On the Spectrum of Isotropic Turbulence

Abstract

Measurements of the spectrum and correlation functions at large Reynolds number (RN ~ 10^5 based on the grid mesh) have been made, as well as a series of accurate spectrum measurements at lower Reynolds number (RN ~ 10^4). The results are compared with the theoretical laws proposed in recent years. It is found that the measurements at large Reynolds numbers exhibit a range of frequencies where the spectrum is nearly of the form n^- 5/3. The largest part of the spectrum in the initial stage of decay at the lower Reynolds number was found to follow closely the simple spectrum A/[B + n^2] , where A and B are constants and n is the frequency of fluctuation. At x/M = 1000 (where x is the distance behind the grid and M is the mesh size) the spectrum approaches a Gaussian distribution. The second, fourth, and sixth moments of the spectrum have been computed from the measurements and are discussed In relation to theoretical results. The significance of the number of zeros of the fluctuating velocity u(t) is discussed and examples of measurements for the determination of the microscale of turbulence [lambda] from zero counts are given.

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