Quantitative flow analysis of swimming dynamics with coherent Lagrangian vortices.
Undulatory swimmers flex their bodies to displace water, and in turn, the flow feeds back into the dynamics of the swimmer. At moderate Reynolds number, the resulting flow structures are characterized by unsteady separation and alternating vortices in the wake. We use the flow field from simulations of a two-dimensional, incompressible viscous flow of an undulatory, self-propelled swimmer and detect the coherent Lagrangian vortices in the wake to dissect the driving momentum transfer mechanisms. The detected material vortex boundary encloses a Lagrangian control volume that serves to track back the vortex fluid and record its circulation and momentum history. We consider two swimming modes: the C-start escape and steady anguilliform swimming. The backward advection of the coherent Lagrangian vortices elucidates the geometry of the vorticity field and allows for monitoring the gain and decay of circulation and momentum transfer in the flow field. For steady swimming, momentum oscillations of the fish can largely be attributed to the momentum exchange with the vortex fluid. For the C-start, an additionally defined jet fluid region turns out to balance the high momentum change of the fish during the rapid start.
Department of Mechanical and Process Engineering, Institute of Mechanical Systems, ETH Zürich, Leonhardtstrasse 21, CH-8092 Zurich, Switzerland.
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Huhn
Chair of Computational Science, ETH Zürich, Clausiusstrasse 33, CH-8092 Zürich, Switzerland.
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van Rees
School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.
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Gazzola
Chair of Computational Science, ETH Zürich, Clausiusstrasse 33, CH-8092 Zürich, Switzerland.
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Rossinelli
Department of Mechanical and Process Engineering, Institute of Mechanical Systems, ETH Zürich, Leonhardtstrasse 21, CH-8092 Zurich, Switzerland.
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Haller
Chair of Computational Science, ETH Zürich, Clausiusstrasse 33, CH-8092 Zürich, Switzerland.
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Koumoutsakos