Merge branch 'pr/1494' into dev/gfdl

docs/parameterizations_vertical.rst

@@ -21,9 +21,12 @@ Interior and bottom-driven mixing
 ---------------------------------
 
 Kappa-shear
-  MOM_kappa_shear implement the shear-driven mixing of :cite:`jackson2008`.
+  MOM_kappa_shear implements the shear-driven mixing of :cite:`jackson2008`.
+
+   :ref:`Internal_Shear_Mixing`
 
 Internal-tide driven mixing
+
   The schemes of :cite:`st_laurent2002`, :cite:`polzin2009`, and :cite:`melet2012`, are all implemented through MOM_set_diffusivity and MOM_diabatic_driver.
 
    :ref:`Internal_Tidal_Mixing`
@@ -33,6 +36,8 @@ Vertical friction
 
 Vertical viscosity is implemented in MOM_vert_frict and coefficient computed in MOM_set_viscosity, although contributions to viscosity from other parameterizations are calculated in those respective modules (e.g. MOM_kappa_shear, MOM_KPP, MOM_energetic_PBL).
 
+   :ref:`Vertical_Viscosity`
+
 Vertical diffusion
 ------------------
 

docs/zotero.bib

@@ -655,6 +655,30 @@ @article{killworth1992
 	pages = {1379--1387}
 }
 
+@article{killworth1999,
+	doi = {10.1175/1520-0485(1999)029<1221:atbblc>2.0.co;2},
+	year = 1999,
+	publisher = {American Meteorological Society},
+	volume = {29},
+	number = {6},
+	pages = {1221--1238},
+	author = {P. D. Killworth and N. R. Edwards},
+	title = {A Turbulent Bottom Boundary Layer Code for Use in Numerical Ocean Models},
+	journal = {J. Phys. Oceanography}
+}
+
+@article{zilitinkevich1996,
+	doi = {10.1007/bf02430334},
+	year = 1996,
+	publisher = {Springer Science and Business Media {LLC}},
+	volume = {81},
+	number = {3-4},
+	pages = {325--351},
+	author = {S. Zilitinkevich and D. V. Mironov},
+	title = {A multi-limit formulation for the equilibrium depth of a stably stratified boundary layer},
+	journal = {Boundary-Layer Meteorology}
+}
+
 @article{gent1995,
 	title = {Parameterizing {Eddy}-{Induced} {Tracer} {Transports} in {Ocean} {Circulation} {Models}},
 	volume = {25},
@@ -800,6 +824,18 @@ @article{jackson2008
 	pages = {1033--1053}
 }
 
+@article{turner1986,
+	doi = {10.1017/s0022112086001222},
+	year = 1986,
+	publisher = {Cambridge University Press ({CUP})},
+	volume = {173},
+	pages = {431--471},
+	author = {J. S. Turner},
+	title = {Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows},
+	journal = {J. Fluid Mech.}
+}
+
+
 @article{reichl2018,
 	title = {A simplified energetics based planetary boundary layer ({ePBL}) approach for ocean climate simulations.},
 	volume = {132},
@@ -1426,6 +1462,18 @@ @article{harrison2008
 	pages = {1894--1912}
 }
 
+@article{danabasoglu2012,
+	doi = {10.1175/jcli-d-11-00091.1},
+	year = 2012,
+	publisher = {American Meteorological Society},
+	volume = {25},
+	number = {5},
+	pages = {1361--1389},
+	author = {G. Danabasoglu and S. C. Bates and B. P. Briegleb and S. R. Jayne and M. Jochum and W. G. Large and S. Peacock and S. G. Yeager},
+	title = {The {CCSM}4 Ocean Component},
+	journal = {J. Climate}
+}
+
 @article{henyey1986,
 	title = {Energy and action flow through the internal wave field: {An} eikonal approach},
 	volume = {91},
@@ -1761,6 +1809,18 @@ @article{large1994
 	pages = {363--403}
 }
 
