If you have a polariser on your lens, you need to adjust (namely turn) it for the desired effect. That's why you can rotate it in the first place, as opposed to other filters. It can be used to block the polarisation of the reflection (making it able to look into the water without reflection) but it also can be used to only admit the polarisation of the reflection which keeps the reflection as-is but reduces everything else in the picture by one stop, in effect bringing the brightness of the reflection up to that of the unreflected image.
Note that polarisation occurs mostly at certain angles but a typical water surface is a good candidate. A polariser does not help against reflections from a flash (unless you put a polarising filter on the flash itself) since the problematic reflection direction is not causing polarisation.
Apropos flash: with contrasts such as the one shown here, a fillin flash at a decent level (-2EV or so) may do a lot of good for shadow detail without spoiling the character of the scene.
You can also do "exposure bracketing", creating 3 photographs at different exposure and then combining them to a "high dynamic range" image. Your camera may offer some help with that kind of job or even the complete job (typically at the cost of not producing a RAW image). Personally, I prefer getting the lighting such that I can make do with a single shot.
Shadow detail by fill-in is one instance where an on-camera flash close to the axis (built-in or even ring flash) makes sense: the usual problem of a lack of perspective since you don't see the shadows is exactly what you want for fill-in flashes in order not to get shadows competing with those of the main lighting.