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

[jsd at AV8N.COM (John Denker)]

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.