+@article{pacanowski1981,
+	doi = {10.1175/1520-0485(1981)011<1443:povmin>2.0.co;2},
+	year = 1981,
+	publisher = {American Meteorological Society},
+	volume = {11},
+	number = {11},
+	pages = {1443--1451},
+	author = {R. C. Pacanowski and S. G. H. Philander},
+	title = {Parameterization of Vertical Mixing in Numerical Models of Tropical Oceans},
+	journal = {J. Phys. Oceanography}
+}
+
 @article{van_roekel2018,
 	title = {The {KPP} {Boundary} {Layer} {Scheme} for the {Ocean}: {Revisiting} {Its} {Formulation} and {Benchmarking} {One}-{Dimensional} {Simulations} {Relative} to {LES}},
 	volume = {10},
@@ -2343,6 +2403,19 @@ @article{hallberg2000
 	pages = {1402--1419}
 }
 
+@article{umlauf2005,
+	doi = {10.1016/j.csr.2004.08.004},
+	year = 2005,
+	publisher = {Elsevier {BV}},
+	volume = {25},
+	number = {7-8},
+	pages = {795--827},
+	author = {L. Umlauf and H. Burchard},
+	title = {Second-order turbulence closure models for geophysical boundary layers. A review of recent work},
+	journal = {Continental Shelf Res.}
+}
+
+
 @article{easter1993,
 	title = {Two Modified Versions of Bott's Positive-Definite Numerical
 	   Advection Scheme},
@@ -2545,11 +2618,60 @@ @article{hallberg2005
 }
 
 @article{bell1975,
-	author = {T. H. Bell},
-	year = {1975},
-	title = {Lee wavews in stratified flows with simple harmonic time dependence"},
-	journal = {J. Fluid Mech.},
+	doi = {10.1017/s0022112075000560},
+	year = 1975,
+	publisher = {Cambridge University Press ({CUP})},
 	volume = {67},
-	pages = {705--722}
+	number = {4},
+	pages = {705--722},
+	author = {T. H. Bell},
+	title = {Lee waves in stratified flows with simple harmonic time dependence},
+	journal = {J. Fluid Mech.}
+}
+
+@article{nikurashin2010a,
+	doi = {10.1175/2009jpo4199.1},
+	year = 2010,
+	publisher = {American Meteorological Society},
+	volume = {40},
+	number = {5},
+	pages = {1055--1074},
+	author = {M. Nikurashin and R. Ferrari},
+	title = {Radiation and Dissipation of Internal Waves Generated by Geostrophic Motions Impinging on Small-Scale Topography: Theory},
+	journal = {J. Phys. Oceanography}
+}
+
+@article{nikurashin2010b,
+	doi = {10.1175/2010jpo4315.1},
+	year = 2010,
+	publisher = {American Meteorological Society},
+	volume = {40},
+	number = {9},
+	pages = {2025--2042},
+	author = {M. Nikurashin and R. Ferrari},
+	title = {Radiation and Dissipation of Internal Waves Generated by Geostrophic Motions Impinging on Small-Scale Topography: Application to the Southern Ocean},
+	journal = {J. Phys. Oceanography}
+}
+
+@article{miles1961,
+	title = {On the stability of heterogeneous shear flows},
+	author = {JW Miles},
+	year = {1961},
+	journal = {J. of Fluid Mech.},
+	volume = {10},
+	pages = {496--508},
+	doi = {10.1017/S0022112061000305}
+}
+
+@article{bryan1979,
+	doi = {10.1029/jc084ic05p02503},
+	year = 1979,
+	publisher = {American Geophysical Union ({AGU})},
+	volume = {84},
+	number = {C5},
+	pages = {2503},
+	author = {K. Bryan and L. J. Lewis},
+	title = {A water mass model of the World Ocean},
+	journal = {J. Geophys. Res.}
 }
 

