Re: smoke-ring paradox

[Gary Turner <turner@MORNINGSIDE.EDU>]

On Tue, 23 Jul 2002 15:53:07 -0700, William Beaty <billb@ESKIMO.COM> wrote:

> On Tue, 23 Jul 2002, Bob Sciamanda wrote:
>
> > If rear flows = forward flows then there is no CM motion.  The equal
> > rear/forward flows in the CM frame are superimposed upon the forward CM
> > flow when viewed from the Lab frame, giving an unbalanced forward flow.
>
> In the lab fram there can be no forward flow without equal rearward flow,
> otherwise the fluid would build up in one place and be lacking in another
> place.
The rearward flow is from the fluid surrounding the ring, which is pushed
around and back behind the ring.  Hence, the ring carries momentum forward
and the fluid through which it travels temporarily carries momentum
backwards (momentum conservation also requires that the source recoils
somewhat).  However, the ambient fluid is pulled back around behind the
ring, colliding with its counterpart from the other side (think about a
slice through a smoke ring as two adjacent counter-rotating vortices).
This act pushes the smoke ring on, overcoming the 'air resistance' that you
might expect to slow the smoke ring down.  Or something like that.

The end result is a static fluid and a ring advecting through it quite
easily, at (almost) constant speed.  The fluid immediately in front of the
ring is deposited immediately behind the ring where it (virtually) stops.

The streamlines are not closed circles, but spirals.  A consequence of this
is that the fluid must be flowing faster through the middle than around the
edges.  Anyone enlighten us on why this occurs?


For a fun experiment, go swimming in a quiet pool (if you can find one) and
try making vortices by just swishing your arm through the water.  They
always occur in counter-rotating pairs and always advect themselves along
as a pair - they basically 'sit' in each others flow.