A Theory for Portions of the Energy Spectrum and for Intermittency of Fine-Scale Turbulence.
Abstract
The paper contains a theory for two ranges of the energy spectrum, k sub e << k << k sub m and k sub m << k << k sub s, where k is wave number, k sub e is the wave number of the energy-containing eddies, k sub m = 1/lambda where lambda is Taylor's microscale and k sub s = 1/eta where eta is the Kolmogorov length. The results are obtained by recognizing the existence of a mesoregion in wave-number space in which the wave number is of order 1/lambda and assuming a new inner behavior of the spectrum function for larger k based on the two scales eta and lambda. Reynolds number similarity is assumed as a first approximation for smaller k (outer region) and an assumption that the mesoregion and the outer region overlap leads to infinite series for the spectrum function in each of the two ranges. The forms reduce to the k to the -5/3 power-law in both ranges in the omit as k/k sub e and k sub s/k get large. Universal constants may be chosen to yield excellent agreement with the data for a tidal channel. The paper concludes with some conjectures on the intermittency of fine-scale turbulence and the geometry of the fine structure. It is suggested that the intermittency factor is proportional to square root of 1/R sub lambda. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1979
- Accession Number
- ADA068743
Entities
People
- Robert R. Long
Organizations
- Johns Hopkins University