This paper demonstrates the maintenance of self-sustaining turbulence in a restricted nonlinear (RNL) model of plane Couette flow. The RNL system is derived directly from the Navier Stokes equations and permits computationally tractable studies of the dynamical system obtained using stochastic structural stability theory (S3T), which is a second order approximation of the statistical state dynamics of the flow.

In this work we examine the turbulence maintained in a Restricted Nonlinear (RNL) model of plane Couette flow. This model is a computationally efficient approximation of the second order statistical state dynamics (SSD) obtained by partitioning the flow into a streamwise averaged mean flow and perturbations about that mean, a closure referred to herein as the RNL$_\infty$ model. The RNL model investigated here employs a single member of the infinite ensemble that comprises the covariance of the RNL$_\infty$ dynamics. The RNL system has previously been shown to support self-sustaining turbulence with a mean flow and structural features that are consistent with DNS. This paper demonstrates that the RNL system's self-sustaining turbulent state is supported by a small number of streamwise varying modes, which form the natural support for the self-sustaining process maintaining RNL turbulence. Remarkably, truncation of the RNL system's support to a single streamwise varying mode can suffice to sustain the turbulent state. The close correspondence between RNL simulations and DNS that has been previously observed along with the results presented here suggest that the fundamental mechanisms underlying wall-turbulence can be analyzed using these highly simplified RNL systems.Comment: 9 Figures, 25 page

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Combustion of hydrocarbon fuels is traditionally separated into slow reaction, cool flame, and ignition regimes based on pressure and temperature. Standard tests, such as the ASTM E659, are used to determine the lowest temperature required to ignite a specific fuel mixed with air at atmospheric pressure. It is expected that the initial pressure and the rate at which the mixture is heated also influences the limiting temperature and the type of combustion. This study investigates the effect of heating rate, between 4 and 15 K/min, and initial pressure, in the range of 25 to 100 kPa, on ignition of n-hexane air mixtures. Mixtures with equivalence ratio ranging from Φ = 0.6 to Φ = 1.2 were investigated. The problem is also modeled computationally using an extension of Semenov's classical autoignition theory with a detailed chemical mechanism. Experiments and simulations both show that in the same reactor either a slow reaction or an ignition event can take place depending on the heating rate. Analysis of the detailed chemistry demonstrates that a mixture which approaches the ignition region slowly undergoes a significant modification of its composition. This change in composition induces a progressive shift of the explosion limit until the mixture is no longer flammable. A mixture that approaches the ignition region sufficiently rapidly undergoes only a moderate amount of thermal decomposition and explodes quite violently.