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Understanding multiscale turbulent statistics is one of the key challenges for
many modern applied and fundamental problems in fluid dynamics. One of the
main challenges is the existence of anomalously strong non-Gaussian
fluctuations, which become more and more important with increasing Reynolds
number. In order to devise turbulence models capable of reproducing these
extreme events with reasonable accuracy, it is helpful to further
understand the structure of the nonlinearity in the Navier-Stokes equations and
related models, and to define a set of multiscale observables to
evaluate the performance of the model. We present analytical and numerical
results focussing on the connection between the geometric structure of the
nonlinearity and the direction of the energy cascade, as well as concerning the
structure and scaling behaviour of multiscale correlations applicable to LES.
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