a spatially inhomogeneous model problem for studying turbulent nonpremixed reacting flow with reversible reaction is proposed, which admits stationary solutions that are periodic in physical space. The thermochemical state of the fluid is characterized by two composition variables: mixture fraction ξ(x,t) and reaction progress variable Y(x,t). A linear gradient in the mean mixture fraction field is imposed in the X_2 direction, so that, in a forced stationary velocity field, the mixture fraction field attains statistical stationarity.
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