advective flows. watershed & water quality modeling technical support center surface water flow...
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Advective FlowsAdvective Flows
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Surface Water Flow OptionsSurface Water Flow Options
1.1. Specified river, tributary flows (net flow)Specified river, tributary flows (net flow)
2.2. Specified lake, estuary flows (separate Specified lake, estuary flows (separate flows)flows)
3.3. Calculated flows using internal kinematic Calculated flows using internal kinematic wave equationswave equations
4.4. Calculated flows from external Calculated flows from external hydrodynamic modelhydrodynamic model
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Surface Water Flow Options – WASP Surface Water Flow Options – WASP ScreenScreen
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Transport Flow FieldsTransport Flow Fields
• Type 1 - Type 1 - Water ColumnWater Column flow carries both flow carries both dissolved and particulate materialdissolved and particulate material
• Type 2 - Type 2 - Pore WaterPore Water flow carries dissolved flow carries dissolved material onlymaterial only
• Type 3,4,5 – Type 3,4,5 – Solids “i”Solids “i” settling/resuspension carries particulate settling/resuspension carries particulate fraction onlyfraction only
• Type 6 – Type 6 – WaterWater evaporation/precipitation evaporation/precipitation adjusts water volume onlyadjusts water volume only
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Transport Fields – WASP ScreenTransport Fields – WASP Screen
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WASP Transport SchemeWASP Transport Scheme
• Each Flow Field can have multiple Each Flow Field can have multiple flow flow patternspatterns and and time functionstime functions..
• WASP sums the individual flows for each WASP sums the individual flows for each segment to determine overall transportsegment to determine overall transport
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Flow Patterns – WASP ScreenFlow Patterns – WASP Screen
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Flow Time Functions – WASP ScreenFlow Time Functions – WASP Screen
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Surface Flow OptionsSurface Flow Options
+ =
1. Net Flow Option
10 cms 5 cms 5 cms
WASP sums and uses net flow
2. Gross Flow Option
+ =5 cms
WASP uses each flow separately
5 cms10 cms
10 cms
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Surface Flow OptionsSurface Flow Options
WASP internally calculatesflows, volumes, depths, widths
3. Kinematic Wave
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Surface Flow OptionsSurface Flow Options
4. Hydrodynamic Linkage
Hydro Hydro
HydrodynamicInterface
WASPWASP
Examples of Specifying FlowsExamples of Specifying Flows
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Flow through Simple Pond Flow through Simple Pond
0 1 0
From Segment
To Segment
Flow Fraction
0 1 1.0
1 0 1.0 05
101520253035404550
0 5 10 15
Flow Time Function
Time, days
Flow Path
Continuity Function
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Upstream Flow Through RiverUpstream Flow Through River
1 2 3 4 5 60 0
From To Fraction0 1 1.01 2 1.02 3 1.03 4 1.04 5 1.05 6 1.06 0 1.0
020406080100120140160180200
0 5 10 15
Flow Time Function
Time, days
Flow Path
Continuity Function
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From To Fraction0 1 1.01 2 1.02 3 1.03 4 1.04 5 1.05 6 1.06 0 1.0
From To Fraction0 7 1.07 4 1.04 5 1.05 6 1.06 0 1.0
Flow through River with TributaryFlow through River with Tributary
1 2 3 4 5 6 0 0
7Flow Path
Continuity Functions
020406080100120140160180200
0 5 10 15
Flow Time Function
Time, days
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Branched Flow through RiverBranched Flow through River
1 7632
4
5
0 0
From To Fraction0 1 1.01 2 1.02 3 1.03 4 0.44 6 0.43 5 0.65 6 0.66 7 1.07 0 1.0
Flow Path Continuity Function
020406080100120140160180200
0 5 10 15
Flow Time Function
Time, days
