport term of T.K.E. equation defined at [C] node via interpolation
    	//       _____________________
    	//      d[(1/2) * (v')^2 * w'] 
    	//	-  ------------------------ 
    	//				dz
    	// [v'v'w'] flux has to be known at all [W] nodes, including walls
    {
    	int k;
    #pragma omp parallel for private(k) shared(_v_TKE_transport)
    	for (k = grid.gcz; k < grid.nz - grid.gcz; k++) {
    		_v_TKE_transport[k] = -(T) 0.5 *
    			(vv_w_flux[k + 1] - vv_w_flux[k]) * grid.dzi[k];
    	}
    }
    // -------------------------------------------------------------------------------------------- //
    
    template< typename T >
    void nse::w_TKE_transport(
    	T* _w_TKE_transport,		// node: [C]
    
    	const T* const ww_w_flux,	// node: [C]
    	const wstGrid3d< T >& grid)
    	// [W] transport component of T.K.E. equation defined at [C] node via interpolation
    	//       _____________________
    	//      d[(1/2) * (w')^2 * w'] 
    	//	-  ------------------------ 
    	//				dz
    	// [w'w'w'] flux has to be known at all [C] nodes and ghost nodes: (k + 1/2), (k - 1/2)
    {
    	int k;
    #pragma omp parallel for private(k) shared(_w_TKE_transport)
    	for (k = grid.gcz; k < grid.nz - grid.gcz; k++) {
    		_w_TKE_transport[k] = -(T) 0.5 * (
    			(ww_w_flux[k + 1] - ww_w_flux[k]) * grid.dzpi[k] +
    			(ww_w_flux[k] - ww_w_flux[k - 1]) * grid.dzmi[k]);
    	}
    }
    // -------------------------------------------------------------------------------------------- //
    
    
    // TKE pressure work
    // -------------------------------------------------------------------------------------------- //
    template< typename T >
    void nse::w_TKE_pressure_work(
    	T* _w_TKE_pressure_work,	// node: [C]
    
    	const T* const pw_flux,		// node: [W]
    	const wstGrid3d< T >& grid)
    	// [W] pressure work component of T.K.E. equation defined at [C] node via interpolation
    	//       ______
    	//      d[p'w'] 
    	//	-  -------- 
    	//		  dz
    	// [p'w'] flux has to be known at all [W] nodes, including walls
    {
    	int k;
    #pragma omp parallel for private(k) shared(_w_TKE_pressure_work)
    	for (k = grid.gcz; k < grid.nz - grid.gcz; k++) {
    		_w_TKE_pressure_work[k] = -(pw_flux[k + 1] - pw_flux[k]) * grid.dzi[k];
    	}
    }
    // -------------------------------------------------------------------------------------------- //
    
    // TKE exchange
    // -------------------------------------------------------------------------------------------- //
    template< typename T >
    void nse::w_TKE_exchange(
    	T* _w_TKE_exchange,			// node: [C]
    
    	const T* const PSww,		// node: [C]
    	const T* const Pressure,	// node: [C]
    	const T* const W,			// node: [W]
    	const wstGrid3d< T >& grid)
    	// [W] energy exchange component of T.K.E. equation defined at [C] node via interpolation
    	// ______
    	//   dw'
    	// p'---
    	//   dz
    	// [W] average has to be known at all [W] nodes, including walls
    {
    	int k;
    #pragma omp parallel for private(k) shared(_w_TKE_exchange)
    	for (k = grid.gcz; k < grid.nz - grid.gcz; k++) {
    		_w_TKE_exchange[k] = PSww[k] - Pressure[k] * ((W[k + 1] - W[k]) * grid.dzi[k]);
    	}
    }
    // -------------------------------------------------------------------------------------------- //
    
    // TKE dissipation
    // -------------------------------------------------------------------------------------------- //
    template< typename T >
    void nse::u_TKE_dissipation(
    	T* _u_TKE_dissipation,			// node: [C]
    
    	const T* const U_dissipation,	// node: [C]
    	const T* const U,				// node: [C]
    	const T c_kinematic_viscosity, const wstGrid3d< T >& grid)
    	// [U] dissipation component of T.K.E. defined at [C] node via interpolation
    	//       ___________
    	//   1      d^2(u')
    	//	-- * u' ------- 
    	//	Re		dx(j)^2
    	// [U] average has be known at all [C] nodes and ghost nodes: (k + 1/2), (k - 1/2)
    {
    	int k;
    #pragma omp parallel for private(k) shared(_u_TKE_dissipation)
    	for (k = grid.gcz; k < grid.nz - grid.gcz; k++) { 
    		_u_TKE_dissipation[k] = U_dissipation[k] -
    			c_kinematic_viscosity * (U[k] *
    			((U[k + 1] - U[k]) * grid.dzp2i[k] - (U[k] - U[k - 1]) * grid.dzm2i[k]));
    	}
    }
    // -------------------------------------------------------------------------------------------- //
    
    template< typename T >
    void nse::v_TKE_dissipation(
    	T* _v_TKE_dissipation,			// node: [C]
    
    	const T* const V_dissipation,	// node: [C]
    	const T* const V,				// node: [C]
    	const T c_kinematic_viscosity, const wstGrid3d< T >& grid)
    	// [V] dissipation component of T.K.E. defined at [C] node via interpolation
    	//       ___________
    	//   1      d^2(v')
    	//	-- * v' ------- 
    	//	Re		dx(j)^2 
    	// [V] average has be known at all [C] nodes and ghost nodes: (k + 1/2), (k - 1/2)
    {
    	int k;
    #pragma omp parallel for private(k) shared(_v_TKE_dissipation)
    	for (k = grid.gcz; k < grid.nz - grid.gcz; k++) {
    		_v_TKE_dissipation[k] = V_dissipation[k] -
    			c_kinematic_viscosity * (V[k] *
    			((V[k + 1] - V[k]) * grid.dzp2i[k] - (V[k] - V[k - 1]) * grid.dzm2i[k]));
    	}
    }
    // -------------------------------------------------------------------------------------------- //
    
