hydraulics for hydrographers natural channel controls and rating curves aquarius time-series...

Hydraulics for HydrographersNatural Channel Controls and Rating Curves

AQUARIUS Time-Series Software™Aquatic Informatics Inc.

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Review of Basic HydrodynamicsWhat is a Control?Section ControlChannel ControlMultiple ControlsControlling Forces

Preview

Uniform flowApproximately valid over short distances if changes in direction and spacing of flow lines are gradual enough.

Steady flowApproximately valid over short enough intervals of time

(H- H0)~Pressure Head = dominant term in Energy Equation for most stream gauging reaches

Velocity Head varies proportional to Pressure HeadAt critical flow, Velocity Head = ½ D therefore Total Head = 1.5 x (H-H0).

Our primary assumptions from Basic Hydrodynamics


That the force in the downstream direction is equal to the resisting force (or else flow would be accelerating or decelerating through the reach)We measure Head (H-H0) as in index of force in the downstream directionThe rating curve parameters are collections of similar terms from the energy balance equation – including the resisting forces

Implications


where Hf=Head loss due to friction, K is a constant, ν = velocity, P= Wetted Perimeter, and L = Length of the channel.‘K’ includes channel rugosity; sinuosity; shape; obstructions; as well as the density and kinematic viscosity of the water

Forces resisting flow


LPvKH f 2

A control is the sum of all of the terms in the Head loss-to-friction equation, including the components of the constant K.Channel control is when L & P are dominant.Section control is the special case (i.e. Froude number = 1), where v2 is a known function of H-H0.

What is a control?


Specific Energy Curve


Froude > 1: Velocity Head and channel control upstream of gauge

Froude = 1: Section Control

Froude < 1: Channel control downstream of gauge

Froude = 1 where there is a sharp break in channel slope (e.g. crest of weir, or riffle); or a channel constrictionFroude > 1 where there are standing wavesFroude < 1 if a wave from a pebble thrown in the stream can propagate in an upstream direction

Approximation of Froude Number


Artificial Controls create the condition of Froude = 1The rating equation can be explicitly evaluated based on geometry when Froude = 1.Naturally occurring section controls are preferred as gauging locationsThe exponent in the rating equation will be approximately 1.5 for a rectangular section; and 2.5 if the banks slope at a 45o angle

Froude Number = 1


Section control exists when the Gauge is immediately upstream of a section where the Froude number of the flow =1

Section Control


Sub-criticalcritical

Sub-critical

critical

Example of a section control, looking upstream


Tranquil flow – Pressure Energy is the dominant force driving flowThe controlling reach extends downstream from the gauge some distanceFactors include: wetted perimeter, length, sinuosity, rugosity, channel shape and obstructionsThe exponent will generally be approximately 1.67 for rectangular channels

Froude < 1


Turbulent flow – Velocity Head is the dominant form of energy driving flow. No information from the channel downstream of the gauge can propagate upstream.The control section can be upstream of the gauge

Froude >1


Unconfined Alluvial streams are Self-Organizing systems that conform to the Least Action Principle (LAP) to trend toward Maximum Flow Efficiency (MFE).However, there are many forces working against MFE – (e.g. geological features that resist erosion and/or transport; and biological encroachment of the floodplain) – and it is usually these forces that determine whether multiple controls exist.

Multiple controls


Section Control at low flow Flow tumbling over streambed cobbles

Channel control at mid-flowCobbles are submerged.Sub-critical flow where the parameters in the rating equation are a function of the channel downstream of the gauge.

Over-bank flow at high stageUsually super-critical flow where the parameters of the rating equation are a function of Velocity Head and of the channel upstream from the gauge.

