This quick tutorial demonstrates how to create object trails in Houdini, and then add a turbulence effect to them. Whether you're new to Side Effects Software's popular 3D production program or a seasoned graphic artist just interested in better acquainting yourself with the application, you're sure to be well served by this free video tutorial. For more information, including detailed instructions, take a look.
PS The creation of the Rank attribute described here is a slightly long way of achieving the result. A better alternative is to create texture coordinates on the curve.