advective flows. watershed & water quality modeling technical support center surface water flow...

Advective FlowsAdvective Flows

Watershed & Water Quality Modeling Technical Support CenterWatershed & Water Quality Modeling Technical Support Center

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


Surface Water Flow Options – WASP Surface Water Flow Options – WASP ScreenScreen


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


Transport Fields – WASP ScreenTransport Fields – WASP Screen


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


Flow Patterns – WASP ScreenFlow Patterns – WASP Screen


Flow Time Functions – WASP ScreenFlow Time Functions – WASP Screen


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



WASP internally calculatesflows, volumes, depths, widths

3. Kinematic Wave



4. Hydrodynamic Linkage

Hydro Hydro

HydrodynamicInterface

WASPWASP

Examples of Specifying FlowsExamples of Specifying Flows


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


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


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


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


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


Kinematic Wave EquationsKinematic Wave Equations

0

t

A

x

Q

Continuity equation (mass balance):

00 SSg f

Momentum equation (momentum balance):

gravity friction


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


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


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


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


River Brandywine Flows – River Brandywine Flows – AnnuminasAnnuminas

• Flow PatternFlow Pattern• Average Flow, Average Flow,

m3/secm3/sec


River Brandywine Flows – HobbitonRiver Brandywine Flows – Hobbiton

• Flow PatternFlow Pattern• Average Flow, Average Flow,

m3/secm3/sec

advective flows. watershed & water quality modeling technical support center surface water flow...

Documents

pore water flow

water column flow

water evaporationprecipitation

net flow option

kinematic wave slide

multiple flow patterns

gross flow option

bqcontinuity flow paths