Investigating and modeling turbulence using numerical simulations

Date

2023-03-13

Authors

Mohan, Prakash, Ph. D.

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Abstract

Turbulence is a complex fluid phenomenon that is present in high Reynolds number flows. It has a profound effect on the flows in which it occurs, and it is therefore important to understand and model its effects. It occurs in multiple domains from flows inside our bodies to ocean currents and atmospheric winds. The difficulty in modeling and simulating turbulence arises from the fact that it is comprised of a wide range of scales that interact with each other non-linearly. The field of turbulence still has many open problems — from fundamental questions about the underlying physics to enabling tractable engineering models. The Navier-Stokes equations are a reliable representation of turbulent flows and solving them with sufficient accuracy gives us the detailed turbulent flow field. These are called Direct Numerical Simulations (DNS) and are an invaluable tool to study the turbulence phenomenon. In this work, we first consider how DNS of forced isotropic turbulence can be used to study time predictability of turbulence using Lyapunov exponents. Further analysis of the DNS field shows that flow instabilities act on the smallest eddies, and that at any time, there are many sites of local instabilities. DNS, however, is generally too expensive for simulating practical flows. Alternatively, Large Eddy Simulations (LES), in which only the largest scales of turbulent motion are simulated, is more promising as an engineering tool. However, in the near-wall region the large, dynamically important eddies are on the order of viscous scales, which makes resolving them very expensive. It is therefore desirable to formulate an approach in which the near-wall region is modeled, leading to the so-called wall-modeled LES. Spectral analysis of DNS data indicates that thin-film type asymptotics is a promising approach to model the interactions between the near-wall layer and the outer flow. For this approach an asymptotic analysis of the filtered Navier-Stokes equations is pursued in the limit in which the horizontal filter scale is large compared to the thickness of the wall layer. In the second part of this work, we present a new wall model formulated using the asymptotic analysis and insights from DNS data.

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