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LECTURE 6 HYDRAULICS AND SEDIMENT TRANSPORT: RIVERS AND TURBIDITY CURRENTS PowerPoint PPT Presentation


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CEE 598, GEOL 593 TURBIDITY CURRENTS: MORPHODYNAMICS AND DEPOSITS. LECTURE 6 HYDRAULICS AND SEDIMENT TRANSPORT: RIVERS AND TURBIDITY CURRENTS. Head of a turbidity current in the laboratory. From PhD thesis of M. H. Garcia.

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LECTURE 6 HYDRAULICS AND SEDIMENT TRANSPORT: RIVERS AND TURBIDITY CURRENTS

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Lecture 6 hydraulics and sediment transport rivers and turbidity currents

CEE 598, GEOL 593

TURBIDITY CURRENTS: MORPHODYNAMICS AND DEPOSITS

LECTURE 6

HYDRAULICS AND SEDIMENT TRANSPORT:

RIVERS AND TURBIDITY CURRENTS

Head of a turbidity current in the laboratory

From PhD thesis of M. H. Garcia


Lecture 6 hydraulics and sediment transport rivers and turbidity currents

STREAMWISE VELOCITY AND CONCENTRATION PROFILES: RIVER AND TURBIDITY CURRENT

u = local streamwise flow velocity averaged over turbulence

c = local streamwise volume suspended sediment concentration averaged over turbulence

z = upward normal direction (nearly vertical in most cases of interest)

z

z


Lecture 6 hydraulics and sediment transport rivers and turbidity currents

VELOCITY AND CONCENTRATION PROFILES BEFORE AND AFTER A HYDRAULIC JUMP

The jump is caused by a break in slope

Garcia and Parker (1989)


Lecture 6 hydraulics and sediment transport rivers and turbidity currents

A

u

utA

x

ut

VOLUME FLUX OF FLOWING FLUID AND SUSPENDED SEDIMENT

The flux of any quantity is the rate at which it crosses a section per unit time per unit area.

So flux = discharge/area

The fluid volume that crosses the section in time t is Aut

The suspended sediment volume that crosses is cAut

The streamwise momentum that crosses is wuAut

The fluidvolume flux = u

The suspended sediment volume flux = uc

The streamwise momentum flux = wu2


Lecture 6 hydraulics and sediment transport rivers and turbidity currents

LAYER-AVERAGED QUANTITIES: RIVER

In the case of a river, layer = depth

H = flow depth

U = layer-averaged flow velocity

C = layer-averaged volume suspended sediment concentration

(based on flux)

Now let

qw = fluid volume discharge per unit width (normal to flow)

qs = suspended sediment discharge per unit width (normal to flow)

discharge/width = integral of flux in upward normal direction


Lecture 6 hydraulics and sediment transport rivers and turbidity currents

FOR A RIVER:

Flux-based average values U and C

Or thus

z


Lecture 6 hydraulics and sediment transport rivers and turbidity currents

LAYER-AVERAGED QUANTITIES: TURBIDITY CURRENT

The upper interface is diffuse!

So how do we define U, C, H?


Lecture 6 hydraulics and sediment transport rivers and turbidity currents

USE THREE INTEGRALS, NOT TWO

Let

qw = fluid volume discharge per unit width

qs = suspended sediment discharge per unit width

qm = forward momentum discharge per unit width

Integrate in z to “infinity.”

z


Lecture 6 hydraulics and sediment transport rivers and turbidity currents

FOR A TURBIDITY CURRENT

Three equations determine three unknowns U, C, H, which can be computed from u(z) and c(z).


Lecture 6 hydraulics and sediment transport rivers and turbidity currents

BED SHEAR STRESS AND SHEAR VELOCITY

Consider a river or turbidity current channel that is wide and can be approximated as rectangular.

The bed shear stress b is the force per unit area with which the flow pulls the bed downstream (bed pulls the flow upstream) [ML-1T-2]

The bed shear stress is related to the flow velocity through a dimensionless bed resistance coefficient (bed friction coefficient) Cf, where

The bed shear velocity u [L/T] is defined as

Between the above two equations,

where Cz = dimensionless Chezy resistance coefficient


Lecture 6 hydraulics and sediment transport rivers and turbidity currents

SOME DIMENSIONLESS PARAMETERS

D = grain size [L]

 = kinematic viscosity of water [L2/T], ~ 1x10-6 m2/s

g = gravitational acceleration [L/T2]

R = submerged specific gravity of sediment [1]

Froude number ~ (inertial force)/(gravitational force)

Flow Reynolds number ~ (inertial force)/viscous force): must be >~ 500 for

turbulent flow

Particle Reynolds number ~ (dimensionless particle size)3/2


Lecture 6 hydraulics and sediment transport rivers and turbidity currents

SOME DIMENSIONLESS PARAMETERS contd.

Shields number ~ (impelling force on bed particle/ resistive force on bed

particle): characterizes sediment mobility

Now let c denote the “critical” Shields number at the threshold of motion of a particle of size D and submerged specific gravity R. Modified Shields relation:


Lecture 6 hydraulics and sediment transport rivers and turbidity currents

SHIELDS DIAGRAM

The silt-sand and sand-gravel borders correspond to the values of Rep computed with R = 1.65,  = 0.01 cm2/s and D = 0.0625 mm and 2 mm, respectively.

motion

no motion


Lecture 6 hydraulics and sediment transport rivers and turbidity currents

CRITERION FOR SIGNIFICANT SUSPENSION

But recall

where

and

Thus the condition

and the relation of Dietrich (1982):

specifies a unique curve

defining the threshold for significant suspension.


