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We propose and apply a Fourier-based symmetry-reduction scheme to remove, or quotient, the streamwise translation symmetry of laser-induced-fluorescence measurements of turbulent pipe flows that are viewed as dynamical systems in a high-dimensional state space. We also explain the relation between Taylor’s hypothesis and the comoving frame velocity
of the turbulent orbit in state space. In particular, in physical space we observe flow structures that deform as they advect downstream at a speed that differs significantly from
. Indeed, the symmetry-reduction analysis of planar dye concentration fields at Reynolds number
reveals that the speed
at which high-concentration peaks advect is roughly 1.43 times
. In a physically meaningful symmetry-reduced frame, the excess speed
can be explained in terms of the so-called geometric phase velocity
associated with the orbit in state space. The ‘self-propulsion velocity’
is induced by the shape-changing dynamics of passive scalar structures observed in the symmetry-reduced frame, in analogy with that of a swimmer at low Reynolds numbers.
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