src/parameterizations/vertical/MOM_set_diffusivity.F90

@@ -198,16 +198,6 @@ module MOM_set_diffusivity
 
 contains
 
-!> Sets the interior vertical diffusion of scalars due to the following processes:
-!! 1. Shear-driven mixing: two options, Jackson et at. and KPP interior;
-!! 2. Background mixing via CVMix (Bryan-Lewis profile) or the scheme described by
-!!    Harrison & Hallberg, JPO 2008;
-!! 3. Double-diffusion, old method and new method via CVMix;
-!! 4. Tidal mixing: many options available, see MOM_tidal_mixing.F90;
-!! In addition, this subroutine has the option to set the interior vertical
-!! viscosity associated with processes 1,2 and 4 listed above, which is stored in
-!! visc%Kv_slow. Vertical viscosity due to shear-driven mixing is passed via
-!! visc%Kv_shear
 subroutine set_diffusivity(u, v, h, u_h, v_h, tv, fluxes, optics, visc, dt, &
                            G, GV, US, CS, Kd_lay, Kd_int, Kd_extra_T, Kd_extra_S)
   type(ocean_grid_type),     intent(in)    :: G    !< The ocean's grid structure.

src/parameterizations/vertical/MOM_set_viscosity.F90

@@ -115,80 +115,6 @@ module MOM_set_visc
 contains
 
 !> Calculates the thickness of the bottom boundary layer and the viscosity within that layer.
-!!
-!! A drag law is used, either linearized about an assumed bottom velocity or using the
-!! actual near-bottom velocities combined with an assumed unresolved velocity.  The bottom
-!! boundary layer thickness is limited by a combination of stratification and rotation, as
-!! in the paper of Killworth and Edwards, JPO 1999. It is not necessary to calculate the
-!! thickness and viscosity every time step; instead previous values may be used.
-!!
-!! \section set_viscous_BBL Viscous Bottom Boundary Layer
-!!
-!! If set_visc_cs.bottomdraglaw is True then a bottom boundary layer viscosity and thickness
-!! are calculated so that the bottom stress is
-!! \f[
-!! \mathbf{\tau}_b = C_d | U_{bbl} | \mathbf{u}_{bbl}
-!! \f]
-!! If set_visc_cs.bottomdraglaw is True then the term \f$|U_{bbl}|\f$ is set equal to the
-!! value in set_visc_cs.drag_bg_vel so that \f$C_d |U_{bbl}|\f$ becomes a Rayleigh bottom drag.
-!! Otherwise \f$|U_{bbl}|\f$ is found by averaging the flow over the bottom set_visc_cs.hbbl
-!! of the model, adding the amplitude of tides set_visc_cs.tideamp and a constant
-!! set_visc_cs.drag_bg_vel. For these calculations the vertical grid at the velocity
-!! component locations is found by
-!! \f[
-!! \begin{array}{ll}
-!! \frac{2 h^- h^+}{h^- + h^+} & u \left( h^+ - h^-\right) >= 0
-!! \\
-!! \frac{1}{2} \left( h^- + h^+ \right) &  u \left( h^+ - h^-\right) < 0
-!! \end{array}
-!! \f]
-!! which biases towards the thin cell if the thin cell is upwind. Biasing the grid toward
-!! thin upwind cells helps increase the effect of viscosity and inhibits flow out of these
-!! thin cells.
-!!
-!! After diagnosing \f$|U_{bbl}|\f$ over a fixed depth an active viscous boundary layer
-!! thickness is found using the ideas of Killworth and Edwards, 1999 (hereafter KW99).
-!! KW99 solve the equation
-!! \f[
-!! \left( \frac{h_{bbl}}{h_f} \right)^2 + \frac{h_{bbl}}{h_N} = 1
-!! \f]
-!! for the boundary layer depth \f$h_{bbl}\f$. Here
-!! \f[
-!! h_f = \frac{C_n u_*}{f}
-!! \f]
-!! is the rotation controlled boundary layer depth in the absence of stratification.
-!! \f$u_*\f$ is the surface friction speed given by
-!! \f[
-!! u_*^2 = C_d |U_{bbl}|^2
-!! \f]
-!! and is a function of near bottom model flow.
-!! \f[
-!! h_N = \frac{C_i u_*}{N} = \frac{ (C_i u_* )^2 }{g^\prime}
-!! \f]
-!! is the stratification controlled boundary layer depth. The non-dimensional parameters
-!! \f$C_n=0.5\f$ and \f$C_i=20\f$ are suggested by Zilitinkevich and Mironov, 1996.
-!!
-!! If a Richardson number dependent mixing scheme is being used, as indicated by
-!! set_visc_cs.rino_mix, then the boundary layer thickness is bounded to be no larger
-!! than a half of set_visc_cs.hbbl .
-!!
-!! \todo Channel drag needs to be explained
-!!
-!! A BBL viscosity is calculated so that the no-slip boundary condition in the vertical
-!! viscosity solver implies the stress \f$\mathbf{\tau}_b\f$.
-!!
-!! \subsection set_viscous_BBL_ref References
-!!
-!! \arg Killworth, P. D., and N. R. Edwards, 1999:
-!! A Turbulent Bottom Boundary Layer Code for Use in Numerical Ocean Models.
-!! J. Phys. Oceanogr., 29, 1221-1238,
-!! <a href="https://doi.org/10.1175/1520-0485(1999)029<1221:ATBBLC>2.0.CO;2"
-!! >doi:10.1175/1520-0485(1999)029<1221:ATBBLC>2.0.CO;2</a>
-!! \arg Zilitinkevich, S., Mironov, D.V., 1996:
-!! A multi-limit formulation for the equilibrium depth of a stably stratified boundary layer.
-!! Boundary-Layer Meteorology 81, 325-351.
-!! <a href="https://doi.org/10.1007/BF02430334">doi:10.1007/BF02430334</a>
-!!
 subroutine set_viscous_BBL(u, v, h, tv, visc, G, GV, US, CS, symmetrize)
   type(ocean_grid_type),    intent(inout) :: G    !< The ocean's grid structure.
   type(verticalGrid_type),  intent(in)    :: GV   !< The ocean's vertical grid structure.

