# Why does the pet's water bowl overflow?

So when i give the pet fresh water in a stainless steel bowl that i place on a mat according to the attached picture, from $$t=0$$ the bowl is at rest, the water normally oscillates in the bowl like a pendulum following the action, but after one or two oscillations, the water seems to gain in momentum and starts to overflow from the bowl. why?

(bowl is a body of revolution)

• Could be any number of things: the floor isn't level, the imperfect human eyes mistake one slosh for two or more, the bowl is still moving a bit, etc. Commented Jul 13 at 18:48
• @paulina does not overflows anymore because used to it, but behaviour happens daily, not always in the same direction : sloshing always reaches higer level towards one rim or the other after one or two sloshes. Commented Jul 13 at 19:35
• Gotta say, nice graphic. Commented Jul 14 at 8:46
• Yes, the graphic is like a NASA Mars landing animation. Commented Jul 14 at 11:57
• “NASA reports water on Mars (because its bowl overflowed)” Commented Jul 14 at 18:52

A guess. Perhaps there are multiple modes present. It takes a while for them to have an interference maximum at the edge of the bowl.

• Angular, radial, transverse should all be there yeah. OP should try setting it down differently Commented Jul 14 at 8:15
• When I've had things like this happen, I'm pretty sure its also for this reason. The water is probably already swishing before you set it down, and then when you do it adds another impulse that causes the interference, or at least that's how it always feels to me.
– JMac
Commented Jul 15 at 12:32
• Are you talking about interference between modes in the water, the steel, or both? Commented Jul 17 at 1:21
• @PM2Ring - Fixed typo. Modes in the water. I expect vibrations in the steel would be sound waves that would not affect the motion of the water. Commented Jul 17 at 1:45
• Sure, the dominant modes in the steel probably have a much higher frequency than the lowest frequency modes of the sloshing water, but I don't know if we can rule out some coupling between the two. Commented Jul 17 at 1:53

If the mat is thick and soft enough to be compliant, then it will couple with the moving mass of the dish and water and allow the dish to tip back and forth, causing the spillage.

This can be directly tested by setting the bowl down on the bare floor instead and seeing if it spills.

Also, try this: carefully place a full water bowl down on top of the mat after first allowing all the sloshing to die down. then press down on the rim of the bowl to tip it slightly and release. Note the sloshing. press briefly down again, timing the press to add to the slosh, and release. With a little care you should be able to reproduce this effect manually, furnishing evidence that the bowl is tipping along with the sloshing water because of the mat's springiness.

Be sure to report back here to share your results!

• This seems to suggest a resonance effect Commented Jul 14 at 17:26
• @PhilFreedenberg - Or simple interference between 2 wave fronts: sometimes interference will be destructive, and sometimes constructive. Commented Jul 16 at 16:32

The two horizontal sloshing modes could have slightly different frequencies (e.g. if the rotational symmetry is not perfect). If you then start with the combination of both, but out of phase, which is a circular sloshing pattern, then sometime later you will have both in the same phase which is diagonal sloshing, with $$\sqrt 2$$ times the original amplitude if no energy has been lost.

Of course the initial movement does not have to be exactly circular, which would probably be noticed immediately. But if there only is some circular component in it, this can still lead to increasing amplitude, just not by the full factor $$\sqrt 2$$.

And the symmetry breaking could come from the mat below it, which might have different compliance in orthogonal directions caused by the way it is manufactured.

• Yes, check the mat to see if it stretches more in length or the width directions. Also, was the fridge or some other device running that generates vibration, roadwork or excavations nearby starting up at 7am your usual pet chore time (far fetched it may have been seismic aftershocks on those few occasions). Commented Jul 14 at 12:58

The reason may be simple, because your container not only has angular movement, initially T-2 tilts forward, then T-1 tilts backward, but also horizontal movement from right to left during this process. This way, water definitely has momentum. So at T-0, in fact, your container is tilted backwards, so water will not overflow, but when the container is level, it may overflow. You can use a transparent container and conduct the experiment using a camera. This will enable more accurate observation.

• The container itself vibrates, so changing to a different material with a different speed of vibration will affect the result. Commented Jul 17 at 1:37

If you check the tide chart for your local area you will find that the bowl overflows only during the incoming tide and is directly proportionate to what stage the tide is at when you set the bowl down. As the mean high tide approaches, the swirling water in the bowl will continue to rise as well. An outgoing tide will have the opposite effect, negatively impacting the water level and causing each swirl around the bowl to be at a lower level than the previous one. Additionally, a waxing moon phase increases water level even further regardless of tidal stage. Conversely a waning moon will negatively affect the swirling water level in the bowl during all tidal stages.

• The tides causing a pet's water bowl to overflow is a bit of a stretch. Commented Jul 16 at 23:31