| From: Kevin Phyland | 19/07/99
10:18:25 |
| Subject: Coriolis effects | post id:
24749 |
| Hi all, I've just seen the umpteenth explanation of water swirling clockwise down the sink in the southern hemisphere and need this cleared up definitively. I would have thought that the effect of the Earth's rotation on a fluid over a distance of thirty centimetres would be infinitesimal and hardly result in such distinct motion. What actually occurs! Yours in frustration, Kevin Phyland Wycheproof P-12 College Wycheproof, Vic. 3527. | |
| From: Chris (Avatar) | 19/07/99
10:43:56 |
| Subject: re: Coriolis effects | post id:
24751 |
Hi again Kevin. The coriolis effect does not show up in your kitchen sink, bathroom, toilet, etc. The effect is far too weak. Definitively. I did all the calculations a while back to demostrate just how weak it was, but can't find them at present. I'll have another look for you, because this one should go in the FAQ (Chris?) Cheers Chris | |
| From: Darren | 19/07/99
10:46:38 |
| Subject: re: Coriolis effects | post id:
24752 |
| The Coriolis effect is only
significant for bodies of water with an order of magnitude of 100's or
1000's of kilometres, not 10's of centimetres. At least, that's what my
first-year Marine Physics lecturer told us many moons ago... The direction of rotation of water down a plug hole in your bathroom is not dictacted by the Coriolis force and can therefore be the same in both the northern and southern hemispheres or different in the same hemisphere. | |
| From: Chris (Avatar) | 19/07/99
13:47:10 |
| Subject: re: Coriolis effects | post id:
24780 |
Here is the Coriolis analysis I presented in January this year… Below is an attempt at analysis to try to answer the two and fro-ing about Coriolis. It is right that the Coriolis effect is always there, however it is definitely negligible in a bathtub sized body of water draining at a reasonable rate: The governing equations for a homogeneous, incompressible inviscid fluid are the Euler equations. When you add the vertical component of the Coriolis force, you get: du/dt + u(du/dx) + v(du/dy) - fv = -g(dh/dx) dv/dt + u(dv/dx) + v(dv/dy) + fu = -g(dh/dy) dh/dt + u(dh/dx) + v(dh/dy) + h(du/dx) + h(dv/dy) = 0 Where u and v are the two horizontal components of the velocity and h is the thickness of the fluid. 'f' is 2*Omega*sin(Phi), with Omega being 2 Pi/(1 day) and Phi being the latitude. When you assume that the velocity scales like U, and the horizontal length scale like L, then the ratio of the nonlinear terms to the Coriolis terms is U / f L For a bathtub, we have U=O(0.1 m/s), L=O(0.1 m), and at mid-latitudes we have f=O(.0001/s). So the ratio is O(10,000), meaning that the nonlinear terms are 4 orders of magnitude bigger than the Coriolis terms. So for a quasi-steady swirling flow, the dominant balance is going to be the nonlinear (centrifugal) terms against the pressure gradient. The Coriolis force will be utterly negligible.... An alternate scaling contrasts the size of the Coriolis term with the size of the acceleration term. The ratio of du/dt over fv is (1/(Tf)), where T is the time scale of the flow. In order for the Coriolis terms to be O(1), the time scale would have to be of the order of (1/f) or 10000 seconds (3 hours). Most of us don't put up with bathtub drains that slow! Hope this helps! Chris | |
| From: steve(primus) | 19/07/99
22:51:34 |
| Subject: re: Coriolis effects | post id:
24911 |
| One easy way of looking at it is
that Coriolis applies a rotation of one revolution per day. Anything
spinning faster than that, water dowm plugholes, tornadoes, waterspouts,
dust devils etc is being influenced by something
else. | |
| From: Terry Frankcombe (Avatar) | 20/07/99
13:21:13 |
| Subject: re: Coriolis effects | post id:
24985 |
| So Steve, you don't believe a
large air mass rotating and contracting could possibly conserve its
angular momentum? | |
| From: steve(primus) | 20/07/99
16:00:51 |
| Subject: re: Coriolis effects | post id:
25072 |
| I didn't say it didn't, Terry.
Conservation of angular momentum is responsible for the low level jet
stream over western Queensland. Coriolis affects anything moving over the
surface of the earth, it is just that the effect is so small, and
progessively weaker as you get closer to the equator, that with small
vortices, other effects determine the direction of the spin. Coriolis can
be seen in action on any beach in summer as the sea breeze gradually backs
during the afternoon. If it starts as an easterly at 10am, by 4pm it will
be a northerly In one quarter of a day, it moves through one quarter of
the circle. | |
| From: Kevin Phyland | 21/07/99
9:09:50 |
| Subject: re: Coriolis effects | post id:
25221 |
| Hey all, Large air mass rotations on a synoptic scale are definitely coriolis influenced...rotating thunderstorms however are much more influenced by wind shear effects (as are tornadoes which are the logical extension via conservation of angular momentum)... Kevin. | |