Sous-vide without a pump using convection? I'm currently planning on creating a sous-vide setup using an induction cooktop and a PID controller. I will be an Arduino micro-controller setup similar to this openschemes.com-manual control of induction cooktop

Most sous-vide setups use circulators that circulate and mix the water in the bath to keep uniform temperatures throughout the bath. I was wondering if a pump is required if I'll be using a pot on top of an induction cooktop. Since the heat source is at the bottom, won't the water rise naturally through convection and keep a constant temperature throughout the bath?
I made a sous-vide setup that uses a slow cooker and no pump. 

I was able to observe as much as a 5 degree temperature gradient from the bottom to the top of the cooker. A big part of the problem was that my target food almost fills the cooker and impedes convection. I didn't measure the temperature gradient with an empty bath.

My setup worked passably well as long as my food was small and my thermometer was positioned at the same depth. I didn't enjoy the precision that commercial products have.

Obviously your setup will have a lot more power than mine. If your bath is much bigger than your target food you would have less of a temperature gradient than I did.
If your bath is much larger than your target food then convection will give you enough water circulation. Even a 5 degree drift will let you do some interesting things, however, It is one more variable to keep track of.

I was not satisfied with my setup and my next attempt will have a stronger heater as well as a circulation pump. Water pumps are cheap.