Fall 2015

Seminars are held on Mondays from 2:30 - 3:30PM in Cullimore Hall, Room 611, unless noted otherwise. For questions about the seminar schedule, please contact David Shirokoff.

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Date: September 14, 2015

Speaker: Xin Tong
Courant Institute of Mathematical Science

Title: "Filtering with Noisy Lagrangian Tracers"

Abstract:

An important practical problem is the recovery of a turbulent velocity field from Lagrangian tracers that move with the fluid flow. Despite the inherent nonlinearity in measuring noisy Lagrangian tracers, it is shown that there are exact closed analytic formulas for the optimal filter. When the underlying velocity field is incompressible, the tracers’ distribution converge to the uniform distribution geometrically fast; concrete asymptotic features, such as information barriers, are obtained for the optimal filter when the number of tracers goes to infinity. On the hand, the filtering of a compressible flow that consists of both geostrophically balanced (GB) modes and gravity waves is also considered. Its performance can be closely approximated by the filter performance of an idealized GB truncation of this model when the Rossby number is small, i.e. the rotation is fast. Such phenomenon is caused by fast-wave averaging and inspires a simplified filtering scheme.