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Kinematic Wave OptionKinematic Wave Option
• Applicable to 1-dimensional, branching Applicable to 1-dimensional, branching streams, riversstreams, rivers
• Calculates flow wave propagation and Calculates flow wave propagation and resulting variable flows, volumes, depths, resulting variable flows, volumes, depths, and velocities throughout the networkand velocities throughout the network
• Default rectangular channel shape unless Default rectangular channel shape unless user specifies hydraulic coefficientsuser specifies hydraulic coefficients
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Kinematic Wave EquationsKinematic Wave Equations
0
t
A
x
Q
Continuity equation (mass balance):
00 SSg f
Momentum equation (momentum balance):
gravity friction
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Kinematic Wave EquationsKinematic Wave EquationsSubstitute in Manning’s equation:
SBA
nQ
2/1
03/2
3/51
01
t
Q
x
Q Q
Kinematic wave differential equation:
SBn
where2/1
0
3/25/3
,5/3
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Kinematic Wave Input DataKinematic Wave Input Data
• Time-variable upstream and tributary Time-variable upstream and tributary inflows (minflows (m33/sec)/sec)
• Continuity flow paths for main stem and Continuity flow paths for main stem and each tributary (IQ, JQ, BQ)each tributary (IQ, JQ, BQ)
• Channel properties:Channel properties:– length (m), width (m), initial depth (m)– hydraulic exponents set to 0– bottom slope (m/m)– Manning’s roughness coefficient
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Wasp6 Flow Wave Profiles at Various Times
0.00
1.00
2.00
3.00
4.00
5.00
6.00
1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77
Distance, km
Flo
w, cm
s
5.201
5.404
5.607
5.803
6.006
Wasp6 Depth Profiles at Various Times
0.00
0.10
0.20
0.30
0.40
0.50
0.60
1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77
Distance, km
Dep
th, m
5.201
5.404
5.607
5.803
6.006
Wasp6 Velocity Profiles at Various Times
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77
Distance, km
Vel
oci
ty, m
/sec
5.201
5.404
5.607
5.803
6.006
Kinematic WaveKinematic WaveDynamic Response ProfilesDynamic Response Profiles
Chapra Kinematic Wave, Example 14.6Chapra Kinematic Wave, Example 14.6
Channel Width, Channel Width, "B", m"B", m
Channel Bottom Channel Bottom Slope, "S", m/mSlope, "S", m/m
Manning's Manning's Roughness Roughness
Coefficient, "n"Coefficient, "n"
1515 0.0040.004 0.070.07
Boundary Pulse Boundary Pulse Flow Period, dayFlow Period, day
Boundary Pulse Boundary Pulse Flow Range, m3/secFlow Range, m3/sec
Duration of Duration of Boundary Pulse, Boundary Pulse,
dayday
0.50.5 2.52.5 0.250.25
Spatial Step, dx, Spatial Step, dx, mm
Time Step, dt, dayTime Step, dt, day
10001000 0.0070.007
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Kinematic WaveKinematic WaveResponse to Stepwise FlowsResponse to Stepwise Flows
Small Stream Flow Test
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Time, days
Flo
w, c
ms
Small Stream, Gentle SlopeDepth versus Flow
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
0.00 1.00 2.00 3.00 4.00 5.00 6.00
Flow, cms
De
pth
, m Results from Wasp6
Steady Kinematic Wave
Small Stream, Gentle SlopeVelocity versus Flow
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.00 1.00 2.00 3.00 4.00 5.00 6.00
Flow, cms
Ve
loc
ity
, m/s
ec
Results from Wasp6
Steady Kinematic Wave
Small Stream, Gentle SlopeSmall Stream, Gentle Slope
SegmentSegmentLengthsLengths
mm
Channel Channel Width Width
mm
ChannelChannel BottomBottom SlopeSlopem/mm/m
Manning'sManning'sRoughnessRoughnessCoefficientCoefficient
10001000 22 0.00010.0001 0.040.04
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River Brandywine Flows – River Brandywine Flows – AnnuminasAnnuminas
• Flow PatternFlow Pattern• Average Flow, Average Flow,
m3/secm3/sec
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River Brandywine Flows – HobbitonRiver Brandywine Flows – Hobbiton
• Flow PatternFlow Pattern• Average Flow, Average Flow,
m3/secm3/sec