Symmetry reduction of turbulent pipe flows

Abstract

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 $U_d$ 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 $U_d$. Indeed, the symmetry reduction analysis of planar dye concentration fields at Reynolds number $\mathsf{Re}=3200$ reveals that the speed $u$ at which high concentration peaks advect is roughly 1.43 times $U_d$. In a physically meaningful symmetry-reduced frame, the excess speed $u-U_d\approx 0.43U_d$ can be explained in terms of the so-called geometric phase velocity $U_g$ associated with the orbit in state space. The 'self-propulsion velocity' $U_g$ 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.

arXiv admin note: substantial text overlap with arXiv:1407.7487

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Cited by in corpus (3)

• Dimensionality Reduction and Reduced Order Modeling for Traveling Wave Physics
• Crest speeds of unsteady surface water waves
• A robust shifted proper orthogonal decomposition: Proximal methods for decomposing flows with multiple transports