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[Phys-L] Re: water outflow (was earthquake)



Pete Lohstreter wrote:

I attribute it mostly to surface tension (cohesion). As the wave starts
rising as it approaches shore, it pulls the water near the shore toward
the center of the bulge.

Other factors may be in play, but I expect this is the major factor.

Nope. Capillarity is not a significant factor in a tsunami.

There's a scaling argument for that, too. Suppose we have a wave with
wavelength L. (Also, we assume the water is deep.)

Capillarity couples to the curvature of the water surface. Small L
means more curvature hence more contribution from capillarity.

In contrast, gravity makes a contribution that is larger for large L.

So there is a distinction between capillary waves and gravity waves.
Capillary waves go faster and faster as L decreases. Gravity waves
go faster and faster as L increases.

When you add the two contributions, there is in fact a minimum in the
dispersion relation at a particular wavelength, L = L* = 1.7cm. That
has the nifty property that in the vicinity of L* you can have
non-dispersive waves.

In case you have trouble remembering the magnitude of L*, note that
it is not wildly different from the size of the largest water drops
you've ever seen, which makes sense since that's another process that
involves a gravity/capillarity tradeoff.

Tsunamis are waaaay bigger than 1 7.cm, so gravity completely dominates
capillarity.