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Difference between revisions of "TAU0"

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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, <math>\tau_0</math>, 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 <math>\tau_0</math> parameter more generally.   
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'''<code>TAU0</code>''' 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, <math>\tau_0</math>, 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 <code>TAU0</code> value in the fort.15 file and the <math>\tau_0</math> parameter more generally.   
  
== fort.15 TAU0 Values ==
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== <code>TAU0</code> Values ==
Because the TAU0 value specified in the fort.15 file can be either a flag (indicating how ADCIRC should operate) or the actual <math>\tau_0</math> 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 <math>\tau_0</math>. 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 <math>\tau_0</math> values are written to the [[fort.90 file]]. More on this below in [[TAU0#Outputting|Outputting]].  
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Because the <code>TAU0</code> value specified in the fort.15 file can be either a flag (indicating how ADCIRC should operate) or the actual <math>\tau_0</math> value used in solving the GWCE, it is important to distinguish between the two. All negative <code>TAU0</code> are flags, all positive <code>TAU0</code> are <math>\tau_0</math>. The following table is a summary of possible <code>TAU0</code> values and their meaning. Note that for <code>TAU0 = -x.1</code> where <code>x</code> is an integer, behavior is the same as <code>-x</code>, but the <math>\tau_0</math> values are written to the [[fort.90 file]]. More on this below in [[TAU0#Outputting|Outputting]].  
  
 
{| class="wikitable"
 
{| class="wikitable"
! style="font-weight:bold;" | fort.15 TAU0
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! style="font-weight:bold;" | fort.15 <code>TAU0</code>
! style="font-weight:bold;" | >=0
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! style="font-weight:bold;" | >= 0
 
! style="font-weight:bold;" | -1
 
! style="font-weight:bold;" | -1
 
! style="font-weight:bold;" | -2
 
! style="font-weight:bold;" | -2
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| 0.002
 
| 0.002
 
| N/A
 
| N/A
| Tau0FullDomainMin
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| <code>Tau0FullDomainMin</code>
 
| N/A
 
| N/A
 
| N/A
 
| N/A
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| 1
 
| 1
 
| 0.2
 
| 0.2
| Tau0FullDomainMax
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| <code>Tau0FullDomainMax</code>
 
| 0.2
 
| 0.2
 
| 0.2
 
| 0.2
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! colspan="8" style="text-align: center; font-weight:bold;" | Code Flags
 
! colspan="8" style="text-align: center; font-weight:bold;" | Code Flags
 
|-
 
|-
! style="font-weight:bold;" | HighResTimeVaryingTau0
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! style="font-weight:bold;" | <code>HighResTimeVaryingTau0</code>
 
| style="background-color:#fffc9e;" | .FALSE.
 
| style="background-color:#fffc9e;" | .FALSE.
 
| style="background-color:#fffc9e;" | .FALSE.
 
| style="background-color:#fffc9e;" | .FALSE.
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| style="background-color:#ffce93;" | .TRUE.
 
| style="background-color:#ffce93;" | .TRUE.
 
|-
 
|-
! style="font-weight:bold;" | FullDomainTimeVaryingTau0
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! style="font-weight:bold;" | <code>FullDomainTimeVaryingTau0</code>
 
| style="background-color:#fffc9e;" | .FALSE.
 
| style="background-color:#fffc9e;" | .FALSE.
 
| style="background-color:#fffc9e;" | .FALSE.
 
| style="background-color:#fffc9e;" | .FALSE.
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| style="background-color:#fffc9e;" | .FALSE.
 
| style="background-color:#fffc9e;" | .FALSE.
 
|-
 
|-
! style="font-weight:bold;" | TimeAveragedTau0
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! style="font-weight:bold;" | <code>TimeAveragedTau0</code>
 
| style="background-color:#fffc9e;" | .FALSE.
 
| style="background-color:#fffc9e;" | .FALSE.
 
| style="background-color:#fffc9e;" | .FALSE.
 
| style="background-color:#fffc9e;" | .FALSE.
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| style="background-color:#fffc9e;" | .FALSE.
 
| style="background-color:#fffc9e;" | .FALSE.
 
