Every time I read about seasteading I have to ask myself if any of the people promoting the idea have ever been at sea in a storm.
No, the folks working on seasteads have no concept of waves. They just plan on putting house boats out in middle of the ocean and having a big party.
http://seasteading.wpengine.netdna-cdn.com/wp-content/uploads/2012/01/Feb2011_Report_p1.pdfThe wave theory considered here is limited to linear deep water gravity waves, i.e. linear in the sense that
‘small’ amplitude waves will be considered, and neglecting nonlinear effects, such as for instance the breaking waves. ‘Deep water’ refers to the fact that the influence of the bottom is neglected; this is a very
reasonable assumption provided the water depth exceeds one-half the wavelength of the longest waves
considered. ‘Gravity’ refers to the restoring force associated with the waves.
By the assumption of linearity, any sea-state may be regarded as being composed of a superposition of
sinusoidal waves. The surface profile of a traveling wave can be described by h=A sin(kx-ωt), where x and
t are space and time coordinates, k and ω are the wave-vector and angular frequency respectively, and A
is the amplitude.
These quantities can be shown to be related as: ω2=gk
Subject to the standard wave relations, T=2πω, f=ω2π, λ=2πk, c=ωk
Thus, every wavelength has a different speed of propagation, a characteristic of deep-water waves. Waves do not merely act on the surface, but their effect extends into the water. The relation between
depth and amplitude of a wave is exponential, and may be represented as a function of depth and
wavelength (or wave-vector) as A(z)= A exp(-k z). Thus, the effect of a wave diminishes quickly with
depth, and shorter waves decay faster than longer ones.
This results in a complete solution for a single wave component in terms of position, depth and time35:
u=ω A cosine (k x – ω t) exp(-k z)
v=ω A sin (k x – ω t) exp (-k z)
p=ρ g A cosine (k x – ω t) exp(-k z)
where u and v are horizontal and vertical velocity components, and p is the pressure disturbance due to
waves (not including hydrostatic pressure).
One relevant yet not intuitively obvious result is that a given patch of water tracked through the motion
of a gravity wave makes circular motion. Objects floating in water not otherwise disturbed will move as
much laterally as vertically.
The above section treats monochromatic waves. The actual waters of the sea can be thought of as a
linear superposition of such waves, of varying frequencies and directions.
The distribution of frequencies is in general not completely arbitrary, but follows a distribution clustered
around a dominant wavelength. This spectrum is typically characterized by two parameters; the
‘significant wave height’, Hs, and the peak period, Tp.
Formally, Hs(1/3), or Hs for short, is defined as the average height of the highest third of wave crests.
Instead of using the complete spectrum, in this report analysis proceeds by a simplified monochromatic
wave matching the parameters of the dominant component of the spectrum. This is of course a
simplification: some crests may be far higher than Hs; in fact, a wave of nearly twice Hs occurs with a
probability of 1/1000. But beyond this amplitude, probability diminishes significantly.
Often, a sea-state is composed of locally generated waves, and the residual waves of a storm in the
distance. This latter component is referred to as swell, and typically has a low frequency. If the swell
comes at an angle to the wind generated waves, the resulting sea is called a cross sea. Such conditions
are potentially hazardous to ships, because the hull cannot be aligned in two directions at once.
One aspect of open-sea waves that is typically underestimated is their length; again, waves coming up to
the shore are not representative, as in the process of running up on the shore, their wavelength is
compressed. On the open sea, the dominant wavelength may be up to hundreds of meters.
