TITLE:

ENERGY CASCADE IN TURBULENT FLOWS; QUANTIFYING EFFECTS OF LOCAL AND NONLOCAL INTERACTIONS

DATE:

Friday, April 18th, 2008

TIME:

3:30 PM

LOCATION:

GMCS 214

SPEAKER:

Julian Andrzej Domaradzki, Aerospace and Mechanical Engineering, University of Southern California

ABSTRACT:

The classical Kolmogorov theory of turbulence is based on the concept of the energy transfer from larger to progressively smaller scales of motion. The theory assumes that bulk of the energy transfer in the inertial range of turbulence occurs between scales of similar size, a process known as the local energy cascade. The assumed locality allows to postulate that after multiple cascade steps the small scale dynamics become universal, i.e., independent of particulars of large scales that are determined by geometry, boundary conditions, and forces causing a particular flow. Yet despite its central role in the Kolmogorov theory the locality assumption cannot be easily verified, neither analytically nor experimentally. This is because, mathematically, the energy transfer is a result of interactions among different scales of motion originating from the nonlinear term in the Navier-Stokes equation that couples all scales. Relevant questions can be productively addressed using databases generated in large scale numerical simulations. We describe such databases and use them to compute detailed energy exchanges between scales of motion with well defined sizes, obtained by decomposing numerical velocity fields using banded filters, and investigate how the detailed transfers contribute to the global quantities such as the classical energy transfer and the energy flux. The developed procedure allows to quantify locality of the energy transfer and to address a persistent controversy concerning the role of nonlocal interactions in this process, i.e., of much larger scales than those transferring energy. The analysis of detailed interactions reveals that the individual nonlocal contributions are always large but significant cancellations lead to the global quantities asymptotically dominated by the local interactions. Apart from an intellectual challenge of clarifying these issues, obtained results have bearing on practical questions of turbulence modeling that will be addressed in the talk.

HOST:

Guus Jacobs

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