# Atmosphere Ocean Science Colloquium

#### Filtering with Noisy Lagrangian Tracers

**Speaker:**
Xin Tong, Courant

**Location:**
Warren Weaver Hall 1302

**Date:**
Wednesday, October 15, 2014, 3:30 p.m.

**Synopsis:**

An important practical problem is the recovery of a turbulent velocity field fromLagrangian tracers that move with the fluid flow. Despite the inherentnonlinearity in measuring noisy Lagrangian tracers, it is shown that there areexact closed analytic formulas for the optimal filter. When the underlyingvelocity field is incompressible, the tracers? distribution converge to theuniform distribution geometrically fast; concrete asymptotic features, such asinformation barriers, are obtained for the optimal filter when the numberof tracers goes to infinity. On the hand, the filtering of a compressible flowthat consists of both geostrophically balanced (GB) modes and gravity waves isalso considered. Its performance can be closely approximated by the filterperformance of an idealized GB truncation of this model when theRossby number is small, i.e. the rotation is fast. Such phenomenon is caused byfast-wave averaging and inspires a simplified filtering scheme.