Transverse Vibrations and Stability of Systems with Gyroscopic Forces

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Abstract
-In the Bray-Moss model for the thermochemistry of premixed turbulent combustion with reaction confined to thin laminar flamelets the temperature at a fixed point within the turbulent flame, suitably idealized and normalized, can be interpreted as a two-valued, zero-one function. Previous work shows that the time autocorrelation of this function plays an important role in the determination of the mean rate of creation of product in such flames. Our purpose here is to develop the partial differential equations for the several space-time correlations of the two-valued functions associated with flamelet crossings in premixed turbulent combustion. Application of each of these equations requires modelling. However, contrary to earlier work we show that a consistent set of models for the equation describing the time autocorrelation leads to no new information on the integral time scale needed in the mean rate of creation. It is concluded that resort must be made either to an alternative theoretical approachto experiment.

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