Jim,

that's a fine puzzle and with a little help from a colleague I have worked out what I think the most probable rational explanation is.

The start of course is that water flows from a higher level to a lower and never vice versa. So there had to be a fluctuation in water level. I then first went a wrong trail of thinking and thought the ten minutes should be a chance coincidence. Only when I made the 10 minutes an integral and necessary part of the solution I succeeded.

Here you go: Like any children's swing each body of water has an Eigen frequency that is the frequency with which it swings to and fro. If you have water in a bowl and you swing the bowl with the Eigen frequency of the water you'll easily make it spill over. Use the wrong frequency and you need much more force to achieve the same effect. Same in your bathtub. With the correct frequency of moving your body you can make a flood easily. The frequency however is lower for your bathtub than for a bowl. With swings, the Eigen frequency is determined by the length of the ropes, with water the main determinator is the mass of the water involved. The more water the lower the frequency. With an enormous reservoir the Eigen frequency can be in the region of minutes.

Now make your bathtub water swing to and fro and imagin observing two connected 'puddles' in the middle, then the water will flow first one way and then the other and change direction about once a second. Hard to see.

Now take your two puddles connected to each other and connected to a large body of water. Assume that the large body of water swings with a very low Eigen frequency of once every ten minutes and that the amplitude of the swing is extremely low and usually not seen. The the 'slope' of the water surface will change every ten minutes so minimally that you can't see it. But if you are at a place where two puddles are connected by something which is an obstacle to the free flow of water (small opening, very shallow connection or so) then the flow of water will be slower than the build up of level differences and in such rare situations you'll see actually the water flow. The same physical principle leads to the famous maelstroms of Norway (I link to a particular one I have seen once).

The last open question is what is the force behind the swing (everybody knows a swing without additional force will come to a standstill under real life conditions). The force behind the maelstroms is the moon and its gravitation. Your account is precise enough to find a possible 'driving force'. The Mississippi it is. It is connected to the swampland and continuously leads to small random perturbations in the reservoir of water we are talking about. These minor perturbations lead the water reservoir to swing continuously with its Eigen frequency of once per ten minutes. Under extreme circumstances like the one you have encountered, this swing can be seen by the unaided eye.

Isn't science fun?

But let's not forget other hypotheses. It could be a big hidden factory run by aliens below the swampland and every ten minutes they pump off the waste water of their activities. Or a band of leprechauns fancied to fool you. Or the earth is a big living being making cosmic music and the ten minutes are the time between two draws of breath when playing a particular invisible instrument....

Wolfgang