Unsteady waves

Question 1

Cause of nonlinearity

Answer 1

-driven by nonlinear FSBC
-larger for steeper waves

Question 2

Formation of regular waves

Answer 2

-1 free wave therefore 1 phase velocity
-applying a moving frame of reference would produce a steady graph

Question 3

Formation of irregular waves

Answer 3

-for >= 2 bound waves so there is no unique phase velocity
-real waves deform with both space and time

Question 4

load predictions

Answer 4

-loads reliable only when the model accurately predicts wave particle kinematics
*drag domination -> F is directly proportional to u2
*stokes is easy to apply but “nonphysical” so inaccurate
-failure is often assessed at the bed as shear or overturning moments
*only loads above the failure surface are considered
*calibration is applies to that surface but requires prior knowledge of the failure mode

Question 5

wave types

Answer 5

swell
- narrow range of low f
- unidirectional and steady-ish

wind
-bread range of high f
-multidirectional with irregularity
-+-20 degrees of directional spread

Question 6

linear random wave theory

Answer 6

-sum the linear regular wave solution for eta and u
*applies the dispersion equation
-based in the fourier analysis of a measured wave and should only be applied to the free linear waves

Accuracy
- nonlinear effects are laegrest near the surface where u and partial du/dt are at their max so this has a big impact on the F/M predctions
-should be applied to the the surface level but errors increase as it is approached
-high f contamination

High f contamination
-small amplitude, high f waves are extrapolated to heights far above their amplitude
-method doesnt account for high f waves on low f ones
-this is all an issue with effective depth

Question 7

wheeler stretching

Answer 7

-empirically reduced velocity at SWL but doesnt satisfy mass continuity and is insufficient to model real fluid flow
-basically incorrect

z* = (z - eta(t)) / (1+eta(t)/d)

Question 8

Nonlinear random wave theory

Answer 8

Bound waves tend to be more significant than the regular waves

For a high f wave on low f wave, both free
-long wave is unchanged
-short wave has higher a and shorter L in the long waves peak but shallower and longer in its trough
* change can be treated as a new bound wave needed to satisfy FSBC
*amplitude modulation as follows

g’ = g + (partial d2eta/dt2)_longwave
mgh = constant, so change in gravity drives change in H

Question 9

Spectra for random wVe theory application

Answer 9

cant separate bound in measure/calculated spectra
-for bound c not = omega/k so the dispersion equations doesnt apply
-1st order has no bound terms
- >= 2nd order has stokes terms with all up to >=2 wave coupling
-2nd order can use bispectral analysis to ID 2 wave coupling

Question 10

Second order random wave theory

Answer 10

-sums the interactions from all possible free wave pairs
-difficult to use for measured data