#include <ERF_TerminalVelocity.H>

Collaboration diagram for TerminalVelocity< RT >:

Public Member Functions
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE RT	RogersYau (const RT a_r) const noexcept
	Terminal velocity - Rogers & Yau, 1989. More...

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE RT	AtlasUlbrich (const RT a_r) const noexcept
	Terminal velocity - Atlas & Ulbrich, 1977. More...

AMREX_GPU_HOST_DEVICE RT	CloudRainShima (const RT a_r, const RT a_rho, const RT a_P, const RT a_T) const noexcept
	Terminal velocity - cloud/rain droplets Shima et al., 2009, "The super-droplet method for the numerical simulation of clouds and precipitation: A particle-based and probabilistic microphysics model coupled with a non- hydrostatic model." Quart. J. Roy. Meteorol. Soc., 135: 1307-1320 https://github.com/Shima-Lab/SCALE-SDM_BOMEX_Sato2018/blob/master/contrib/SDM/sdm_motion.f90. More...

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE RT	vz_b_x (const RT a_x) const noexcept
	Compute vz_b(x) More...

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE RT	vz_c_x (const RT a_x) const noexcept
	Compute vc_b(x) More...

Public Attributes
RT	m_rho

Member Function Documentation

◆ AtlasUlbrich()

template<typename RT >

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE RT TerminalVelocity< RT >::AtlasUlbrich ( const RT a_r ) const

inlinenoexcept

Terminal velocity - Atlas & Ulbrich, 1977.

     {
         static const RT a = amrex::Real(3.778);
         static const RT b = amrex::Real(0.67);
         RT D = 2*a_r*1000; // meter -> mm
         return a*(std::exp(b*std::log(D)));
     }

◆ CloudRainShima()

template<typename RT >

AMREX_GPU_HOST_DEVICE RT TerminalVelocity< RT >::CloudRainShima	(	const RT	a_r,
		const RT	a_rho,
		const RT	a_P,
		const RT	a_T
	)		const

inlinenoexcept

Terminal velocity - cloud/rain droplets Shima et al., 2009, "The super-droplet method for the numerical simulation of clouds and precipitation: A particle-based and probabilistic microphysics model coupled with a non- hydrostatic model." Quart. J. Roy. Meteorol. Soc., 135: 1307-1320 https://github.com/Shima-Lab/SCALE-SDM_BOMEX_Sato2018/blob/master/contrib/SDM/sdm_motion.f90.

Parameters

a_r	radius
a_rho	density
a_P	pressure
a_T	temperature

     {
         RT lb4l = amrex::Real(6.62E-6);    // base length[cm] for mean free path  of air molecules
         RT visb4l = amrex::Real(1.818E-4); // base dynamic viscosity[g/(cm*s)] for mean free path of air molecules
         RT pb4l = amrex::Real(1013.25);    // base pressure[hPa] for mean free path of air molecules
         RT tb4l = amrex::Real(293.15);     // base temperature[20C] for mean free path of air molecules
  
         RT P_hPa = a_P / amrex::Real(100.0);           // [Pa] -> [hPa]
         RT T_degC = a_T - amrex::Real(273.15);         // [K] -> [deg Celsius]
         RT diameter_cm = two*a_r*amrex::Real(100.0);   // [m] -> [cm]
         RT rho_mat_cgs = m_rho/amrex::Real(1000.0);    // [kg/m^3] -> [g/cm^3]
         RT rho_air_cgs = a_rho/amrex::Real(1000.0);    // [kg/m^3] -> [g/cm^3]
         RT grav_cgs = CONST_GRAV * 100;   // [m/s^2] -> [cm/s^2]
  
         RT gxdrow = grav_cgs * ( rho_mat_cgs - rho_air_cgs );
  
         RT viscosity = zero;
         if (T_degC >= 0) {
             viscosity = (amrex::Real(1.7180) + amrex::Real(4.9e-3)*T_degC) * amrex::Real(1.0e-4);
         } else {
             viscosity = (  amrex::Real(1.7180) + amrex::Real(4.9e-3)*T_degC
                          - amrex::Real(1.2e-5)*T_degC*T_degC     ) * amrex::Real(1.0e-4);
         }
  
