Lagrangian data assimilation for point vortex systems

• Published in: Journal of turbulence Vol. 3; no. 3; p. N53
• Main Authors: Ide, Kayo, Kuznetsov, Leonid, Jone, Christopher K R T
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 01.01.2002
• ISSN: 1468-5248; 1468-5248
• DOI: 10.1088/1468-5248/3/1/053

A new method for directly assimilating Lagrangian tracer observations for flow state estimation is presented. It is developed in the context of point vortex systems. With tracer advection equations augmenting the point vortex model, the correlations between the vortex and tracer positions allow one to use the observed tracer positions to update the non-observed vortex positions. The method works efficiently when the observations are accurate and frequent enough. Low-quality data and large intervals between observations can lead to divergence of the scheme. Nonlinear effects, responsible for the failure of the extended Kalman filter, are triggered by the exponential rate of separation of tracer trajectories in the neighbourhoods of the saddle points of the velocity field. This article was chosen from Selected Proceedings of the 4th International Workshop on Vortex Flows and Related Numerical Methods (UC Santa-Barbara, 17-20 March 2002) ed E Meiburg, G H Cottet, A Ghoniem and P Koumoutsakos.