Statistical Models of Turbulent Fields

When the correction functions were calculated in the last chapter, for different characteristics of the velocity fluctuation field, the “true” velocity field or, more precisely, its spectral energy tensor, was specified in each case. This transition from the “true” field to the correction function suffers from a logical difficulty, namely, the correction to the measured field variable relies on information about the true distribution of this variable. However, this information is either not available, in which case, the correction cannot be made, or it is available, in which case there is no need for correction. This sequence of events is dictated by the structure of the general relationships in Section 3.1, which enable us to determine the results of measurements if the field is known by not the other way round. The problem facing the experimenter, on the other hand, is the converse: to determine the statistical characteristics of the field acting on the transducer from the measured values of the field. The question is whether it is possible to invert the relationships obtained in Section 3.1. It turns out that this leads to certain fundamental difficulties.