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With the continuing progress in large eddy simulations (LES), and ever increasing computational resources, it is currently possible to numerically solve the time-dependent and anisotropic large scales of turbulence in a wide variety of flows. For some applications this large-scale resolution is satisfactory. However, a wide range of engineering problems involve flows at very large Reynolds numbers where the subgrid-scale dynamics of a practical LES are critically important to design and yet are out of reach given the com- putational demands of solving the Navier Stokes equations; this difficulty is particularly relevant in wall-bounded turbulence where even the large scales are often below the implied filter width of modest cost wall modeled LES. In this paper we briefly introduce a scale enrichment procedure which leverages spatially and spectrally localized Gabor modes. The method provides a physically consistent description of the small-scale velocity field without solving the full nonlinear equations. The enrichment procedure is appraised against its ability to predict small-scale contributions to the pressure field. We find that the method accurately extrapolates the pressure spectrum and recovers pressure variance of the full field remarkably well when compared to a computationally expensive, highly resolved LES. The analysis is conducted both in a priori and a posteriori settings for the case of homogeneous isotropic turbulence. 

A turbulence enrichment model for subfilter-scale motions in large eddy simulations (LES) is comprehensively evaluated in the context of a posteriori analysis. The paper further develops the Gabor mode enrichment model first introduced in Ghate & Lele (J. Fluid Mech., vol. 819, 2017, pp. 494–539) by analysing three key requisites of LES enrichment using solenoidal small-scale velocity fields: (a) consistent spectral extrapolation and improvement of resolved single- and two-point second-order correlations; (b) ability to accurately capture the flow physics responsible for temporal decorrelation at small scales; and (c) accurate representation of spatially localized and intermittent interscale energy transfer between scales resolved by the coarse-grid LES and subfilter scales. We argue that the spatially and spectrally localized Gabor wavepackets offer an optimal basis to represent small-scale turbulence within quasi-homogeneous regions, although the alignment of fine-scale vorticity with large-scale strain appears to be somewhat overemphasized. Consequently, we interpret the resulting subfilter scales as those induced by a set of spatially dispersed Burgers–Townsend vortices with orientations determined by the larger scale velocity gradients resolved by the coarse-grid LES. Enrichment of coarse-grid simulations of two high Reynolds number flow configurations, homogeneous isotropic turbulence and a rough-wall turbulent boundary layer show promising results. 

A new methodology to construct three-dimensional, temporally stationary but spatially inhomogeneous, incompressible turbulence is presented. The method combines use of the data-driven spectral proper orthogonal decomposition (SPOD) to identify and isolate large-scale coherent motions of the flow, together with a physics-based enrichment algorithm using spatiotemporally localized Gabor modes that capture the inertial range turbulence. This fusion of data-driven and physics-based methods enables a statistically correct reconstruction of broadband turbulent flows using fewer modes than would be required using SPOD alone. To demonstrate the approach, we consider the problem of reconstructing wake turbulence on a plane downstream of a dragging actuator disk impinged by homogeneous isotropic turbulence. The reconstructed flow has single- and two-point correlations that are consistent with the reference high-resolution simulation data and could be used to generate statistically consistent inflow boundary conditions for subsequent simulations. 

In the last decade, many research groups have reported predictions of jet noise using high-fidelity large-eddy simulations (LES) of the turbulent jet flow and these methods are beginning to be used more broadly. A brief overview of the publications since the review of Bodony and Lele (2008, AIAA J., Vol. 56, 346-380) is undertaken to assess the progress and overall contributions of LES towards a better understanding of jet noise. In particular, we stress the meshing, numerical and modeling advances which enable detailed geometric representation of the nozzle shape variations intended to impact the noise radiation, and sufficiently accurate capturing of the turbulent boundary layer at the nozzle exit. Examples of how LES is currently being used to complement experiments for challenging conditions (such as highly heated pressure mismatched jets with afterburners) and guide jet modeling efforts are highlighted. Some of the physical insights gained from these numerical studies are discussed, in particular on crackle, screech and shock-associated noise, impingement tones, acoustic analogy models, wave packet dynamics and resonant acoustic waves within the jet core. We close with some perspectives on the remaining challenges and upcoming opportunities for future applications. This article is part of the theme issue `Frontiers of aeroacoustic research: theory, computation and experiment'.