This is campfire example.
To achieve this effect add two force fields.
First one: Shift+A > Force Field > Turbulence
Then change Noise to 5.
Second one: Shift+A > Force Field > Vortex
Change Noise to 2 and Strenght to 0.1.
Blend file:
http://blend-exchange.giantcowfilms.com/embedImage.png?bid=2217
Final toughts:
I don't know your full setup so some values may vary. You can try change position of force fields and strength/noise values.
Edit:
Based on provided blend file I've change all Force Fields to Force with negative strenght and noise. Also I've zeroed Velocity > Emitter Oject > X and Random.
Updated blend file:
http://blend-exchange.giantcowfilms.com/embedImage.png?bid=2220