BED, BANK & SHORE BED, BANK & SHORE PROTECTION - CHAPTER 2 pps

Turbulence can then be expressed in various ways, such as:total kinetic energy in a turbulent flow fluctuation intensities of u, v and w, relatively... Resistance in laminar and turbule

BED, BANK & SHORE

PROTECTION

Faculty of Coastal Engineering

Chapter 2

(3 class hours)

Seconds short waves seconds turbulence

Velocity field in various situations

averaged velocity values (ū = Q/A)

Chezy's law for uniform flow: ū = C √ (Ri)

Reynolds dye experiment

Reynolds number

• Laminar flow occurs at low Reynolds numbers (Re<1000)

• Turbulent flow occurs at high Reynolds numbers (Re>2000)

vs - mean fluid velocity,

L - characteristic length (h: water depth)

μ - (absolute) dynamic fluid viscosity

ν - kinematic fluid viscosity: ν = μ / ρ = 10-6 m2/s (water)

ρ - fluid density

2.2 Turbulence

Turbulence motion: velocity and pressure show irregular fluctuations

u = u + u v = v + v w = w + w p = p + p ′ ′ ′ ′

Turbulence variations:

Turbulence can then be expressed in various ways, such as:

total kinetic energy in a

turbulent flow fluctuation intensities of

u, v and w, relatively

2 2

inertia press visc.

Reynolds stresses:

2 2 2

inertia press visc Reynolds stresses

mean values turb fluctuations

Exchange of momentum due to turbulence

Resistance in laminar and turbulent flow

2.3 Uniform wall flow

¾ 20 m3/s of water flows in a 10 m wide channel with vertical banks,

a bed slope of 1/1000 and a roughness of 0.2 m What is the

depth, the velocity, the Chezy-value, the relative turbulence

intensity and the relative turbulent shear stress?

u= C√RI

Q* = bhuQ* = Q

Stop

non uniform flow

The growth of a boundary layer when an

infinitely thin plate is placed in a flow with u = u0.

Influence of pressure gradient on velocity

profile

Turbulence in windtunnel contraction

The total amount of turbulent kinetic energy, k, remains approximately

constant

Due to the increased velocity in the contraction, the relative turbulence, r,

using the local mean velocity decreases

Flow and velocities in jets

2

2

0.693 0

0.693 0

R b

Turbulent fluctuations in circular jet

instability of an axisymmetric jet

effect of strong pressure gradients

2.5 Combination of wall flow and Free flow

Flow separation around blunt and round body

Vertical constriction and expansion (sill)

Vertical expansion (backward-facing step)

Horizontal expansion

Horizontal constriction and expansion

(groyne)

Detached

bodies

2.6 Load Reduction

The end Chapter 2