Toward a new turbulence culture

While evidence of deterministic chaos in turbulence data is now commonly reported, turbulence is still usually treated statistically. The signature of chaos most often reported for turbulence data is a low value for the dimension of the dynamical attractor governing the temporal variability of a measurement at a single spatial location. This means that deterministic algorithms can be found for predicting the future evolution of the turbulence within the limits-to-predictability constraint applicable to chaos, or for retrieving one dynamical variable from another within those same constraints. Such algorithms use a sequence of instantaneous measured observables as input rather than statistical averages of the observables. Since the underlying dynamical model is usually not known, the data are often used to train an artificial neural network to output the desired turbulence quantity. Examples of the above procedure are described below. These examples have exposed both advantages and limitations of the deterministic treatment of turbulence. Therefore, a proposed new treatment of turbulence is briefly outlined that promises to achieve the optimal balance of stochastic and deterministic data processing. The new method, originated by Crutchfield and Young (1989), is termed “E-machine construction”. Incorporating this method in large computer modeling efforts would help to establish a new turbulence culture where data are used to build new models rather than to test old ones