examples/advection_in_gyre/advection_in_gyre.rst

1c8cebb321 Jeff*0001 .. _sec_gyre_advection:
d67096e55c Jeff*0002
                0003 Ocean Gyre Advection Schemes
                0004 ============================
                0005
                0006   (in directory: :filelink:`verification/tutorial_advection_in_gyre/`)
                0007
                0008 This set of examples is based on the barotropic and baroclinic gyre
                0009 MITgcm configurations, that are described in
                0010 :numref:`sec_eg_baro` and :numref:`tutorial_baroclinic_gyre`.
                0011 The examples in this section explain how to introduce a passive tracer
                0012 into the flow field of the barotropic and baroclinic gyre setups and
                0013 looks at how the time evolution of the passive tracer depends on the
                0014 advection or transport scheme that is selected for the tracer.
                0015
                0016 Passive tracers are useful in many numerical experiments. In some cases
                0017 tracers are used to track flow pathways, for example in Dutay et al. (2002)
                0018 :cite:`dutay:02` a passive tracer is used to track pathways
                0019 of CFC-11 in 13 global ocean models, using a numerical configuration
                0020 similar to the example described in
                0021 :numref:`sec_eg_offline_cfc`). In other cases tracers are used
                0022 as a way to infer bulk mixing coefficients for a turbulent flow field,
                0023 for example in Marshall et al. (2006) :cite:`marshall:06` a tracer is used to infer
                0024 eddy mixing coefficients in the Antarctic Circumpolar Current region. Typically, in
                0025 biogeochemical and ecological simulations large numbers of tracers are
                0026 used that carry the concentrations of biological nutrients and
                0027 concentrations of biological species. When using
                0028 tracers for these and other purposes it is useful to have a feel for the
                0029 role that the advection scheme employed plays in determining properties
                0030 of the tracer distribution. In particular, in a discrete numerical model,
                0031 tracer advection only approximates the continuum behavior in space and
                0032 time and different advection schemes introduce different approximations
                0033 so that the resulting tracer distributions vary. In the following text
                0034 we illustrate how to use the different advection schemes available in
                0035 MITgcm, and discuss which properties are well represented by each
                0036 scheme. The advection schemes selections also apply to active tracers (e.g.,
                0037 :math:`T` and :math:`S`) and the character of the schemes also affects
                0038 their distributions and behavior.
                0039
                0040 Advection and tracer transport
                0041 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
                0042
                0043 In general, the tracer problem we want to solve can be written
                0044
                0045 .. math::
0bad585a21 Navi*0046    \frac{\partial C}{\partial t} = -\vec{\bf U} \cdot  \nabla  C + S
d67096e55c Jeff*0047    :label: eg-adv-gyre-generic-tracer
                0048
0bad585a21 Navi*0049 where :math:`C` is the tracer concentration in a model cell, :math:`\vec{\bf U}=(u,v,w)`
d67096e55c Jeff*0050 is the model 3-D flow field. In
                0051 :eq:`eg-adv-gyre-generic-tracer`, :math:`S` represents
                0052 source, sink and tendency terms not associated with advective transport.
                0053 Example of terms in :math:`S` include (i) air-sea fluxes for a dissolved
                0054 gas, (ii) biological grazing and growth terms (for a biogeochemical
                0055 problem) or (iii) convective mixing and other sub-grid parameterizations
                0056 of mixing. In this section we are primarily concerned with
                0057
                0058 #. how to introduce the tracer term, :math:`C`, into an integration
                0059
0bad585a21 Navi*0060 #. the different discretized forms of the :math:`-\vec{\bf U} \cdot  \nabla  C` term
d67096e55c Jeff*0061    that are available
                0062
                0063 Introducing a tracer into the flow
                0064 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
                0065
                0066 The MITgcm ptracers package (see section :numref:`sub_phys_pkg_ptracers`
                0067 for a more complete discussion of the ptracers package and section
                0068 :numref:`using_packages` for a
                0069 general introduction to MITgcm packages) provides pre-coded support for
                0070 a simple passive tracer with an initial distribution at simulation time
                0071 :math:`t=0` of :math:`C_0(x,y,z)`. The steps required to use this
                0072 capability are
                0073
                0074 #. **Activating the ptracers package.** This simply requires adding the
                0075    line ``ptracers`` to the file :filelink:`code/packages.conf <verification/tutorial_advection_in_gyre/code/packages.conf>`.
                0076
                0077 #. **Setting an initial tracer distribution.**
                0078
                0079 Once the two steps above are complete we can proceed to examine how the
                0080 tracer we have created is carried by the flow field and what properties
                0081 of the tracer distribution are preserved under different advection
                0082 schemes.
                0083
                0084 Selecting an advection scheme
                0085 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
                0086
                0087 - flags in :filelink:`input/data <verification/tutorial_advection_in_gyre/input/data>`
                0088   and :filelink:`input/data.ptracers <verification/tutorial_advection_in_gyre/input/data.ptracers>`
                0089
                0090 - overlap width
                0091
                0092 - ``#define`` CPP option :varlink:`PTRACERS_ALLOW_DYN_STATE` in
                0093   :filelink:`code/PTRACERS_OPTIONS.h <verification/tutorial_advection_in_gyre/code/PTRACERS_OPTIONS.h>` as required for SOM case
                0094
                0095 Comparison of different advection schemes
                0096 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
                0097
                0098 #. Conservation
                0099
                0100 #. Dispersion
                0101
                0102 #. Diffusion
                0103
                0104 #. Positive definite
                0105
                0106 .. figure:: figs/adv_gyre_maps.png
                0107    :width: 100%
                0108    :align: center
                0109    :alt: Dye evolving in double gyre
                0110    :name: fig_adv_gyre_maps
                0111
                0112    Dye evolving in a double gyre with different advection schemes. The
                0113    figure shows the dye concentration one year after injection into a
                0114    single grid cell near the left boundary.
                0115
                0116 .. figure:: figs/adv_gyre_stats.png
                0117    :width: 100%
                0118    :align: center
                0119    :alt: Max Min and Std Dev
                0120    :name: fig_adv_gyre_stats
                0121
                0122    Maxima, minima and standard deviation (from left) as a function of
                0123    time (in months) for the gyre circulation experiment from
                0124    :numref:`fig_adv_gyre_maps`.
                0125