Changes between Version 5 and Version 6 of 2016WP/SIMPLIF-5_ACC

Timestamp:

2016-03-10T13:38:08+01:00 (8 years ago)

Author:

acc

Comment:

--

2016WP/SIMPLIF-5_ACC

@@ -80 +80 @@
 Once the PI has completed this section, he should send a mail to the previewer(s) asking them to preview the work within two weeks.
 }}}
+
+= Jointly agreed plan (after preview) =
+
+== Description == 
+This task reimplements a spatially varying eddy viscosity coefficient proportional
+to the local deformation rate and grid scale (Smagorinsky 1993). This reimplementation
+takes advantage of the recently reorganised and simplified LDF modules which means the
+scheme can be implemented as a simple alternative to the existing scheme for a space
+and time varying coefficient (nn_aht_ijk_t=31).  This will provide a much cleaner
+implementation than the version which was removed from v3.6_STABLE and requires very
+few additional arrays and no preprocessor keys
+
+== Implementation ==
+The changes will occur primarily in ldfdyn.F90. 
+
+Firstly, in MODULE ldfdyn which will acquire the following name list additions:
+
+{{{
+                                         !! If nn_ahm_ijk_t = 32 a time and space varying Smagorinsky viscosity
+                                         !! will be computed. 
+   REAL(wp), PUBLIC ::   rn_csmc         !: Smagorinsky constant of proportionality 
+   REAL(wp), PUBLIC ::   rn_cfacmin      !: Multiplicative factor of theorectical minimum Smagorinsky viscosity
+   REAL(wp), PUBLIC ::   rn_cfacmax      !: Multiplicative factor of theorectical maximum Smagorinsky viscosity
+}}}
+
+The majority of code changes then occur in ldf_dyn where the CASE statement is extended
+to respond to CASE 32 by setting coefficients according to the Smagorinsky scheme
+as revisited in Griffies and Hallberg (2000). For efficiency it is useful to define
+module-private 2D arrays to store some calculated terms:
+
+{{{
+   REAL(wp),         ALLOCATABLE, SAVE, DIMENSION(:,:)   ::   dtensq       !: horizontal tension squared         (Smagorinsky only)
+   REAL(wp),         ALLOCATABLE, SAVE, DIMENSION(:,:)   ::   dshesq       !: horizontal shearing strain squared (Smagorinsky only)
+   REAL(wp),         ALLOCATABLE, SAVE, DIMENSION(:,:)   ::   esqt, esqf   !: Square of the local gridscale (e1e2/(e1+e2))**2
+}}}
+
+The length-squared terms (L^2^) are geometric invariants that can be calculated once
+at start (ldf_dyn_init). The horizontal tension (D,,T,,= du/dx - dv/y) is calculated at
+T-points using the before velocities. The horizontal shearing strain (D,,S,, = du/dy +
+dv/dx) is calculated at F-points using the same velocities. Storing the squares of
+these terms means that computing viscosity coefficients at T & F points is merely a
+case of combining different averages of these arrays.
+
+Using the relationship given by Griffies and Hallberg (2000); namely:
+
+{{{
+     B_smag = A_smag * L^2 / 8
+}}}
+
+means that the biharmonic coefficients (if required) can be computed from a simple
+scaling of the harmonic values. Note that the new implementation of the biharmonic
+operator as a re-rentrant laplacian means that the square root of the biharmonic
+coefficient should be returned by this routine.
+
+
+== Reference manual ==
+
+The description of the Smagorinsky scheme in the current reference will be altered to
+reflect the new method of activation. At this stage there are no plans to implement the
+additional  experimental options in the previous implementation (i.e. the ability to
+control the contribution of the sheer term with an additional name list parameter and
+the option to apply a Smagorinsky type criterion to a space a time varying diffusion
+coefficient.
+
+Details of the new implementation will be added and will include both the continuous
+and discrete forms of the operators used.
+
+'''Griffies, S., M., and W. Hallberg, R''' , Biharmonic friction with a Smagorinsky-like
+viscosity for use in large-scale eddy-permitting ocean models, Mon. Wea. Rev., 128(8),
+2935-2946, 2000.
 
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