Determining flow field singularities from drifter trajectories

Halide, Halmar (1992) Determining flow field singularities from drifter trajectories. Masters thesis, Memorial University of Newfoundland.

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Abstract

This thesis is concerned with techniques for determining the properties of singularities in the flow field. Okubo and Ebbesmeyer (1976) and Molinari and Kirwan (1975) developed a regression technique that has become a standard for determining velocity gradients of the flow field. Kirwan (1988) has pointed out that this regression technique is fundamentally inadequate because is assumes a paradigm with the flow centre fixed to the centroid of the drifter cluster. Kirwan et al., (1988) formulated a solution to this dilemma by inverting non-linear solutions obtained by Okubo (1970) for motion near a flow field singularity with specified differential kinematic properties (DKP). The DKP are horizontal divergence, vorticity, stretching and shearing deformation rate. We solve the non-linear equations of Kirwan et al., (1988) to obtain DKP and the position and velocity of a flow field singularity from a single drifter trajectory. This solution (henceforth called the OK solution) is mathematically more concise than that presented in Kirwan et al., (1988) and corrects previously undetected algebraic errors in the published literature. It has been successfully tested using artificially generated data. The method is fundamentally limited due to the requirement that DKP are time invariant. It also has the undesirable feature that it requires fourth order time derivatives of data. A new method, the HS method, that uses regression without artificially setting a flow centre to the cluster centroid is presented. It has also been successfully tested by application to artificially generated data. The DKP are successfully recovered by the HS providing all drifters in the cluster are being moved by the same unique singularity in the flow field. -- Applying all three methods to three neighbouring drifter tracks measured on Sable Island Bank clearly indicated the limitations of all three methods. The regression technique Okubo and Ebbesmeyer (1976), the OE method, ‘failed’ because the flow centre was not at the cluster centroid position. The OK method gives ambiguous results in that it can not distinguish between solid body rotation about a point and a slab that oscillates. The lack of a single well defined flow centre for all three drifter trajectories was sufficient to ensure the HS method gave meaningless DKP that had large intermittent fluctuations. Nevertheless, given trajectories near a well-defined flow field singularity, we can be assured that both the HS and OK method can be used to obtain the position, velocity and SKP of the singularity. Depending upon the separation scales of the drifters, the HS method can be much less or more sensitive to noise than the OK method.

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