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In the flamelet regime of turbulent premixed combustion the enhancement in the burning rates originates primarily from surface wrinkling. In this work we investigate the Reynolds number dependence of burning rates of spherical turbulent premixed methane/air flames in decaying isotropic turbulence with direct numerical simulations. Several simulations are performed by varying the Reynolds number, while keeping the Karlovitz number the same, and the temporal evolution of the flame surface is compared across cases by combining the probability density function of the radial distance of the flame surface from the origin with the surface density function formalism. Because the mean area of the wrinkled flame surface normalized by the area of a sphere with radius equal to the mean flame radius is proportional to the product of the turbulent flame brush thickness and peak surface density within the brush, the temporal evolution of the brush and peak surface density are investigated separately. The brush thickness is shown to scale with the integral scale of the flow, evolving due to decaying velocity fluctuations and stretch. When normalized by the integral scale, the wrinkling scale defined as the inverse of the peak surface density is shown to scale with Reynolds number across simulations and as turbulence decays. As a result, the area ratio and the burning rate are found to increase as , in agreement with recent experiments on spherical turbulent premixed flames. We observe that the area ratio does not vary with turbulent intensity when holding the Reynolds number constant.

The interaction between scales is investigated in a turbulent mixing layer. The large-scale amplitude modulation of the small scales already observed in other works depends on the crosswise location. Large-scale positive fluctuations correlate with a stronger activity of the small scales on the low speed-side of the mixing layer, and a reduced activity on the high speed-side. However, from physical considerations we would expect the scales to interact in a qualitatively similar way within the flow and across different turbulent flows. Therefore, instead of the large-scale fluctuations, the large-scale gradients modulation of the small scales has been additionally investigated. INTRODUCTION AND MOTIVATION In the present work the interaction between turbulence scales in a mixing layer is investigated at relatively high Reynolds number (1). The interaction between the large and the small scales has been the topic of several studies. Recent investigations showed that in a boundary layer the large scales of turbulence modulate the small-scale motions (2) (3). Close to the wall, large-scale positive fluctuations are associated with a stronger activity of the small-scale motions, whereas they are related with reduced small-scale activity in the outer region. The top-down interaction between large and small scales presents an important phase delay, and therefore it is not concurrent (4). These findings were based on time series from hot-wire anemometry. The interaction between scales was studied experimentally in a jet by Fiscaletti et al. (5), using hot-wire anemometry, and PIV. It was found that the small-scale signal is stronger in amplitude if it is conditioned on positive large-scale fluctuations. Surprisingly, the strength of the small-scale amplitude modulation in the spatial signal obtained with PIV was only 25% of the value obtained from the time signal from hot-wire anemometry. The elevated level of the amplitude modulation from hot-wire anemometry was attributed to the fixed spectral band filter used to obtain the large- and the small-scale signals, which does not consider the local convection velocity. Moreover, the inhomogeneous distribution of the structures of vorticity, and their preferential location in high velocity regions of the flow could explain the spatial amplitude modulation. Buxton & Ganapathisubramani (2014) (6) investigated experimentally the fully developed region of a mixing layer. They found that negative large-scale fluctuations coincide with regions characterized by a high amplitude of the small-scale signal. Large and small scales appear therefore to interact similarly to the outer region of the turbulent boundary layer. The work did not consider different crosswise locations within the mixing layer. Therefore, the first goal of the present study is the investigation of the interaction between the large and the small scales of turbulence at different crosswise locations in the mixing layer. A strong flow dependency with respect to the nature of the scale interaction, i.e. increased vs decreased small activity with positive large scale fluctuations, has been observed (Bandyopadhyay & Hussein 1984, (2)). In addition, the location within the same flow seems to affect large-scale amplitude modulation. On the other hand, this appears at conflict with the classical theories of turbulence, according to which the transfer of turbulent kinetic energy across the scales is a universal process. Then, we would expect the scale interactions to be qualitatively similar across flows. Recent findings have related the activity of the viscous scales to the large-scale shear layers within the flow ((7), (8)). Large-scale shear layers, characterized by strong velocity gradients are expected to play an important role in the cascade of turbulent kinetic energy. As a second goal of this work, we intend to examine possible interactions between the large-scale gradients (rather than the large-scale velocity used before) and the small scales of turbulence, by determining the correlation between the large-scale gradients and the local activity of the small scales (local enstrophy). METHODS