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TAU0 is an input in the fort.15 file that influences the degree of numerical diffusion in ADCIRC's governing equations. Specifically, it influences the weighting factor that determines the relative contribution of the primitive and wave portions of the the Generalized Wave-Continuity Equation (GWCE). The weighting factor, , is affected by values in both the fort.15 file and the fort.13 file, if the primitive weighting in continuity equation or min and max primitive weighting in continuity equation nodal attributes are specified. This page addresses both the
TAU0 value in the fort.15 file and the parameter more generally.
TAU0 value specified in the fort.15 file can be either a flag (indicating how ADCIRC should operate) or the actual value used in solving the GWCE, it is important to distinguish between the two. All negative
TAU0 are flags, all positive
TAU0 are . The following table is a summary of possible
TAU0 values and their meaning. Note that for
TAU0 = -x.1 (where
x is an integer), behavior is the same as
-x, but the values are written to the fort.90 file. More on this below in Outputting.
|Varies in space||no||yes||yes||yes||yes||yes||yes|
|Varies in time||no||no||no||yes||yes||yes||yes|
|Requires nodal attribute||no||no||no||yes||no||yes||no|
For all positive values, the value specified in the fort.15 file is spatially and temporally constant and applied directly, i.e.
TAU0 = , so:
TAU0 = 0, the GWCE is a pure wave equation
TAU0 = 1, the GWCE behaves like a pure primitive continuity equation
0 < TAU0 < 1, the GWCE is a weighted sum of the primitive and wave portions of the equation
Spatially varying, temporally constant
TAU0 = -1, is computed as follows:
If depth >= 10; then = 0.005
If depth < 10; then = 0.020
TAU0 = -2, is is computed according to depth as follows:
If depth >= 200; then = 0.005
If 1 < depth < 200; then = 1/depth
If depth < 1; then
Spatially and temporally varying
TAU0 = -3, is computed from
TAU0Base(read in from the nodal attribute file) as follows:
If TAU0Base < 0.025; then = TAU0Base(constant in time)
If TAU0Base >= 0.025; then = TAU0Base+1.5*TKwhere
TAU0 = -5, is computed similar to
TAU0 = -3as follows:
- It is limited by
Tau0FullDomainMin <= <= Tau0FullDomainMax, which are specified on the line following
TAU0in the fort.15 file (only when
TAU0 = -5)
- If the min and max primitive weighting in continuity equation nodal attribute is used, then the nodal minimum and maximum values replace the full-domain values in the above calculation.
TAU0 = -6, is defined using the rules for
TAU0 = -3, and then is set equal to the time-average of the current and previous (time-averaged) values.
TAU0 = -7, is defined using the rules for
TAU0 = -3, and then is set equal to the weighted time-average of the current and previous (time-averaged) values as follows:
= AlphaTau0*TAU0VAR + (1.0-AlphaTau0)*LastTau0, where
AlphaTau0 = 0.25is hard-coded into the model, this means that is weighted 75% toward older values
Spatial and Temporal Updating
TAU0 = -3, -5, -6, or -7, is updated (via the
CalculateTimeVaryingTau0 subroutine) in space and in time. An initial "update" is done when the model starts. After this, updates are done only after a time step in which there is a change in wet/dry state somewhere in the model domain. For use cases that contain large number of nodes near the wet/dry boundary, this can be the equivalent of updating every time step. However, for use cases that have little or no wet/dry changes, there may be little or no updating. The rules listed above in TAU0 Values are applied during the update. Each node's is then spatially averaged with all immediate neighbors. Time-averaging (for
TAU0 = -6 or -7 is applied last.
For positive values (
TAU0=), a good rule of thumb for setting
TAU0 is to set it equal to the largest value of an equivalent linear friction factor: for linear friction
TAU0 = TAU; for quadratic friction
TAU0 = max(speed*Cd/depth). Typical values for
TAU0 are in the range of 0.005 – 0.1.
TAU0 = -3, paired with the primitive weighting in continuity equation nodal attribute is generally the most popular formulation. In this case,
TAU0Base nodal attribute values can be generated with the ADCIRC utility program tau0_gen.f. The program bases generation on the following logic applied to each node individually:
If the avg. dist. to neighboring nodes < 1750 m; then TAU0Base = 0.03
If depth < 10m; then TAU0Base = 0.02(
TAU0is constant in time)
If depth > 10m; then TAU0Base = 0.005(
TAU0is constant in time)
TAU0 formulations that vary spatially or temporally, ADCIRC can output the internally-calculated nodal values. They are written to the fort.90 file, which has the same format and output frequency as the water surface elevation output file (fort.63). fort.90 output is activated by placing a 1 in the tenths place of
TAU0 in the fort.15 file. For example, if
TAU0 = -3.1, the calculation of is still carried out according to the description of
TAU0 = -3 above, and the fort.90 output file will also be produced.