uequation.F90 7.26 KB
 dumoda01 committed Jan 19, 2011 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 !$Id: uequation.F90,v 1.11 2006-11-06 13:36:45 hb Exp$ #include"cppdefs.h" !----------------------------------------------------------------------- !BOP ! ! !ROUTINE: The U-momentum equation\label{sec:uequation} ! ! !INTERFACE: subroutine uequation(nlev,dt,cnpar,tx,num,gamu,Method) ! ! !DESCRIPTION: ! This subroutine computes the transport of momentum in ! $x$-direction according to ! ! \label{uEq} ! \dot{U} ! = {\cal D}_U ! - g \partder{\zeta}{x} + \int_z^{\zeta} \partder{B}{x} \,dz' ! - \frac{1}{\tau^U_R}(U-U_{obs})-C_f U \sqrt{U^2+V^2} ! \comma ! ! where $\dot{U}$ denotes the material derivative of $U$, $\zeta$ ! the free surface elevation and $B$ the mean buoyancy defined ! in \eq{DefBuoyancy}. ${\cal D}_U$ is the sum of the turbulent ! and viscous transport terms modelled according to ! ! \label{Du} ! {\cal D}_U ! = \frstder{z} ! \left( ! \left( \nu_t + \nu \right) \partder{U}{z} ! - \tilde{\Gamma}_U ! \right) ! \point ! ! In this equation, $\nu_t$ and $\nu$ are the turbulent and ! molecular diffusivities of momentum, respectively, and ! $\tilde{\Gamma}_U$ denotes the non-local flux of momentum, ! see \sect{sec:turbulenceIntro}. ! ! Coriolis rotation is accounted for as described in ! \sect{sec:coriolis}. ! The external pressure gradient (second term on right hand side) ! is applied here only if surface slopes are ! directly given. Otherwise, the gradient is computed as ! described in \sect{sec:extpressure}, see \cite{Burchard99}. ! The internal pressure gradient (third ! term on right hand side) is calculated in {\tt intpressure.F90}, see ! \sect{sec:intpressure}. ! The fifth term on the right hand side allows for nudging the velocity ! to observed profiles with the relaxation time scale $\tau^U_R$. ! This is useful for initialising ! velocity profiles in case of significant inertial oscillations. ! Bottom friction is implemented implicitly using the fourth term ! on the right hand side. Implicit friction may be ! applied on all levels in order to allow for inner friction terms such ! as seagrass friction (see \sect{sec:seagrass}). ! ! Diffusion is numerically treated implicitly, see equations \eq{sigmafirst}- ! \eq{sigmalast}. ! The tri-diagonal matrix is solved then by a simplified Gauss elimination. ! Vertical advection is included, and it must be non-conservative, ! which is ensured by setting the local variable {\tt adv\_mode=0}, ! see section \ref{sec:advectionMean} on page \pageref{sec:advectionMean}. ! ! !USES: use meanflow, only: gravity,avmolu use meanflow, only: h,u,uo,v,w,avh use meanflow, only: drag,SS use observations, only: w_adv_method,w_adv_discr use observations, only: uProf,vel_relax_tau,vel_relax_ramp use observations, only: idpdx,dpdx use util, only: Dirichlet,Neumann use util, only: oneSided,zeroDivergence IMPLICIT NONE ! ! !INPUT PARAMETERS: ! number of vertical layers integer, intent(in) :: nlev ! time step (s) REALTYPE, intent(in) :: dt ! numerical "implicitness" parameter REALTYPE, intent(in) :: cnpar ! wind stress in x-direction ! divided by rho_0 (m^2/s^2) REALTYPE, intent(in) :: tx ! diffusivity of momentum (m^2/s) REALTYPE, intent(in) :: num(0:nlev) ! non-local