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
wave refraction formulas
sin(alph,1)/sin(alph,2)=c1/c2
b/cos(alpha) = const.
=> sqrt(b1/b2)=sqrt(cos(alph,1)/cos(alph,2)) =k,r kr= refraction coefficient
equation of wave steepness:
s=H/L
wave height H, steepness s, wave length L
longitudinal wave vs transverse wave
A longitudinal wave is created once, for example in the case of a dam break , the opening of a contactor, a torrent or a tsunami. Transverse waves occur regularly , for example gravity waves such as wind waves or capillary waves.
wave transformation effects in shallow water
-Shoaling
-Refraction
-Breaking waves
wave transformation effects in shallow and deep water
-Diffraction
-Reflection
Define Refraction
Refraction describes the change of wave height and wave direction due to grounding of waves which are oblique to the depth contours. Refraction does not appear if waves are entering perpendicular to the depth contours. Refraction cannot appear without shoaling.
Define Reflection
Waves hit a barrier and reflect in the other direction (angle of entry = angle of exit)
Define Shoaling
Shoaling is the change of wave height while a wave enters shallow water under normal wave attack (θ = 0°). At first, the wave height slightly declines, afterwards it increases constantly.
Define Diffraction
Diffraction is the spreading of waves behind obstacles, e.g. structures. The diffraction area, also known as shadow area, is not directly exposed to the sea state. The waves we observe in the diffraction area are ascribed to diffraction
effects.
Define Breaking waves
Shoaling causes the wave height to increase in shallow water. In theory, it increases into infinity. However, this effect is physically limited. When reaching the breaker height, a wave breaks and its energy is dissipated.
Shoaling coefficient
K,s=H2/H1=sqrt(cg1/cg2)=sqrt(n1c1/n2c2)
Snellius Law
sin(alpha1)/sin(alpha2)=c1/c2
Refraction Coefficient
Kr=H2/H1=sqrt(b1/b2) = sqrt(cos(alpha1)/cos(alpha2))
Breaking Criteria for deep water, transient zone and shallow water
Deep Water:
H/L=1/7
Transient Zone:
H/L=(1/7)tanh(2pid/L)
shallow water:
H/d=0,78
which are the conditions for refraction?
-change in depth
-oblique wave attack
