Measurements of the Nusselt number Nu and of a Reynolds number Re(eff) for Rayleigh-Bénard convection (RBC) over the Rayleigh-number range 10(12)≲Ra≲10(15) and for Prandtl numbers Pr near 0.8 are presented. The aspect ratio Γ≡D/L of a cylindrical sample was 0.50. For Ra≲10(13) the data yielded Nu∝Ra(γ(eff)) with γ(eff)≃0.31 and Re(eff)∝Ra(ζ(eff)) with ζ(eff)≃0.43, consistent with classical turbulent RBC. After a transition region for 10(13)≲Ra≲5×10(14), where multistability occurred, we found γ(eff)≃0.38 and ζ(eff)=ζ≃0.50, in agreement with the results of Grossmann and Lohse for the large-Ra asymptotic state with turbulent boundary layers which was first predicted by Kraichnan.
We review the problem of spectral estimation from velocity data
sampled irregularly in time by a laser Doppler anemometer (LDA) from very early
estimators based on slot correlation to more refined estimators, which build
upon a signal reconstruction and an equidistant re-sampling in time. The
discussion is restricted to single realization anemometry, i.e. excluding
multiple particle signals. We classify the techniques and make an initial
assessment before describing currently used methods in more detail. An
intimately related subject, the simulation of LDA data, is then briefly
reviewed, since this provides a means of evaluating various estimators. Using
the expectation and variance as figures of merit, the advantages and
disadvantages of several estimators for varying types of turbulent velocity
spectral distributions are discussed. A set of recommendations is put forward
as a conclusion.
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