flux of momentum (m^2/s^2) REALTYPE, intent(in) :: gamu(0:nlev) ! method to compute external ! pressure gradient integer, intent(in) :: method ! ! ! !DEFINED PARAMETERS: REALTYPE, parameter :: long=1.0D15 ! !REVISION HISTORY: ! Original author(s): Lars Umlauf ! (re-write after first version of ! Hans Burchard and Karsten Bolding) ! ! $Log: uequation.F90,v$ ! Revision 1.11 2006-11-06 13:36:45 hb ! Option for conservative vertical advection added to adv_center ! ! Revision 1.10 2006-04-03 08:39:12 lars ! fixed bug in relaxation times - Thanks to Adolf Stips ! ! Revision 1.9 2005-11-17 09:58:20 hb ! explicit argument for positive definite variables in diff_center() ! ! Revision 1.8 2005/06/27 13:44:07 kbk ! modified + removed traling blanks ! ! Revision 1.7 2004/08/18 11:44:49 lars ! updated documentation ! ! Revision 1.6 2003/03/28 09:20:35 kbk ! added new copyright to files ! ! Revision 1.5 2003/03/28 08:56:56 kbk ! removed tabs ! ! Revision 1.4 2003/03/10 08:50:07 gotm ! Improved documentation and cleaned up code ! ! Revision 1.3 2001/05/31 12:00:52 gotm ! Correction in the calculation of the shear squared calculation ! --- now according to Burchard 1995 (Ph.D. thesis). ! Also some cosmetics and cleaning of Makefiles. ! !EOP ! ! !LOCAL VARIABLES: integer :: adv_mode=0 integer :: posconc=0 integer :: i integer :: DiffBcup,DiffBcdw integer :: AdvBcup,AdvBcdw REALTYPE :: DiffUup,DiffUdw REALTYPE :: AdvUup,AdvUdw REALTYPE :: dzetadx REALTYPE :: Lsour(0:nlev) REALTYPE :: Qsour(0:nlev) REALTYPE :: URelaxTau(0:nlev) REALTYPE, save :: runtime=_ZERO_ ! !----------------------------------------------------------------------- !BOC ! save old value uo = u ! set boundary conditions DiffBcup = Neumann DiffBcdw = Neumann DiffUup = tx DiffUdw = _ZERO_ ! bottom friction treated as a source term AdvBcup = zeroDivergence AdvBcdw = oneSided AdvUup = _ZERO_ AdvUdw = _ZERO_ ! set external pressure gradient if (method .eq. 0) then dzetadx = dpdx else dzetadx = _ZERO_ endif ! set vector of relaxation times if (vel_relax_ramp .lt. long) then runtime=runtime+dt if (runtime .lt. vel_relax_ramp) then URelaxTau=vel_relax_tau*vel_relax_ramp/(vel_relax_ramp-runtime) else URelaxTau=vel_relax_tau end if else URelaxTau=vel_relax_tau end if ! compute total diffusivity avh=num+avmolu do i=1,nlev Qsour(i) = _ZERO_ Lsour(i) = _ZERO_ ! add external and internal pressure gradients Qsour(i) = Qsour(i) - gravity*dzetadx + idpdx(i) #ifdef SEAGRASS Lsour(i) = -drag(i)/h(i)*sqrt(u(i)*u(i)+v(i)*v(i)) #endif ! add non-local fluxes #ifdef NONLOCAL ! Qsour(i) = Qsour(i) - ( gamu(i) - gamu(i-1) )/h(i) #endif end do ! implement bottom friction as source term Lsour(1) = - drag(1)/h(1)*sqrt(u(1)*u(1)+v(1)*v(1)) ! do advection step if (w_adv_method.ne.0) then call adv_center(nlev,dt,h,h,w,AdvBcup,AdvBcdw, & AdvUup,AdvUdw,w_adv_discr,adv_mode,U) end if ! do diffusion step call diff_center(nlev,dt,cnpar,posconc,h,DiffBcup,DiffBcdw, & DiffUup,DiffUdw,avh,Lsour,Qsour,URelaxTau,uProf,U) return end subroutine uequation !EOC !----------------------------------------------------------------------- ! Copyright by the GOTM-team under the GNU Public License - www.gnu.org !-----------------------------------------------------------------------