# Presentation: 885163

## Advective Flows

## Surface Water Flow Options

- Specified river, tributary flows (net flow)
- Specified lake, estuary flows (separate flows)
- Calculated flows using internal kinematic wave equations
- Calculated flows from external hydrodynamic model

## Surface Water Flow Options – WASP Screen

## Transport Flow Fields

- Type 1 - **Water Column** flow carries both dissolved and particulate material
- Type 2 - **Pore Water** flow carries dissolved  material only
- Type 3,4,5 – **Solids “i”** settling/resuspension carries particulate fraction only
- Type 6 – **Water** evaporation/precipitation adjusts water volume only

## Transport Fields – WASP Screen

## WASP Transport Scheme

- Each Flow Field can have multiple **flow patterns** and **time functions**.
- WASP sums the individual flows for each segment to determine overall transport

## Flow Patterns – WASP Screen

## Flow Time Functions – WASP Screen

## Surface Flow Options

- +

- =

- 1. Net Flow Option

- 2. Gross Flow Option

- +

- =

## Surface Flow Options

- 3. Kinematic Wave

## Surface Flow Options

- 4. Hydrodynamic Linkage

- Hydro

**Hydrodynamic**
**Interface**

- WASP

## Examples of Specifying Flows

## Flow through Simple Pond 

- Flow Time Function

- Time, days

- Flow Path
- Continuity Function

## Upstream Flow Through River

- Flow Time Function

- Time, days

- Flow Path
- Continuity Function

## Flow through River with Tributary

- Flow Path
- Continuity Functions

- Flow Time Function

- Time, days

## Branched Flow through River

## Kinematic Wave Option

- Applicable to 1-dimensional, branching streams, rivers
- Calculates flow wave propagation and resulting variable flows, volumes, depths, and velocities throughout the network
- Default rectangular channel shape unless user specifies hydraulic coefficients

## Kinematic Wave Equations

**Continuity equation (mass balance):**

**Momentum equation (momentum balance):**

- gravity

- friction

## Kinematic Wave Equations

**Substitute in Manning’s equation:**

**Kinematic wave differential equation:**

## Kinematic Wave Input Data

- Time-variable upstream and tributary inflows (m3/sec)
- Continuity flow paths for main stem and each tributary (IQ, JQ, BQ)
- Channel properties:
- length (m), width (m), initial depth (m)
- hydraulic exponents set to 0
- bottom slope (m/m)
- Manning’s roughness coefficient

## Kinematic WaveDynamic Response Profiles

- Kinematic WaveDynamic Response Profiles

| Chapra Kinematic Wave, Example 14.6 |  |  |
| --- | --- | --- |
|   |  |   |
| Channel Width, "B",    m | Channel Bottom Slope, "S", m/m | Manning's Roughness Coefficient, "n" |
| 15 | 0.004 | 0.07 |
| Boundary Pulse Flow Period, day | Boundary Pulse Flow Range, m3/sec | Duration of Boundary Pulse, day |
| 0.5 | 2.5 | 0.25 |
| Spatial Step, dx, m | Time Step, dt, day |   |
| 1000 | 0.007 |   |

## Kinematic WaveResponse to Stepwise Flows

| Small Stream, Gentle Slope |  |  |  |
| --- | --- | --- | --- |
| Segment
Lengths
m | Channel 
Width 
m | Channel
 Bottom
 Slope
m/m | Manning's
Roughness
Coefficient |
| 1000 | 2 | 0.0001 | 0.04 |

## River Brandywine Flows – Annuminas

- Flow Pattern
- Average Flow, m3/sec

## River Brandywine Flows – Hobbiton

- Flow Pattern
- Average Flow, m3/sec