Wave and Current Interaction in the Ocean - Wave Propagation in Drilling, Well Logging and Reservoir Applications - page 331

7
Wave and Current Interaction in the Ocean

In this chapter, we will describe ocean applications for kinematic wave
theory using simple examples, assuming an elementary background in
hydrodynamics (the reader should review Chapters 2 and 3). The solution
methodologies offered are powerful, but the specific results are even more so.
They are, for example, particularly useful in estimating wave forces for offshore
applications. Some of these may include loadings on drilling platforms, their
effects on dynamic positioning, marine riser cables and pipelines. Also, we will
show how results which are in themselves limited can be integrated to form
usable global models for other applications.
7.1 Wave Kinematics and Energy Summary.
Again, when the complex dispersion relation corresponding to an
elementary plane wave

(k,x,t) =

r (k,x,t) + i i (k,x,t)

(7.1)

is known, either analytically or experimentally, the wave energy and momentum
densities E and M evolve in space-time according to

E/ t + (

r k (k,x,t)E)/ x = E{2 i + r t (k,x,t)/ r } (7.2)

M/ t + (

r k (k,x,t)M)/ x = M{2 i - r x (k,x,t)/k} (7.3)

These results, given in Chapter 2, apply to all varieties of elastic, fluid-dynamic,
electromagnetic wave propagation, and so on.

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