People kept falling through the ice at Arlington's Spy Pond over the weekend; police, firefighters have a simple tip to prevent that

Most any lake has flowing water (ignoring endorheic lakes for this), it just depends on how quickly it flows. The Charles was dammed in 1910 and the level is controlled by the dam (which was replaced further downstream in 1978). The Charles used to be tidal, but today water flows into the river in the vicinity of Watertown, and out at the Dam, but if it "flows" in between it does so quite slowly, especially in the wide basin downstream of the the BU Bridge.

Some quick math. Under a low flow situation like right now (cold, no recent precip), the Charles flows at a rate of about 300 cubic feet per second at Waltham, which accounts for most of its basin (the flow can also be controlled into the Neponset at Mother Brook). There are also storm sewer outfalls, but those only really run appreciably when there is rainfall or melt. The Charles River basin is about 1 square mile, or 640 acres, and it averages somewhere on the order of 12 feet deep. So it contains about 7680 acre-feet, or about 335 million cubic feet, of water. If you divide all this together (335000000/300/24/3600) you get 13 days … water coming in at Watertown takes just shy of two weeks to get to the Dam.

This is called "residence time" or "retention time" and while 13 days relatively fast for lakes, it's certainly in the lake category (flowing rivers would have retention time measured in seconds). In other words, if the water moved as a single mass (it doesn't) for the 10 miles from Watertown to Boston, it would move at a rate of about 1/30th mile per hour.

Now, remember that this is only for low-flow periods with appreciable rain or precipitation. When there is a lot of rain the Charles River Dam can pump more than 8000 cfs (nearly double the peak observed flow at Waltham, although there would be significantly more urban runoff) over the dam itself (to keep the river from overfilling during a high tide) and if the locks are opened at low tide a similar amount of water can be let out. During these times there is definitely a current through these narrow sluices and the residence time would be something more on the order of a few hours, and there would be a lot more current in the river. And storm sewer outfalls would flow as well. But that's not the case right now.

The biggest worry is that if there was a wet storm approaching and meltwater or runoff was expected, the Dam operators may proactively lower the river level, which could lead to the ice being suspended above the water rather than floating on top, which would make it much more likely to break, although this would probably be quite evident. But ice safety on the Charles requires a long period of much colder than normal temperatures, minimal liquid precipitation or snowmelt during that time and no major warm ups that break up the ice. Snowfall can insulate the ice and slow the process (although if it crusts over, it can spread the additional weight of a person to avoid thin spots). Even then it's a relatively dangerous game to play, and actual safe ice only occurs maybe once a decade.

All that said, every year I ski in a cross country ski race which ends with a two mile crossing of Lake Hayward in Wisconsin, which is a similar water body: about the same depth, slightly smaller, slightly less flow, similar retention time. Only rarely has ice thickness been an issue, and they drive 10,000-pound grooming equipment across it. Of course, it's colder in Hayward, but the average temperature in Hayward in February is about what the average temperature was in Boston in 2015, so, when it's cold enough, the Charles can freeze pretty darn solid. (Feb 2015 averaged 19˚, 12˚ below normal, the last 26 days of 2004 averaged 18˚, a similar departure, and had barely any rainfall or snowfall; in both cases, the temperature did not rise above 40˚, there was no liquid precipitation, and the ice was probably a foot thick; in 2015, the river didn't ice out until early April.)