|-
 
|-
! style="font-weight:bold;" | BackLoadedTimeAveragedTau0
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! style="font-weight:bold;" | <code>BackLoadedTimeAveragedTau0</code>
 
| style="background-color:#fffc9e;" | .FALSE.
 
| style="background-color:#fffc9e;" | .FALSE.
 
| style="background-color:#fffc9e;" | .FALSE.
 
| style="background-color:#fffc9e;" | .FALSE.
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'''Positive values'''<br/>
 
'''Positive values'''<br/>
For all positive values, the value specified in the fort.15 file is spatially and temporally constant and applied directly:
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For all positive values, the value specified in the fort.15 file is spatially and temporally constant and applied directly, i.e. <code>TAU0 = <math>\tau_0</math></code>, so:
*= 0, the GWCE is a pure wave equation
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*<code>TAU0 = 0</code>, the GWCE is a pure wave equation
*= 1, the GWCE behaves like a pure primitive continuity equation
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*<code>TAU0 = 1</code>, 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
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*<code>0 < TAU0 < 1</code>, the GWCE is a weighted sum of the primitive and wave portions of the equation
  
 
'''Negative Values'''<br/>
 
'''Negative Values'''<br/>
 
''Spatially varying, temporally constant''
 
''Spatially varying, temporally constant''
*= -1, <math>\tau_0</math> is spatially varying but constant in time; it is calculated according to depth as follows:  
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*<code>TAU0 = -1</code>, <math>\tau_0</math> is spatially varying but constant in time; it is calculated according to depth as follows:  
**If the depth is >=10, <math>\tau_0</math> = 0.005
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**<code>If depth >= 10; <math>\tau_0</math> = 0.005</code>
**If the depth is < 10, <math>\tau_0</math> = 0.020
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**<code>If depth < 10; <math>\tau_0</math> = 0.020 </code>
*= -2, TAU0 is spatially varying but constant in time; it is calculated according to depth as follows:  
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*<code>TAU0 = -2</code>, <math>\tau_0</math> is spatially varying but constant in time and calculated according to depth as follows:  
**If the depth is >=200 <math>\tau_0</math>=0.005
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**<code>If depth >= 200; <math>\tau_0</math> = 0.005</code>
**If the depth is < 200 but > 1, <math>\tau_0</math>=1/depth
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**<code>If 1 < depth < 200; <math>\tau_0</math> = 1/depth</code>
**If depth < 1, <math>\tau_0</math>=1.0
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**<code>If depth < 1; <math>\tau_0 = 1</math></code>
  
 
''Spatially and temporally varying''<br/>
 
''Spatially and temporally varying''<br/>

Revision as of 22:06, 18 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 Wave-Continuity Equation (GWCE). The weighting factor, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau_0} 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau_0} value used in solving the GWCE, it is important to distinguish between the two. All negative TAU0 are flags, all positive TAU0 are Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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, i.e. TAU0 = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau_0} , 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

Negative Values
Spatially varying, temporally constant

  • TAU0 = -1, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau_0} is spatially varying but constant in time; it is calculated according to depth as follows:
    • If depth >= 10; Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau_0} = 0.005
    • If depth < 10; Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau_0} = 0.020
  • TAU0 = -2, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau_0} is spatially varying but constant in time and calculated according to depth as follows:
    • If depth >= 200; Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau_0} = 0.005
    • If 1 < depth < 200; Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau_0} = 1/depth
    • If depth < 1; Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau_0 = 1}

Spatially and temporally varying

  • = -3, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau_0} varies in space and time. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau_0} is computed from TAU0Base (read in from the nodal attribute file) as follows:
    • If TAU0Base < 0.025; Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau_0} = TAU0Base (constant in time)
    • If TAU0Base >= 0.025; Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau_0} = TAU0Base + 1.5 TK(i) where TK(i)=Cd|U|/H
  • = -5, FullDomainTimeVaryingTau0 is set to .True. and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau_0} is dependent on the local friction as follows:
    • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau_0} is updated in space and in time.

Outputting Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau_0}

For TAU0 formulations that vary spatially or temporally, ADCIRC can output the internally-calculated nodal Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau_0}

For positive values (TAU0=Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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)