         RT v_terminal = zero;
         if (diameter_cm < amrex::Real(1.9e-3)) {
             // small cloud droplets
             RT sd_l = lb4l * (viscosity/visb4l) * (pb4l/P_hPa) * std::sqrt(a_T/tb4l);
             RT c1  = gxdrow / (amrex::Real(18.0)*viscosity);
             RT csc = one + amrex::Real(2.510) * (sd_l/diameter_cm);
             v_terminal = c1 * csc * diameter_cm * diameter_cm;
         } else if (diameter_cm < amrex::Real(1.07e-1)) {
             // large cloud droplets and small raindrops
             RT sd_l = lb4l * (viscosity/visb4l) * (pb4l/P_hPa) * std::sqrt(a_T/tb4l);
             RT c2 = rho_air_cgs * (amrex::Real(4.0)*gxdrow)/(three*viscosity*viscosity);
             RT nda = c2 * diameter_cm * diameter_cm * diameter_cm;
             RT csc = one + amrex::Real(2.510) * ( sd_l / diameter_cm );
             RT nre = csc * std::exp(vz_b_x(std::log(nda)));
             v_terminal = (viscosity*nre)/(rho_air_cgs*diameter_cm);
         } else {
             // large raindrops
             RT tau = one - a_T/amrex::Real(647.0960);
             RT sigma = amrex::Real(0.2358) * std::exp( amrex::Real(1.2560)*std::log(tau) )
                                 * ( one - amrex::Real(0.6250)*tau );
             if( a_T<amrex::Real(267.5) ) {
                 tau = std::tanh( (a_T-amrex::Real(243.9))/amrex::Real(35.35) );
                 sigma = sigma - amrex::Real(2.854E-3) * tau + amrex::Real(1.666E-3);
             }
             sigma = sigma * amrex::Real(1.E+3); // N/m => g/s^2
             RT c3 = (amrex::Real(4.0)*gxdrow)/(three*sigma);
             RT bond = c3 * diameter_cm * diameter_cm;
             RT npp =    (rho_air_cgs*rho_air_cgs) * (sigma*sigma*sigma)
                         / (gxdrow*viscosity*viscosity*viscosity*viscosity);
             npp = std::exp( std::log(npp)/amrex::Real(6.0) );
             RT nre = npp * std::exp(vz_c_x(std::log(bond*npp)));
             v_terminal = (viscosity*nre)/(rho_air_cgs*diameter_cm);
         }
  
         v_terminal /= amrex::Real(100.0); // [cm/s] -> [m/s]
         return v_terminal;
     }

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◆ RogersYau()

template<typename RT >

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE RT TerminalVelocity< RT >::RogersYau ( const RT a_r ) const

inlinenoexcept

Terminal velocity - Rogers & Yau, 1989.

     {
         static const RT k1 = amrex::Real(1.233e8); // m^{-1} s^{-1}
         return (k1 * a_r * a_r);
     }

◆ vz_b_x()

template<typename RT >

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE RT TerminalVelocity< RT >::vz_b_x ( const RT a_x ) const

inlinenoexcept

Compute vz_b(x)

Parameters

a_x x

     {
         RT x1 = a_x;
         RT x2 = x1 * x1;
         RT x3 = x1 * x2;
         RT y = - amrex::Real(0.318657E+1)
                + amrex::Real(0.9926960)    * x1
                - amrex::Real(0.153193E-2)  * x2
                - amrex::Real(0.987059E-3)  * x3
                - amrex::Real(0.578878e-3)  * x2*x2
                + amrex::Real(0.855176E-4)  * x3*x2
                - amrex::Real(0.327815E-5)  * x3*x3;
         return y;
     }

Referenced by TerminalVelocity< RT >::CloudRainShima().

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◆ vz_c_x()

template<typename RT >

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE RT TerminalVelocity< RT >::vz_c_x ( const RT a_x ) const

inlinenoexcept

Compute vc_b(x)

Parameters

a_x x

     {
         RT x1 = a_x;
         RT x2 = x1 * x1;
         RT x3 = x1 * x2;
         RT y = - amrex::Real(0.500015E+1)
                + amrex::Real(0.523778E+1)  * x1
                - amrex::Real(0.204914E+1)  * x2
                + amrex::Real(0.47529400)   * x3
                - amrex::Real(0.542819E-1)  * x2*x2
                + amrex::Real(0.238449E-2)  * x3*x2;
         return y;
     }