Papers › The Objective Deformation Component of a Velocity Field
The Objective Deformation Component of a Velocity Field
Bálint Kaszás, Tiemo Pedergnana, George Haller
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For an arbitrary velocity field 𝐯 defined on a finite, fixed spatial domain, we find the closest rigid-body velocity field 𝐯_(RB) to 𝐯 in the L² norm. The resulting deformation velocity component, 𝐯_d=𝐯-𝐯_(RB), turns out to be frame-indifferent and physically observable. Specifically, if 𝐐_(RB)(t) is the rotation tensor describing the motion of the closest rigid body frame, then 𝐯 is seen as 𝐐_(RB)ᵀ𝐯_d by an observer in that frame. As a consequence, the momentum, energy, vorticity, enstrophy, and helicity of the flow all become frame-indifferent when computed from the deformation velocity component 𝐯_d.
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