Lecture 6 hydraulics and sediment transport rivers and turbidity currents

SHIELDS DIAGRAM WITH CRITERION FOR SIGNIFICANT SUSPENSION

Suspension is significant when u/vs >~ 1


Lecture 6 hydraulics and sediment transport rivers and turbidity currents

NORMAL OPEN-CHANNEL FLOW IN A WIDE CHANNEL

Normal flow is an equilibrium state defined by a perfect balance between the downstream gravitational impelling force and resistive bed force. The resulting flow is constant in time and in the downstream, or x direction.

  • Parameters:

  • x = downstream coordinate [L]

  • H = flow depth [L]

  • U = flow velocity [L/T]

  • qw = water discharge per unit width [L2T-1]

  • B = width [L]

  • Qw = qwB = water discharge [L3/T]

  • g = acceleration of gravity [L/T2]

  • = bed angle [1]

    tb = bed boundary shear stress [M/L/T2]

  • S = tan = streamwise bed slope [1]

  • (cos   1; sin   tan   S)

  • w = water density [M/L3]

The bed slope angle  of the great majority of alluvial rivers is sufficiently small to allow the approximations


Lecture 6 hydraulics and sediment transport rivers and turbidity currents

THE DEPTH-SLOPE RELATION FOR NORMAL OPEN-CHANNEL FLOW

Conservation of water mass (= conservation of water volume as water can be treated as incompressible):

Conservation of downstream momentum:

Impelling force (downstream component of weight of water) =

resistive force

Reduce to obtain depth-slope product rule for normal flow:


Lecture 6 hydraulics and sediment transport rivers and turbidity currents

THE CONCEPT OF BANKFULL DISCHARGE IN RIVERS

Let  denote river stage (water surface elevation) [L] and Q denote volume water discharge [L3/T]. In the case of rivers with floodplains,  tends to increase rapidly with increasing Q when all the flow is confined to the channel, but much less rapidly when the flow spills significantly onto the floodplain. The rollover in the curve defines bankfull discharge Qbf.

Bankfull flow ~ channel-forming flow???

Minnesota River and floodplain, USA, during the record flood of 1965


Lecture 6 hydraulics and sediment transport rivers and turbidity currents

PARAMETERS USED TO CHARACTERIZE BANKFULL CHANNEL GEOMETRY OF RIVERS

In addition to a bankfull discharge, a reach of an alluvial river with a floodplain also has a characteristic average bankfull channel width and average bankfull channel depth. The following parameters are used to characterize this geometry.

Definitions:

Qbf = bankfull discharge [L3/T]

Bbf = bankfull width [L]

Hbf = bankfull depth [L]

S = bed slope [1]

Ds50 = median surface grain size [L]

n = kinematic viscosity of water [L2/T]

R = (rs/r – 1) = sediment submerged specific gravity (~ 1.65 for natural

sediment) [1]

g = gravitational acceleration [L/T2]


Lecture 6 hydraulics and sediment transport rivers and turbidity currents

SETS OF DATA USED TO CHARACTERIZE RIVERS

Sand-bed rivers D  0.5 mm

Sand-bed rivers D > 0.5 mm

Large tropical sand-bed rivers

Gravel-bed rivers

Rivers from Japan (gravel and sand)


Lecture 6 hydraulics and sediment transport rivers and turbidity currents

SHIELDS DIAGRAM AT BANKFULL FLOW

Compared to rivers, turbidity currents have to be biased toward this region to be suspension-driven!


Lecture 6 hydraulics and sediment transport rivers and turbidity currents

FROUDE NUMBER AT BANKFULL FLOW

Turbidity currents?


Lecture 6 hydraulics and sediment transport rivers and turbidity currents

DIMENSIONLESS CHEZY RESISTANCE COEFFICIENT AT BANKFULL FLOW

Turbidity currents?


Lecture 6 hydraulics and sediment transport rivers and turbidity currents

DIMENSIONLESS WIDTH-DEPTH RATIO AT BANKFULL FLOW

Turbidity currents?


Lecture 6 hydraulics and sediment transport rivers and turbidity currents

THE DEPTH-SLOPE RELATION FOR BED SHEAR STRESS DOES NOT NECESSARILY WORK FOR TURBIDITY CURRENTS!

In a river, there is frictional resistance not only at the bed, but also at the water-air interface. Thus if I denotes the interfacial shear stress, the normal flow relation generalizes to:

But in a wide variety of cases of interest, I at an air-water interface is so small compared to b that it can be neglected.


Lecture 6 hydraulics and sediment transport rivers and turbidity currents

A TURBIDITY CURRENT CAN HAVE SIGNIFICANT FRICTION ASSOCIATED WITH ITS INTERFACE

If a turbidity current were to attain normal flow conditions,

where

and Cf denotes a bed friction coefficient and Cfi denotes an interfacial frictional coefficient.

But turbidity currents do not easily attain normal flow conditions!


Lecture 6 hydraulics and sediment transport rivers and turbidity currents

REFERENCES

Garcia and Parker (1989)


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