Difference between revisions of "TAU0"
Taylorgasher (talk  contribs) (Corrected mathematical and practical bounds of tau_0) 
Taylorgasher (talk  contribs) (Added vague info about weird nodal attribute interactions with TAU0) 

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'''Negative Values'''<br/>  '''Negative Values'''<br/>  
''Spatially varying, temporally constant''  ''Spatially varying, temporally constant''  
+  Unexpected behavior may arise if nodal attributes are specified alongside one of these values, and this is discouraged.  
+  *<code>TAU0 >= 0</code> and the [[primitive weighting in continuity equation]] nodal attribute is specified in the fort.15 file, <math>\tau_0</math> is set equal to the nodal attribute values.  
*<code>TAU0 = 1</code>, <math>\tau_0</math> is computed as follows:  *<code>TAU0 = 1</code>, <math>\tau_0</math> is computed as follows:  
**<code>If depth >= 10; then <math>\tau_0</math> = 0.005</code>  **<code>If depth >= 10; then <math>\tau_0</math> = 0.005</code> 
Revision as of 13:58, 19 February 2019
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 WaveContinuity 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 Values
Because the 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 . Furthermore, some values are overridden by the primitive weighting in continuity equation nodal attribute. 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.
fort.15 TAU0

>= 0  1  2  3  5  6  7 

Varies in space  no  yes  yes  yes  yes  yes  yes 
Varies in time  no  no  no  yes  yes  yes  yes 
Spaceaveraged  no  no  no  yes  yes  yes  yes 
Timeaveraged  no  no  no  no  no  yes  yes 
Expects nodal attribute  no  no  no  yes  yes  yes  yes 
Minimum  N/A  0.002  0.002  N/A  Tau0FullDomainMin

N/A  N/A 
Maximum  N/A  0.005  1  0.2  Tau0FullDomainMax

0.2  0.2 
Code Flags  
HighResTimeVaryingTau0

.FALSE.  .FALSE.  .FALSE.  .TRUE.  .FALSE.  .TRUE.  .TRUE. 
FullDomainTimeVaryingTau0

.FALSE.  .FALSE.  .FALSE.  .FALSE.  .TRUE.  .FALSE.  .FALSE. 
TimeAveragedTau0

.FALSE.  .FALSE.  .FALSE.  .FALSE.  .FALSE.  .TRUE.  .FALSE. 
BackLoadedTimeAveragedTau0

.FALSE.  .FALSE.  .FALSE.  .FALSE.  .FALSE.  .FALSE.  .TRUE. 
Positive values
A positive value is ignored if the primitive weighting in continuity equation nodal attribute is specified in the fort.15 file. For all positive values, the value specified in the fort.15 file is spatially and temporally constant and applied directly, i.e. TAU0 =
. Practical guidance on setting a constant TAU0
is provided below in Selecting Tau0. Mathematically, the GWCE is a pure wave equation for , and approaches a pure primitive equation as , however in practice, it behaves like a pure primitive equation once reaches 1 or so.
Negative Values
Spatially varying, temporally constant
Unexpected behavior may arise if nodal attributes are specified alongside one of these values, and this is discouraged.
TAU0 >= 0
and the primitive weighting in continuity equation nodal attribute is specified in the fort.15 file, is set equal to the nodal attribute values.TAU0 = 1
, is computed as follows:If depth >= 10; then = 0.005
If depth < 10; then = 0.020
 This value is ignored if primitive weighting in continuity equation is specified in the fort.15 file.
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
 This value is ignored if primitive weighting in continuity equation is specified in the fort.15 file.
Spatially and temporally varying
In the unlikely event that one of the below options not paired with its corresponding nodal attribute (the code will exit if this is done for some TAU0
), then default values are set using the TAU0 = 1
logic.
TAU0 = 3
, is computed fromTAU0Base
(read in from the nodal attribute) as follows:If TAU0Base < 0.025; then = TAU0Base
(constant in time)If TAU0Base >= 0.025; then = TAU0Base+1.5*TK
whereTK=speed*Cd/depth
TAU0 = 5
, is computed similar toTAU0 = 3
as follows:= Tau0Min+1.5*TK
 It is limited by
Tau0FullDomainMin <= <= Tau0FullDomainMax
, which are specified on the line followingTAU0
in the fort.15 file (only whenTAU0 = 5
)  If the min and max primitive weighting in continuity equation nodal attribute is used, then the nodal minimum and maximum values replace the fulldomain values in the above calculation.
TAU0 = 6
, is defined using the rules forTAU0 = 3
, and then is set equal to the timeaverage of the current and previous (timeaveraged) values.TAU0 = 7
, is defined using the rules forTAU0 = 3
, and then is set equal to the weighted timeaverage of the current and previous (timeaveraged) values as follows:= AlphaTau0*TAU0VAR + (1.0AlphaTau0)*LastTau0
, whereTAU0VAR
isTau0Base
after spatial averaging, andAlphaTau0 = 0.25
is hardcoded into the model. This means that is weighted 75% toward older values.
Spatial and Temporal Updating
For 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. Timeaveraging (for TAU0 = 6 or 7
) is applied last.
Selecting Tau0
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
 Otherwise
If depth < 10m; then TAU0Base = 0.02
(TAU0
is constant in time)If depth > 10m; then TAU0Base = 0.005
(TAU0
is constant in time)
Outputting
For TAU0
formulations that vary spatially or temporally, ADCIRC can output the internallycalculated 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.