I actually found a amazing site that really helps make things much more clear called NexFlowAir.. http://nexflowair.com/vortex_tube.php
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if you are refering to a hilsch vortex tube, there are two lines of thought. The first is that air is made up of a range of molecules at different temperatures and energy levels, and the average of all these temperatures is what shows up on a thermometer. In a hilsch vortex, the different molecules get separated with the cooler molecules that have a lower energy level and thus vibrate less being thrown to the outside and the warmer higher energy molecules that vibrate more would float to the center of the vortex.
The other theory says that most air molecules are near the same temperature and energy level and in the vortex the molecules stay roughly in their same location radially as the vortex spins. The energy ends up moving from the outer edge of the vortex towards the center. This would result in cooling the outside air and heating the center air.
The Vortex Tube is truly an amazing device that can literally fit in the palm of your hand. The Vortex Tube is an effective, low cost solution to a wide variety of industrial spot cooling and process cooling needs. Compressed air is injected into the vortex tube, flows at a rate of up to 1,000,000 RPM towards the 'hot' end of the tube. Once this hot air reaches the end, a small amount is exhausted through a control valve. The rest of the air is forced backwards towards the other end and exits as 'cold' air.For more information regarding the Vortex Tube, how it's constructed, visual animations, etc. Click on the below link..https://www.streamtek.ca/products/vortextubes/vortex-tube.php
A Vortex Tube actually contains two oppositely rotating streams of air, one inside the other. The outer vortex is created when the supply air enters the tube at an angle, creating the rotation along the inner diameter, towards one end of the tube. A valve at the end of the tube allows some of this air to escape, in the form of heat. This end of the tube is called the hot end. The remaining air then reverses its direction and forms a smaller vortex inside the other one. This air is at a colder temperature since having lost some of its energy in the form of heat. All of the air in this colder air stream exits out the end of the Vortex Tube opposite the cold end. This end is thus called the cold end of the tube.The heat transfer between the two air vortices is furthered by the loss of angular momentum of the inner vortex being gained by the outer vortex. This increases the temperature of the outer vortex, while decreasing the temperature of the inner vortex. This heat transfer allows the two vortices to rotate in the same angular direction, while maintaining the same angular velocity. If you want more information, as well as a visual demonstration, click this link:http://www.exair.com/en-US/Primary%20Navigation/Products/Vortex%20Tubes%20and%20Spot%20Cooling/Vortex%20Tubes/Pages/How%20a%20Vortex%20Tube%20Works.aspx
if you're referring to something like https://www.instructables.com/id/Tornado-in-a-Bottle-its-more-of-a-vortex-though/, then its the outward force centriptial(centrifugal) force of the water pushing against the sides of the container (as it wants to keep moving outward from the ever speeding up rotation)