Phenomenology and Scaling Theories

  • Emily S. C. ChingEmail author
Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)


The statistics of the velocity and temperature differences, between measurements taken at two points separated by a distance \(l\), can reveal the structure of turbulence. These structure functions often exhibit power laws or scaling laws in \(l\). We introduce the important concept of energy cascade in turbulent flows and the different theories for the scaling behavior of the velocity and temperature fluctuations. We start with the scaling theory for non-buoyant turbulent flows and then discuss how the presence of buoyancy would affect and modify the scaling behavior. A crossover between the two types of scaling behavior is expected to occur at a length scale, the Bolgiano length, above which buoyancy is significant. Furthermore, there are corrections to these scaling theories due to the intermittent nature of turbulent fluctuations, and we discuss the idea of refined similarity hypothesis used to account for these corrections.


Energy cascade Kolmogorov scaling Four-fifth law Obukhov–Corrsin scaling Bolgiano–Obukhov scaling Bolgiano length 


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© The Author(s) 2014

Authors and Affiliations

  1. 1.Department of PhysicsThe Chinese University of Hong KongHong KongHong Kong SAR

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