[![Final better][1]][1]

This is campfire example.

To achieve this effect add two force fields.

**First one:** <kbd>Shift</kbd>+<kbd>A</kbd> > *Force Field* > *Turbulence*

Then change *Noise* to 5.

[![Turbulance][2]][2]

**Second one:** <kbd>Shift</kbd>+<kbd>A</kbd> > *Force Field* > *Vortex*

Change *Noise* to 2 and *Strenght* to 0.1.

[![Vortex][3]][3]

**Blend file:**

[<img src="http://blend-exchange.giantcowfilms.com/embedImage.png?bid=2217" />](http://blend-exchange.giantcowfilms.com/b/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*.

This is how it looks with *Motion Blur.*

[![Finalfinal][4]][4]

**Updated blend file:**

[<img src="http://blend-exchange.giantcowfilms.com/embedImage.png?bid=2220" />](http://blend-exchange.giantcowfilms.com/b/2220/)


  [1]: https://i.sstatic.net/cIItc.gif
  [2]: https://i.sstatic.net/PKndd.jpg
  [3]: https://i.sstatic.net/8rL3I.jpg
  [4]: https://i.sstatic.net/MVf9r.jpg