Dedication [to Tony Leonard]

Abstract

Over more than 30 years, Tony Leonard's contributions to fluid mechanics, continuum mechanics and numerical methods have been dense and seminal. He has worked in diverse areas including vortex dynamics, vortex-based numerical methods, wall-bounded turbulence, quantized turbulence, Large–Eddy Simulation (LES), Lagrangian mixing, spectral numerical methods, bluff body flows and flow-induced vibrations. Tony's first paper on LES, "Energy Cascade in Large–Eddy Simulation of Turbulent Fluid Flows" appeared as an article in a review series, "Advances in Geophysics", in 1974. It proposed the concept of spatial filtering that has since been a cornerstone of LES. The idea of numerically simulating the evolution of large scales of turbulence while modeling the small scales was not new in the 1970s but it lacked a firm theoretical framework for the conceptual separation of the resolved or computed scales, and the subgrid or unresolved scales. Tony Leonard's 1974 introduction of the convolution operation of a field with a filter to produce the resolvable-scale function, and its application to the Navier Stokes equations of motion provided the means of identifying "resolved scales" while isolating and grouping those filtered products of subgrid fields with themselves and with resolved-scale fields, that required modeling. Tony's filter formalism has had a profound impact on the development of LES methodology and indeed is the starting point for most modern expositions on this topic. There is little doubt that his 1974 paper, which has not been published elsewhere, has become an unquantified citation classic.

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