The work (rotating a waterwheel) will be done at the expense of what energy? The first hypothesis that comes to mind is:
At the expense of electric energy. The system is, essentially, an electric motor.
However close inspection would suggest that the hypothesis is untenable. Scientists use triply distilled water to reduce the conductivity and the electric current passing through the system to minimum. If, for some reason, the current is increased, the motion stops - such system cannot be an electric motor.
If the system is not an electric motor, then it is a heat engine violating the second law of thermodynamics. Here arguments describing such heat engines as impossible, idiotic, etc. are irrelevant - the following conditional is valid:
IF THE SYSTEM IS NOT AN ELECTRIC MOTOR, then it is a a heat engine violating the second law of thermodynamics.
In other words, if the work is not done at the expense of electric energy, it is done at the expense of ambient heat. No third source of energy is conceivable.
In the electric field between the plates of a capacitor, the same turbulent motion can be seen:
In the capacitor system the rising water can repeatedly do work, e.g. by lifting floating weights. The crucial question is:
The work (lifting floating weights) will be done at the expense of what energy?
Obviously "electric energy" is not the correct answer - the capacitor is not an electric motor. Then the only possible answer remains "ambient heat". The system is a heat engine violating the second law of thermodynamics!