High-fidelity pseudo-spectral simulations of isotropic turbulence: Large eddy simulations with semi-adaptive parametrization of residual flow scales

In the present work, we begin with assessing a well-known spectral closure in large eddy simulations (LES) of isotropic turbulence at high Reynolds numbers. The original model has been developed assuming the existence of an infinite inertial range energy spectrum. The results show that although the energy is transferred among resolved flow scales at approximately correct rate, some characteristic features of the inertial subrange are not recovered despite the existence of the k−5/3 scaling. The issue appears to follow from insufficient resolution of flow scales relevant to LES and suboptimal functional form of the spectral eddy-viscosity, leading to excessive energy dissipation in the low-wavenumber range. Using a differential regulator which requires a predefined energy spectrum, we develop a new model that adaptively determines the spectral eddy-viscosity, taking into account the finite spatial resolution of the simulation. The results confirm that the adaptively determined closure facilitates the development of the inertial subrange and has a negligible computational overhead. Moreover, we demonstrate that the LES enriched with the newly developed model can provide reliable insight into the physics of large flow scales, particularly at high Reynolds numbers. We introduce a new resolution criterion for LES which is expressed in terms of the Taylor microscale λ and estimate that a significant part of the inertial subrange in isotropic turbulence at Reλ∼10 000 can be accurately resolved with at most ∼16 3843 modes, which is currently achievable using modern exascale computing resources.