tracing – Plot of a tornado shape as surface

I like the "surface synthesis" questions. Here is a simple model that combines an Archimedean spiral with a power law curve:

With[{h = 1/10, n = 24, c = 4, p = 2/3},
     ParametricPlot3D[{t (h Cos[n t] + Cos[v]), t (h Sin[n t] + Sin[v]), (c t) ^ p},
{t, 0, 3}, {v, 0, 2 π}, Axes -> None, In Box -> False,
Lighting -> "Neutral", Mesh -> False, PlotPoints -> 85,
PlotStyle -> Opacity[3/4, Black], ViewPoint -> {3.2, -1.6, 1.}]]

twister?

Adjust the parameters as seen.