Re: Ocean/air disappearance and side-effects...

On Apr 14, 12:40 am, Johnny1a <shermanl...@xxxxxxxxxxx> wrote:

If I read this right it looks like the energy release as ocean and air
rush in would be determined by pressure times the volume of the
sphere

You could do it that way, but it's a bit of a tricky integration. How
about this. Initial state: 1000 meter radius hemispherical "hole" in
the ocean. Final state: smooth ocean with the same surface elevation
(it's an ocean; a paltry 2 cubic kilometer of water being removed
isn't going to alter mean sea level by enough to sneeze at). Compare
the potential energy of those two states, and I get an energy change
of 1.84 Mt (assuming constant density of water at 1000 kg/m^3, and
ignoring the air entirely).

I'm not quite sure how to estimate the second-order effects of this
situation...

I'm not positive either. The instant after the the sphere is removed,
you have a free surface with a huge pressure differential. The result
should be a spherical implosion but not a uniform one (higher pressure
at the bottom), with a rarefaction wave propagating into the
surrounding water; that's going to happen rapidly, but not result in a
lot of material. Bulk flow will take a lot longer, just to get that
much water moving, but move it will. The thing is, initially all that
energy is going to end up almost entirely in kinetic energy - mostly
really large waves. Larger than for a similar energy scale impact, as
there's no easy way to couple the energy into heat. If I use numerical
estimates of impacts (which should underestimate the waves), then I
get a wave height of 22 meters at a distance of about 10 km from the
"impact".

I strongly suspect I'm missing something, but not too much. The result
is the wave isn't catastrophic, but it sure would be interesting if
you were "too close".

The point about Coriolis force having a role in the aftereffects might
be interesting, but I suspect again overplayed. The water isn't moving
far - on the order of a kilometer or so. Even at high speeds, that's
not a lot for rotation to play a role. If artillery shells fired 10's
km at ballistic velocities only shift on the order of 10's of meters,
then the transverse velocity built up in this situation is going to be
similarly small - perhaps 1/1000's of the inward velocity? Vertical
Coriolis effects are going to be even smaller, as the vertical scale
is roughly the same, but the vertical velocity is likely to be much
smaller due to gravity. I suspect pre-existing current gradients
across the initial "hole" would have a larger effect.

The hydrodynamics would be interesting, however, but I think it's
going to take a simulation.

what form can I expect this energy to take: heat, wave
action, sound, wind, a tiny tsunami, or what?

A lot of wind, but dissipating radially. Very little heat. Think of
how much stirring water heats it up... not very significant, and the
only shock front heating is going to be at the very center of the
sphere, a small volume. You might get some interesting effects there,
but small volume, and any jet thrown skyward is agin going to be
small, but I'm not sure how to get a handle on it. Sound, yes, wind,
yes. but I'm estimating that better than 90% of the energy ends up in
waves.

--
Brian Davis


.

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