Eulerian spatial and temporal autocorrelations: assessment of Taylor's hypothesis and a model

ABSTRACT

We present measurements of Eulerian longitudinal velocity autocorrelations in homogeneous, isotropic, high-intensity (∼9%) free-stream turbulence behind an active grid. Spatial correlations are measured using particle image velocimetry as well as with two-point hot-wire anemometry (HWA), while temporal correlations are measured using HWA. The temporal correlations are transformed into spatial correlations by using Taylor's ‘frozen’ hypothesis with both the mean as well as instantaneous velocities. A model relating Eulerian spatial and temporal autocorrelations is also used for this purpose. The differences from the measured spatial correlation resulting from the use of Taylor's hypothesis on the temporal correlation is quantified; even at this moderately high level of turbulent intensity, the result from the use of the instantaneous velocity as convection velocity is practically indistinguishable from that obtained using the mean velocity. Use of the model produces a good agreement between the estimates of the spatial correlation function. A relation between Eulerian spatial and temporal integral scales is also derived.

KEYWORDS:

• Taylor's hypothesis
• isotropic turbulence
• Eulerian velocity autocorrelations