TAU0

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, $\tau _{0}$, 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 $\tau _{0}$ parameter more generally.

fort.15 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 $\tau _{0}$ 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 $\tau _{0}$. 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 $\tau _{0}$ 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
Space-averaged	no	no	no	yes	yes	yes	yes
Time-averaged	no	no	no	no	no	yes	yes
Requires nodal attribute	no	no	no	yes	no	yes	no
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
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
Spatially varying, temporally constant

• = -1, $\tau _{0}$ is spatially varying but constant in time; it is calculated according to depth as follows:
  • If the depth is >=10, $\tau _{0}$ = 0.005
  • If the depth is < 10, $\tau _{0}$ = 0.020
• = -2, TAU0 is spatially varying but constant in time; it is calculated according to depth as follows:
  • If the depth is >=200 $\tau _{0}$=0.005
  • If the depth is < 200 but > 1, $\tau _{0}$=1/depth
  • If depth < 1, $\tau _{0}$=1.0

Spatially and temporally varying

• = -3, $\tau _{0}$ varies in space and time. $\tau _{0}$ is computed from TAU0Base (read in from the nodal attribute file) as follows:
  • If TAU0Base < 0.025; $\tau _{0}$ = TAU0Base (constant in time)
  • If TAU0Base >= 0.025; $\tau _{0}$ = TAU0Base + 1.5 TK(i) where TK(i)=Cd|U|/H
• = -5, FullDomainTimeVaryingTau0 is set to .True. and $\tau _{0}$ is dependent on the local friction as follows:
  • $\tau _{0}$=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

Spatial and Temporal Updating

For TAU0=-3, -5, -6, or -7, $\tau _{0}$ is updated in space and in time.

Outputting $\tau _{0}$

For TAU0 formulations that vary spatially or temporally, ADCIRC can output the internally-calculated nodal $\tau _{0}$ 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 $\tau _{0}$ is still carried out according to the description of TAU0=-3 above, and the fort.90 output file will also be produced.

Selecting $\tau _{0}$

For positive values (TAU0=$\tau _{0}$), 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.

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:

• 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)