A ‘Hypothetical’ Multi-Control Scenario


Overbank flow


Out of Channel (i.e. overbank flow) always requires special attention


Rugosity refers to the roughness of the stream-bed and stream banks.A channel may be carved out of clays and silts, or paved with cobbles over the full range of stage in which case rugosity is captured in the rating curve coeficient.Substantial changes in rugosity with respect to stage can result in a multiple-control rating – affecting both the coefficient and the exponent but not the offset

Controlling Forces – Rugosity


Sinuosity refers to meanders in the stream channelSinuosity is primarily a consideration for tranquil flow where the control reaches for a long distance downstream of the gaugeThe effect of sinuosity is captured in the coefficient of the rating curve.

Controlling Forces - Sinuosity


Channel shape has a profound effect on the exponent of the rating curve, controlling the Head-Area relation, which in turn determines the specific weight of water available to generate velocityChannel shape also affects the position of H0 and the Point of Zero Flow.Channel shape can be quite dynamic, being affected by both geomorphologic and biologic forces

Controlling Forces - Shape


The shape of the channel can also control ratings


Murray River in September Murray River in June

Natural obstructions, such as remnant boulders, may create channelized flow at low stage and critical flow at mid stage.Man-made obstructions are generally continuous across the stream.At a high enough stage, streambed obstructions become ‘drowned-out’ resulting in a multi-control rating curve

Controlling Forces - Obstructions


The Density and Kinematic Viscosity of water both change as a function of temperature and of sediment load.If a stream always has a high sediment load at high-flow and a low sediment load at low-flow, then the effects of these variables are captured in the exponent of the rating curveIf the pattern of sediment loading is not consistent with respect to stage then these factors will result in scatter around the rating curveHigh Sediment Load increases Viscosity, which increases drag in the laminar layer thus altering the shape of the vertical velocity profile. If the vertical velocity profile is assumed, rather than measured, then these measurements will plot to the left of the rating curve

Controlling Forces – Properties of Water


Velocity dominates the shape of the rating curve when Froude > 1.

Controlling Forces – v2


The wetted perimeter is an important factor in the shape of the rating curve in complex channelsA change in control is likely when emergent obstructions become submergent. A gradual change in control is likely as the effect of a relatively High-P stream bed gives way to relatively Low-P stream-banks at higher flows.A change in control is likely when the stage encroaches on riparian vegetation which increases wetted perimeter

Controlling Forces - P


The length of the control section can be very short for a section control or very long for tranquil flow.The length dimension changes as a function of velocity, which in turn changes as a function of Head. As such, the effect of length is generally captured in the exponent of the rating curve and does not typically result in a change in control.

Controlling Forces - L


The controlling features of stream channels are subject to change. In the lesson “Channel Dynamics and shift corrections” we will look at some of the causes of change and how AQUARIUS can accommodate those dynamic conditions

Preview


Recommended, on-line, self-guided, learning resources

USGS GRSAT traininghttp://wwwrcamnl.wr.usgs.gov/sws/SWTraining/Index.htm

World Hydrological Cycle Observing System (WHYCOS) training materialhttp://www.whycos.org/rubrique.php3?id_rubrique=65#hydrom

University of Idahohttp://www.agls.uidaho.edu/bae450/lessons.htm

Humboldt Collegehttp://gallatin.humboldt.edu/~brad/nws/lesson1.html

Comet Training – need to register – no costhttp://www.meted.ucar.edu/hydro/basic/Routing/print_version/05-stage_discharge.htm#11

http://wwwrcamnl.wr.usgs.gov/sws/SWTraining/Index.htm

http://www.whycos.org/rubrique.php3?id_rubrique=65#hydrom

http://www.agls.uidaho.edu/bae450/lessons.htm

http://gallatin.humboldt.edu/~brad/nws/lesson1.html

http://www.meted.ucar.edu/hydro/basic/Routing/print_version/05-stage_discharge.htm#11

http://www.meted.ucar.edu/hydro/basic/Routing/print_version/05-stage_discharge.htm#11


Thank you from the AI TeamWe hope that you enjoy AQUARIUS!

hydraulics for hydrographers natural channel controls and rating curves aquarius time-series...

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