papers cited by Nagano (1999) or Johansson & Wikström (1999, J&W), they have mostly been performed at Re τ up to 180 only to our knowledge, J&W report so far the highest Re τ = 265 value for heated/cooled channel flow DNS with no net heating of the area we have chosen it as a particular case of study. Although there is a selection of DNS computations of heated channel flow reported in the literature, cf. The PDF algorithm and program developed by the authors ( Pozorski & Minier 1998) have been used with further modifications to accomplish the present computation. Minier, in Engineering Turbulence Modelling and ExperimePDF COMPUTATION RESULTS If the temperature is assumed not to be a function of time and space, the experiment can be viewed as the measurement of N realizations of the same random variable or as the measurement of one realization of N distinct random variables that all have the same distribution. If the auxiliary variables are themselves uncertain, then they must be treated as data and the inverse problem becomes an implicit one with a much more complicated distribution than the above problem exhibits.Īs an example of constructing the distribution for a set of data, consider an experiment in which the temperature d i in some small volume of space is measured N times. This is why we differentiated between data and auxiliary variables in Chapter 1 the latter must be known exactly. One approach to inverse theory (which will be pursued in Chapter 5) is to use the data to determine the distribution and thus the values of the model parameters.įor the Gaussian distribution ( Equation 2.24) to be sensible, g( m) must not be a function of any random variables. The model parameters now have the interpretation of a set of unknown quantities that define the shape of the distribution for the data.
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