R. Manasseh Papers
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However, the nonlinear terms are not always important. The ocean system is sometimes in this condition:
These are scalings or estimates
of the sizes of some of the various quantities that
appear in the equations.
Assuming that 
and
is like saying the conditions are such that the
local speed of the
water in the ocean could change by 1 metre per second by
moving `something like'
100 metres away. This is very different to the dramatic
`splash' in figure 1,
where (if the splash is a small part of a breaking wave)
a change of
could occur over a few tens of centimetres!
Also, assuming 
is like saying the ocean is
`something like' 50 m deep:
the water speed must be zero right at the bottom, under
the last sand
grain, so that it is the ocean depth that gives the
vertical scale over which
changes in speed must be reckoned. When the
scalings are substituted into the acceleration in the
Newton's Second Law
equation (1.10),
the different types of acceleration can be `weighed up'
to assess
their importance:
The nonlinear terms are only a hundredth of the linear
term - they can be neglected for
this particular ocean
condition.
