It could be as simple as a vacuum leak but without knowing what year, make, model and engine it is hard to tell you what it may be.
bad battery. it gives off the rest of its power when its about dead. and that's what causes surging
Engine surging is usually due to insufficient fuel supply. Probable causes could be an air leak in the fuel system, or possibly a dirty fuel filter, causing fuel restriction.
Separation of the ethanol due to water in the gasoline.
That only usually only happens in a manual transmission
If it has an idler control valve, and most do, I'd go with that.
The fuel pump surging at first could be caused by the fuel pressure bleeding off and the pump has to build the pressure up.
It is important to know the causes of problems in a vehicle. A surging idle can be cause by a bad o2 sensor, bad fuel pump, or a computer starting to go bad.
Sounds like a bad/failed water pressure regulator.
the water was surging over the rocks
If you're referring to a jolting sensation while traveling in the car, it's probably kangaroo petrol.
Governor hunting or surging is a problem that causes the engine to constantly speed up rapidly and then slow down rapidly.
It could be as simple as a vacuum leak but without knowing what year, make, model and engine it is hard to tell you what it may be.