src/parameterizations/vertical/_Internal_tides.dox

@@ -4,7 +4,7 @@ Two parameterizations of vertical mixing due to internal tides are
 available with the option INT_TIDE_DISSIPATION. The first is that of
 \cite st_laurent2002 while the second is that of \cite polzin2009. Choose
 between them with the INT_TIDE_PROFILE option. There are other relevant
-paramters which can be seen in MOM_parameter_doc.all once the main tidal
+parameters which can be seen in MOM_parameter_doc.all once the main tidal
 dissipation switch is turned on.
 
 \section section_st_laurent St Laurent et al.
@@ -69,7 +69,7 @@ case the maximum of all the contributions is used.
 
 The vertical diffusion profile of \cite polzin2009 is a WKB-stretched
 algebraic decay profile. It is based on a radiation balance equation,
-which links the dissipation profile associtated with internal breaking to
+which links the dissipation profile associated with internal breaking to
 the finescale internal wave shear producing that dissipation. The vertical
 profile of internal-tide driven energy dissipation can then vary in time
 and space, and evolve in a changing climate (\cite melet2012). \cite melet2012
@@ -135,9 +135,9 @@ at the ocean floor, so that in both formulations:
    \int_{0}^{H} \epsilon (z) dz = \frac{qE}{\rho} .
 \f]
 
-Whereas \cite polzin2009 assumed tthat the total dissipation was locally in balance with the
+Whereas \cite polzin2009 assumed that the total dissipation was locally in balance with the
 barotropic to baroclinic energy conversion rate \f$(q=1)\f$, here we use the \cite simmons2004 value
-of \f$q=1/3\f$ to retain as much consistency as passible between both parameterizations.
+of \f$q=1/3\f$ to retain as much consistency as possible between both parameterizations.
 
 \subsection subsection_vertical_decay_scale Vertical decay-scale reformulation
 
@@ -212,5 +212,16 @@ of the Earth. This allows the buoyancy fluxes to tend to zero in regions
 of very weak stratification, allowing a no-flux bottom boundary condition
 to be satisfied.
 
+\section Nikurashin Lee Wave Mixing
+
+If one has the INT_TIDE_DISSIPATION flag on, there is an option to also turn on
+LEE_WAVE_DISSIPATION. The theory is presented in \cite nikurashin2010a
+while the application of it is presented in \cite nikurashin2010b. For
+the implementation in MOM6, it is required that you provide an estimate
+of the TKE loss due to the Lee waves which is then applied with either
+the St. Laurent or the Polzin vertical profile.
+
+\todo Is there a script to produce this somewhere or what???
+
 */