    template< typename T >
    void nse::w_TKE_dissipation(
    	T* _w_TKE_dissipation,			// node: [C]
    
    	const T* const W_dissipation,	// node: [W]
    	const T* const W,				// node: [W]
    	const T c_kinematic_viscosity, const wstGrid3d< T >& grid)
    	// [W] dissipation component of T.K.E. defined at [C] node via interpolation
    	//       ___________
    	//   1      d^2(w')
    	//	-- * w' ------- 
    	//	Re		dx(j)^2 
    	// [W] average has to be known at all [W] nodes, including walls
    	// *Note:
    	//		computing dissipation at [W] nodes, setting 
    	//		boundary conditions for turbulence dissipation (assuming = 0 at walls)
    	//		and interpolating to [C] node
    {
    	T* w_diss;
    	int buf_id = memStx::get_buf(&w_diss, grid.nz);
    
    	int k;
    
    	// computing at [W] nodes:
    #pragma omp parallel for private(k) shared(w_diss)
    	for (k = grid.gcz; k < grid.nz - grid.gcz; k++) {
    		w_diss[k] = W_dissipation[k] -
    			c_kinematic_viscosity * (W[k] *
    			((W[k + 1] - W[k]) * grid.dzm2i[k] - (W[k] - W[k - 1]) * grid.dzp2i[k - 1]));
    	}
    
    	// setting boundary conditions:
    	w_dirichlet_bc_z(w_diss, (T)0, (T)0, grid);
    
    	// interpolation [W]->[C]:
    #pragma omp parallel for private(k) shared(_w_TKE_dissipation, w_diss)
    	for (k = grid.gcz; k < grid.nz - grid.gcz; k++) {
    		_w_TKE_dissipation[k] = 
    			(T) 0.5 * (w_diss[k] + w_diss[k + 1]);
    	}
    
    	memStx::free_buf(buf_id);
    }
    // -------------------------------------------------------------------------------------------- //
    
    // TKE iso dissipation
    // -------------------------------------------------------------------------------------------- //
    template< typename T >
    void nse::u_TKE_iso_dissipation(
    	T* _u_TKE_iso_dissipation,			// node: [C] node
    
    	const T* const U_iso_dissipation,	// node: [C] node
    	const T* const U,					// node: [C] node
    	const T c_kinematic_viscosity, const wstGrid3d< T >& grid)
    	// [U] isotropic dissipation component of T.K.E. equation defined at [C] node via interpolation
    	//       _____________
    	//   1   d(u')   d(u')
    	//-	-- * ----- * -----
    	//	Re	 dx(j)   dx(j)
    	// [U] average has be known at all [C] nodes and ghost nodes: (k + 1/2), (k - 1/2)
    {
    	int k;
    #pragma omp parallel for private(k) shared(_u_TKE_iso_dissipation)
    	for (k = grid.gcz; k < grid.nz - grid.gcz; k++) {
    		_u_TKE_iso_dissipation[k] = -(U_iso_dissipation[k] -
    			c_kinematic_viscosity * (
    			(T)0.5 * (U[k + 1] - U[k]) * (U[k + 1] - U[k]) * grid.dzp2i[k] +
    			(T)0.5 * (U[k] - U[k - 1]) * (U[k] - U[k - 1]) * grid.dzm2i[k]));
    	}
    }
    // -------------------------------------------------------------------------------------------- //
    
    template< typename T >
    void nse::v_TKE_iso_dissipation(
    	T* _v_TKE_iso_dissipation,			// node: [C] node
    
    	const T* const V_iso_dissipation,	// node: [C] node
    	const T* const V,					// node: [C] node
    	const T c_kinematic_viscosity, const wstGrid3d< T >& grid)
    	// [V] isotropic dissipation component of T.K.E. equation defined at [C] node via interpolation
    	//       _____________
    	//   1   d(v')   d(v')
    	//-	-- * ----- * -----
    	//	Re	 dx(j)   dx(j)
    	// [V] average has be known at all [C] nodes and ghost nodes: (k + 1/2), (k - 1/2)
    {
    	int k;
    #pragma omp parallel for private(k) shared(_v_TKE_iso_dissipation)
    	for (k = grid.gcz; k < grid.nz - grid.gcz; k++) {
    		_v_TKE_iso_dissipation[k] = -(V_iso_dissipation[k] -
    			c_kinematic_viscosity * (
    			(T)0.5 * (V[k + 1] - V[k]) * (V[k + 1] - V[k]) * grid.dzp2i[k] +
    			(T)0.5 * (V[k] - V[k - 1]) * (V[k] - V[k - 1]) * grid.dzm2i[k]));
    	}
    }
    // -------------------------------------------------------------------------------------------- //
    
    template< typename T >
    void nse::w_TKE_iso_dissipation(
    	T* _w_TKE_iso_dissipation,			// node: [C]
    
    	const T* const W_iso_dissipation,	// node: [W]
    	const T* const W,					// node: [W]
    	const T c_kinematic_viscosity, const wstGrid3d< T >& grid)
    	// [W] isotropic dissipation component of T.K.E. equation defined at [C] node via interpolation
    	//       _____________
    	//   1   d(w')   d(w')