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# TAU0

TAU0 is a term in ADCIRC's governing equations that influences the degree of numerical diffusion. Specifically, it is the Generalized Wave-Continuity Equation (GWCE) weighting factor that weighs the relative contribution of the primitive and wave portions of the GWCE. TAU0 is affected by both the TAU0 value in the fort.15 file and the fort.13 file if the primitive weighting in continuity equation nodal attribute is specified. Since the purpose of TAU0 is to achieve model stability, while minimizing distortion of the governing equations,

## 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 values of TAU0 are flags, all positive values are not. The following is a list of possible TAU0 values in the fort.15 file and their meaning.

Positive values
For all positive values, the value specified in the fort.15 file is spatially and temporally constant and applied directly:

• = 0, the GWCE is a pure wave equation
• = 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

Negative Values
Note that for TAU0 = -x.1 where x is an integer, behavior is the same as -x, but the TAU0 values are written to the fort.90 file. More on this below in Outputting.
Spatially varying, temporally constant

• = -1, TAU0 is spatially varying but constant in time; it is calculated according to depth as follows:
• If the depth is >=10, TAU0 is set to 0.005
• If the depth is < 10, TAU0 is set to 0.020
• = -2, TAU0 is spatially varying but constant in time; it is calculated according to depth as follows:
• If the depth is >=200 TAU0 is set to 0.005
• If the depth is < 200 but > 1, then TAU0 is set to 1/depth
• If depth < 1, TAU0 is set to 1.0

Spatially and temporally varying

• = -3, TAU0 varies in space and time. TAU0 is computed from TAU0Base (read in from the nodal attribute file) as follows:
• If TAU0Base < 0.025; TAU0 = TAU0Base (constant in time)
• If TAU0Base >= 0.025; TAU0 = TAU0Base + 1.5 TK(i) where TK(i)=Cd|U|/H
• = -5, FullDomainTimeVaryingTau0 is set to .True. and TAU0 is dependent on the local friction as follows:
• TAU0=Tau0Min+1.5*TK(i)
• It is limited to a range specified by Tau0FullDomainMin and Tau0FullDomainMax, which are specified on the following line of the fort.15 file when TAU0 is -5

## Outputting

For TAU0 formulations that vary spatially or temporally, ADCIRC can write the nodal TAU0 values that it calculates internally. These values 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 the TAU0 input value in the fort.15 file. For example, if TAU0=-3.1, the calculation of TAU0 is still carried out according to the description of TAU0=-3 above, and the fort.90 output file will also be produced.

## Selecting TAU0

For positive values, a good rule of thumb for setting TAU0 is to set it equal to the largest value of an equivalent linear friction factor (e.g, for linear friction TAU0 = TAU; for quadratic friction TAU0 = maximum (speed*CF/depth). Typical values for TAU0 are in the range of 0.005 – 0.1.

If TAU0 = -3 in the fort.15 file, then the TAU0Base nodal attribute values can be generated with the ADCIRC utility program tau0_gen.f. The program bases generation on the following logic:

• If the avg. distance between a node and its neighbors < 1750 m TAU0Base = 0.03
• If the avg. distance between a node and its neighbors > 1750 m AND depth < 10m; TAU0Base = 0.02 (TAU0 is constant in time)
• If the avg. distance between a node and its neighbors > 1750 m AND depth > 10m; TAU0Base = 0.005 (TAU0 is constant in time)