Can I recirculate water from an open reservoir to the bottom of a bigger, closed one, without a pump? A fountain head pumps water out of the main tank into a 'pond' reservoir. Can the water recirculate back into the main tank without the help of another pump?
I'm sorry if this a dumb question. I'm guessing it would not function as the diagram shows, as the pressure of the water in the main tank would not let any water in at the bottom,right? Any solutions? (not requiring additional pumps)

 A: The set up shown will work just fine, though to be safe I'd put the check valve on the pump so as to prevent water and or air from flowing back into the tank from above.
I also made a few assumptions:-


*

*The free space in the top of the tanks is small enough

*The tank is not too tall (less than about $9~\text{m}$ should suffice)

*The volume of the pond is large enough

*Water cannot flow back through the pump

*The diameter of the outflow pipe is small compared to the tank diameter.
At first, the pressure of the air gap in the tank is at atmospheric pressure: this means it has a gauge pressure (pressure above atmospheric) of 0.
Check valve must be placed on the outlet pipe as close to the pump as possible.
Before the pump is turned on, the weight of the water will cause it to flow out into the pond through the bottom pipe connecting the two. As this does, the volume of the air gap will increase, and thus it's pressure will drop. Eventually the pressure will reach a point such that the force it exerts on the water will cancel out the gravitational force pulling the water out. (Negative gauge pressure)
When the pump turns on, it will remove water from the main tank again increasing the air gap volume. This will mean there is an overall negative gauge pressure at the tank side of the inlet pipe, thus causing water to be drawn into the tank to replace the water removed by the pump.
The reason this all works is due to the difference of the external pressure and the internal pressure, and works on a similar principle this.
A: The water level in the pond must be the same as in the tank, so:

:-)
A: How about:

open valve 2 to transfer water from the reseroir to the tank. Close valve 2 to create the 'fountain' feature. Open valve 3 to transfer water from tank to reservoir.
A: 
@phillip_0008 
Pretty sure this one would work! 
Basically, no need for valve 3. And wouldn't be able to access valve 2.
So split pump inlet between bottom of tank and bottom of reservoir, directly outlet to fountain. 
Water coming out of fountain sits in reservoir until it gets sucked back in thru pump.
makes sense in my mind but let me know if you see anything i didn't!
A: The answer is no, simply because the pressure on the check valve on the side of the open pond must be greater than that within the main tank before the valve can open and let water flow from the open pond and the main tank.
This will only happen if either:


*

*The open pond's water level is higher than that of the open tank; as drawn, the system will simply overflow the open pond and keep draining the main tank until the two tank levels are equal;

*A pump raises the pressure of the water from the open tank to force the valve to open and push water back into the main tank.
A: Another suggestion:

close valve 1 and 2 and turn on pump to make 'fountain' effect. Close  valve 1 and open valve 2 and turn on pump to transfer water from reservoir to tank. Close valve 2, open valve 1 and turn off pump, to transfer water from tank to reservoir.
A: Huh, people? :-)
He says the main tank is closed!
That means it can be pressurised, and the pressure will ofc push out water, depending on pump efficiency.
Nothing else needed than a valve that hinders the water from flowing back to the open reservoir when the pump is off.
In the pic below a self-adjusting system. 
- If there is too little water in the main tanh, it pushes out air until the water level rises to touch the pipe, after which it pushes out water.
- The amount of air defines the functionality, and need be matched against the pump efficiency. Some component dimensioning needed, after which it must work :-).

