onsdag 24 mars 2010

Self Similarity of Temperature Graphs

The Reference Frame suggests that temperature graphs are self-similar e.g. in the sense of
red noise or Brownian motion with temperatures changes of size t^0.5 = squareroot of t,
over time intervals of length t.

In other words, temperature graphs are Hölder continuous with exponent 1/2, or something
of that size like 1/3.

This connects to a basic property of turbulent incompressible flow, namely that velocities are Hölder continuous with exponent 1/3, as we show computationally in Computational Turbulent Incompressible Flow, with support by analysis.

This gives hope that turbulent climate dynamics can be simulated computationally.

3 kommentarer:

  1. OK, I specifically said that the exponent is not exactly 1/2. Even when it's not 1/2, it's still self-similar.

  2. Yes, of course, but the point is that turbulent flow has exponent 1/2.

  3. It is rather 1/3 if I check my own documents.