Does “global temperature” exist? Good question

I wonder about this question in respect to the “Introduction to turbulence” course. This week we’ll go through Reynolds averaging and Reynolds stresses. The introduction to this subject is through the definitions of time average (the usual one, the integral over time) \frac{1}{T} \int\limits_0^T u dt, ensemble average, defined as a discrete average of the multiple repetitions of the same flow \frac{1}{N} \sum\limits_{i=0}^{N} u_i and spatial average, which is possible to define only in HOMOGENEOUS systems. This part was always puzzling for me when we talked about analysis of Particle Image Velocimetry (PIV) and 3D Particle Tracking Velocimetry (3D-PTV). How ‘bad’ are ensemble and spatial averages? Recently, due to some technology progress, the time-resolved measurements became possible and it means that somebody will (very soon :-)) investigate the difference between time average and ensemble average, for example.

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