2. Theory |
2.1 Contour Dynamics
2.2 Equations of Cotour Dynamics
2.3 Theory of an Elliptical Vortex
2.4 Finite-Time Lyapunov Analysis on Fluid Deformation
2.4 Finite-Time Lyapunov Analysis on Fluid Deformation
Yoden and Nomura(1993) did a finite-time Lyapunov analysis in phase space. The same analysis is done here in physical space to introduce a linear measure of deformation of a fluid percel.Trajectory of a fluid particle is given as a solution of the equation
(2.16)
Time evolution of a small perturbation from the solution can be described by a tangent linear equation of (2.16):
(2.17)
where J is Jacobian matrix of u at x( t ).
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