mom_wave_structure mom_wave_structure::wave_structure_cs subroutine, public subroutine, public mom_wave_structure::wave_structure (h, tv, G, GV, US, cn, ModeNum, freq, CS, En, full_halos) wave_structure h h tv tv G G GV GV US US cn cn ModeNum ModeNum freq freq CS CS En En full_halos full_halos This subroutine determines the internal wave velocity structure for any mode. This subroutine solves for the eigen vector [vertical structure, e(k)] associated with the first baroclinic mode speed [i.e., smallest eigen value (lam = 1/c^2)] of the system d2e/dz2 = -(N2/cn2)e, or (A-lam*I)e = 0, where A = -(1/N2)(d2/dz2), lam = 1/c^2, and I is the identity matrix. 2nd order discretization in the vertical lets this system be represented as -Igu(k)*e(k-1) + (Igu(k)+Igl(k)-lam)*e(k) - Igl(k)*e(k+1) = 0.0 with rigid lid boundary conditions e(1) = e(nz+1) = 0.0 giving (Igu(2)+Igl(2)-lam)*e(2) - Igl(2)*e(3) = 0.0 -Igu(nz)*e(nz-1) + (Igu(nz)+Igl(nz)-lam)*e(nz) = 0.0 where, upon noting N2 = reduced gravity/layer thickness, we get Igl(k) = 1.0/(gprime(k)*H(k)) ; Igu(k) = 1.0/(gprime(k)*H(k-1)) The eigen value for this system is approximated using "wave_speed." This subroutine uses these eigen values (mode speeds) to estimate the corresponding eigen vectors (velocity structure) using the "inverse iteration with shift" method. The algorithm is Pick a starting vector reasonably close to mode structure and with unit magnitude, b_guess For n=1,2,3,... Solve (A-lam*I)e = e_guess for e Set e_guess=e/|e| and repeat, with each iteration refining the estimate of e g The ocean's grid structure. gv The ocean's vertical grid structure. us A dimensional unit scaling type h Layer thicknesses [H ~> m or kg m-2] tv A structure pointing to various thermodynamic variables. cn The (non-rotational) mode internal gravity wave speed [L T-1 ~> m s-1]. modenum Mode number freq Intrinsic wave frequency [T-1 ~> s-1]. cs The control structure returned by a previous call to wave_structure_init. en Internal wave energy density [R Z3 T-2 ~> J m-2] full_halos If true, do the calculation over the entire computational domain. mom_error_handler::mom_error tridiag_solver mom_internal_tides::propagate_int_tide subroutine subroutine mom_wave_structure::tridiag_solver (a, b, c, h, y, method, x) tridiag_solver a a b b c c h h y y method method x x Solves a tri-diagonal system Ax=y using either the standard Thomas algorithm (TDMA_T) or its more stable variant that invokes the "Hallberg substitution" (TDMA_H). a lower diagonal with first entry equal to zero. b middle diagonal. c upper diagonal with last entry equal to zero. h vector of values that have already been added to b; used for systems of the form (e.g. average layer thickness in vertical diffusion case): [ -alpha(k-1/2) ] * e(k-1) + [ alpha(k-1/2) + alpha(k+1/2) + h(k) ] * e(k) + [ -alpha(k+1/2) ] * e(k+1) = y(k) where a(k)=[-alpha(k-1/2)], b(k)=[alpha(k-1/2)+alpha(k+1/2) + h(k)], and c(k)=[-alpha(k+1/2)]. Only used with TDMA_H method. y vector of known values on right hand side. method A string describing the algorithm to use x vector of unknown values to solve for. mom_error_handler::mom_error wave_structure subroutine, public subroutine, public mom_wave_structure::wave_structure_init (Time, G, param_file, diag, CS) wave_structure_init Time Time G G param_file param_file diag diag CS CS Allocate memory associated with the wave structure module and read parameters. time The current model time. g The ocean's grid structure. param_file A structure to parse for run-time parameters. diag A structure that is used to regulate diagnostic output. cs A pointer that is set to point to the control structure for this module. mom_error_handler::mom_error mom_internal_tides::internal_tides_init Vertical structure functions for first baroclinic mode wave speed.