There are several types of stabilizers for trawlers:
1. Paravanes- Requires robust midships mounted booms with rigging
for the paravanes. Can be difficult to deploy and retrieve so are only used on long passages. You can rig a valve tray device on one or both of the booms to use at anchor
2. Hydraulic vanes- Expensive, takes a hydraulic take off from the engine
to drive them. Little effect at anchor
3. Flywheel/gyroscope system- Works equally well underway or at anchor. Rarely used.
4. Static water
ballast- This is a long athwartships water
tank with baffles. The water moving back and forth creates a rolling resistance underway or at anchor. Must be designed for ships roll period, weigh a lot and take up a lot of room. Rqrely used.
So probably 95% of stabilized trawlers use the hydraulic vane with the balance paravanes.