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Center for Nonlinear Studies |
In this talk I will discuss analytical and numerical results obtained in the study of two-dimensional Navier-Stokes-$\alpha$ turbulence model. The use of numerical models for the Navier-Stokes equations of fluid dynamics is an established practice in the study of turbulent flows. The calculation of flow from a model, instead of the underlying Navier-Stokes equations, allows for the use of less computing resources for a given flow. The Navier-Stokes-$\alpha$ model uses a smoothed velocity field to transport a rough velocity field. The expectation is that the smoothed field will be sufficent to recover many of the relevant properties of the flow. Our analysis shows three possible effects of this model on the energy spectrum of two-dimensional turbulence. These three effects stem from the fact that there are three physical timescales in the model equations: one from the smoothed field, the second from the rough field, and a third from a combination of the two. Our numerical simulations reveal that the timescale corresponding to the rough field is responsible for the dominant effects of the model in the small scales. The implication is that the rough field continues to affect the smooth field even though the latter is the postulated candidate for the modeled turbulence. The main goal of this project is to understand the small scale dynamics of this model. This knowledge will help us determine how to tune the parameter alpha appropriately to simulate the large scale dynamics of fluid flows at a more accessible computational requirement.
Host: Markus Berndt