Inertial range scaling law

A model for inertial range intermittency and anomalous scaling of velocity structure functions is proposed. The Navier–Stokes equation is used to derive a basic Reynolds number dependent law for the instantaneous velocity difference between two points. This gives incomplete information about the dependence on scale and requires a statistical hypothesis in order to compute structure functions and other quantities. The specific assumptions made here relate the singular scaling exponent to the velocity amplitude. Anomalous exponents and Reynolds number dependent structure functions and velocity difference probability density functions are calculated which agree with the experiments.

Key Words:

• Turbulence
• Structure Functions
• Scaling Exponents
• Intermittency