The left picture above from J. Gordon Leishman, Principles of Helicopter Aerodynamics, depicts the Vortex Ring State where the wake below the rotor is re-ingested on top of it. A dangerous situation indeed, since adding power may result in higher vortex velocities only.
In section 5.3 of the Leishman book a further detailed discussion of the VRS can be found. A quantification is given as induced power loss in VRS: measured data shows a power loss factor of almost 2 in some circumstances, and here lies one of the issues in trying to recover with adding power. The engine is simply not dimensioned to deal with such effective power loss.
Another problem is flow fluctuation, leading to fluctuations in thrust of up to 40% depending on disk loading:
The VRS is accompanied by an extremely unsteady (aperiodic) flow field surrounding the rotor.
All in all a dangerous situation to be in, since the flow fluctuations associate with a loss of predictability. Best avoided, although one of the methods to recover is to reduce rotor Angle of Attack:
Notice that the fluctuations drop off quickly as the disk AoA decreases below 50° and is consistent with piloting experience on helicopters, which shows that a forward speed component causes the rotor to quickly exit the VRS.
After tuning the flight controls of a CH-53 helicopter simulator and going for a test ride, I inadvertently got the sim in a VRS in the thin mountain air surrounding the modelled airbase. The instructor told me to give full left lateral, wait for the helicopter to reach a considerable roll angle, then full right lateral, then mid again; then regain horizontal attitude while pressing cyclic forward. The initial lateral movement indeed changed the disk AoA enough to exit the VRS quite rapidly.
I don't know if this is taught as a recovery practice in the real helicopter though, or if it only works in the (high fidelity military) simulator.