Wave theory and wave transformation Flashcards
Define Coast
▪ Transition between sea and land
▪ Coastline is defined as the area between seaward and
landward influence of waves
▪ Total length: approx. 356,000 km to 1,634,701 km (??)
▪ Longest coastlines: 1. Canada, 2. Indonesia, 3. Russia
▪ Germany: Place 50, coastal length: 2,389 to 3,624 km
▪ Economic value of coastal ecosystems: 12,568 billion US$ =
38% of all ecosystems
▪ Gross product of earth population: 18,000 billion US$/a
▪ 66% of the earth population live in an area of <300km from
the coast
▪ Megacities: 8/10 at the coast (>21,000,000 inhabitants)
Which phenomena occur at the coast?
▪ Tidal dynamics
▪ Storm Surges
▪ Currents
▪ Waves
▪ Sediment transport
▪ Morphodynamics
Coastal Problems
➢ Coastal Erosion
➢ Salinity Intrusion
➢ Coastal Pollution
➢ Drainage
➢ Loss of Biodiversity
Use of the Coastal Area
- Coastal protection
- Ports & shipping
- Offshore wind power plants
- Offshore plants
- Nature protection
- Industry
- Tourism
- Agriculture
- Fishery
What is coastal protection?
Flood protection + Erosion protection
Common coastal structures:
-Seadikes
-Revetments
-Breakwaters
-Complex Structures
-Vertical Structures
-Rubble moundStructures
types of breakwaters
-caisson
-concrete-rubble-mound (vandermeer)
-rock-rubble-mound (hudson)
cube, antifer-cube, tetrapods, dolos
Transtidal / trans gravity waves
Period: >24h
Primary disturbing force: sun, moon
Primary restoring force: coriolis force
long-period waves
Period: 5 min - 24h
Primary disturbing force: storm systems , tsunamis
Primary restoring force: coriolis force
infragravity waves
Period: 30s - 5 min
Primary disturbing force: wind
Primary restoring force: gravity
gravity waves
Period: 1s - 30s
Primary disturbing force: wind
Primary restoring force: gravity
ultragravity waves
Period: 0,1s - 1s
Primary disturbing force: wind
Primary restoring force: gravity / surface tension
capillary waves
Period: <0,1s
Primary disturbing force: wind
Primary restoring force: surface tension
assumptions of linear wave theory:
- Flow is incompressible
density of water = const. - Water depth h is constant
- Waves are periodic
- irrotational
- inviscid flow
Deep water
d/L >1/2
L=(gT^2)/2pi
C=L/T=gT/2pi
transient zone
1/20 < d/L < 1/2
L=((gT^2)/2pi)tanh(2pid/L)
C=L/T=((gT)/2pi)tanh(2pid/L)
shallow water
d/L < 1/20
L= Tsqrt(gd)
C=L/T= sqrt(g*d)
progressive wave vs standing wave:
horizontal orbital velocity u,
vertical orbital velocity v:
u=umax in zerocrossing (oscillation node) with standing waves, u=zero in zerocrossing (oscillation node) with progressive waves.
v=vmax in antinode of standing waves
equation for the wave number k
k=2*pi/L
Wave energy
E= 1/8 rho,wgH^2
Flow of Energy equation
F,m= 1/16* rho,wgH^2*c(1+ 2kh/sinh(2kh))
group velocity equation
Cg= Fm/E = (1/2)*c(1+2kh/sinh(2kh))
spilling, plunging, surging:
xi, occurance,
xi= tan(alpha)/sqrt(H/L)
xi,spilling < 0,5
0,5 < xi,plunging < 3,3
xi,surging > 3,3
spilling: natural beaches
plunging: dikes and revetments with flat embankments
surging: dikes and revetments with steep embankments
which equation applies when waves run perpendicular to the coast (θ=0°)
Ec,g = nc*E = const.
Wave energy E, group velocity c,g ,wave velocity c, wave number n
