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## Revised manuscript submitted to Journal of Experimental Mechanics Special Issue on Locomotion

### Citations

285 |
Vortex dynamics.
- Saffman
- 1992
(Show Context)
Citation Context ...e loops around the bodies) in an inviscid problem. The force exerted by the fluid on a body (or set of bodies) in viscous or inviscid flow can be written in terms of rates of change of linear impulse =-=[16, 19]-=-, F f = − d dt (P ω + P γ + P b) , (3) where the impulses are defined, respectively, as P ω = ∫ Af x× ω dA, P γ = ∮ S x× γ ds, P b = ∮ S x× (n× ub) ds. (4) 2 α0−θ1 θ2 X0 x y X0 x y α0 κ(s,t)=K(s)cos[2... |

55 | Product Formulas and Numerical Algorithms,"
- Chorin, J, et al.
- 1978
(Show Context)
Citation Context ... they reduce in a straightforward way to those obtained from geometric mechanics. This formulation is based on the viscous splitting of the Navier–Stokes equations, argued rigorously by Chorin et al. =-=[4]-=-. The core idea of this concept is that each time step can be divided into substeps: one devoted to inviscid convection of existing vorticity, another devoted to viscous diffusion in a stationary flui... |

49 | Locomotion of articulated bodies in a perfect fluid”.
- Kanso, Marsden, et al.
- 2005
(Show Context)
Citation Context ... have convincingly demonstrated that locomotion in inviscid flows is best studied within the framework of geometric mechanics, with the help of a boundary element solver to compute the potential flow =-=[10, 17, 8, 9]-=-. This approach essentially leads to a view of locomotion as a 1 natural consequence of global conservation laws for the fluid–body system, and produces an attractively clean algorithm for computing t... |

41 |
Self-propelled anguilliform swimming: simultaneous solutions of the two-dimensional Navier-Stokes equations and Newton’s laws of motion
- Carling, Williams, et al.
- 1998
(Show Context)
Citation Context ...inct advantage of this form of the equations is that it places no restrictions on the intrinsic mass of the bodies; in contrast, many previous formulations are challenged by special cases of massless =-=[3, 11]-=- or neutrally buoyant bodies [1, 18]. Unfortunately, the geometric mechanics framework is not readily extendible to problems of finite Reynolds number. However, we will show in this paper that the dyn... |

37 |
Boundary conditions for viscous vortex methods,"
- Koumoutsakos, Leonard, et al.
- 1994
(Show Context)
Citation Context ...ce, by the flux of the vortex sheet associated with the no-flow-through condition into the adjacent fluid. This has been used as the basis for a numerical algorithm with vortex particle methods (e.g. =-=[12, 6, 7]-=-) and a Cartesian grid method [15]. For the purposes of the present paper, we can regard each timestep as split into two subseps: in the first, fluid vorticity evolves by convection and the body evolv... |

32 | Unsteady aerodynamics of fluttering and tumbling plates J. Fluid Mech.
- Andersen, Pesavento, et al.
- 2005
(Show Context)
Citation Context ...quations is that it places no restrictions on the intrinsic mass of the bodies; in contrast, many previous formulations are challenged by special cases of massless [3, 11] or neutrally buoyant bodies =-=[1, 18]-=-. Unfortunately, the geometric mechanics framework is not readily extendible to problems of finite Reynolds number. However, we will show in this paper that the dynamical equations for a body in visco... |

32 |
A Cartesian Grid Method for Modeling Multiple Moving Objects in 2D Incompressible Viscous Flow,
- Russell, Wang
- 2003
(Show Context)
Citation Context ...ciated with the no-flow-through condition into the adjacent fluid. This has been used as the basis for a numerical algorithm with vortex particle methods (e.g. [12, 6, 7]) and a Cartesian grid method =-=[15]-=-. For the purposes of the present paper, we can regard each timestep as split into two subseps: in the first, fluid vorticity evolves by convection and the body evolves by its own dynamics, but their ... |

26 |
The mechanics and control of robotic locomotion with applications to aquatic vehicles,
- Kelly
- 1998
(Show Context)
Citation Context ... have convincingly demonstrated that locomotion in inviscid flows is best studied within the framework of geometric mechanics, with the help of a boundary element solver to compute the potential flow =-=[10, 17, 8, 9]-=-. This approach essentially leads to a view of locomotion as a 1 natural consequence of global conservation laws for the fluid–body system, and produces an attractively clean algorithm for computing t... |

23 |
Numerical investigation of the hydrodynamics of carangiform swimming in the transitional and inertial flow regimes
- Borazjani, Sotiropoulos
- 2008
(Show Context)
Citation Context ...es – arising from both the body and the fluid – play an important role. Indeed, much can be learned about the nature of locomotion by comparing the self-propulsion of the same system in both settings =-=[5, 2]-=-. However, the computational approaches to studying inviscid and finite Reynolds number propulsion have evolved separately. Finite Reynolds number studies, for the most part, have relied on a grid-bas... |

21 |
Theory for Aerodynamic Force and Moment in Viscous Flows”,
- Wu
- 1981
(Show Context)
Citation Context ...ummations over all bodies’ surfaces. Regardless of whether the flow is inviscid or viscous, the total vorticity of the global system of bodies and fluid is constrained by Kelvin’s circulation theorem =-=[19]-=-, d dt (Γω + Γγ + Γb) = 0, (1) where the total vorticities are defined, respectively, as Γω = ∫ Af ω dA, Γγ = ∮ S γ ds Γb = ∮ S n× ub ds. (2) The first integral accounts for the total vorticity in the... |

20 |
Simulations of optimized anguilliform swimming
- Kern, Koumoutsakos
- 2006
(Show Context)
Citation Context ...inct advantage of this form of the equations is that it places no restrictions on the intrinsic mass of the bodies; in contrast, many previous formulations are challenged by special cases of massless =-=[3, 11]-=- or neutrally buoyant bodies [1, 18]. Unfortunately, the geometric mechanics framework is not readily extendible to problems of finite Reynolds number. However, we will show in this paper that the dyn... |

17 |
Numerical Simulation of The Fluid Dynamics Of 2D Rigid Body Motion With The Vortex Particle Method”
- Eldredge
- 2006
(Show Context)
Citation Context ...ce, by the flux of the vortex sheet associated with the no-flow-through condition into the adjacent fluid. This has been used as the basis for a numerical algorithm with vortex particle methods (e.g. =-=[12, 6, 7]-=-) and a Cartesian grid method [15]. For the purposes of the present paper, we can regard each timestep as split into two subseps: in the first, fluid vorticity evolves by convection and the body evolv... |

10 |
Numerical simulations of undulatory swimming at moderate reynolds number
- Eldredge
- 2006
(Show Context)
Citation Context ...es – arising from both the body and the fluid – play an important role. Indeed, much can be learned about the nature of locomotion by comparing the self-propulsion of the same system in both settings =-=[5, 2]-=-. However, the computational approaches to studying inviscid and finite Reynolds number propulsion have evolved separately. Finite Reynolds number studies, for the most part, have relied on a grid-bas... |

10 |
Boundary layer theory”.
- Lighthill
- 1963
(Show Context)
Citation Context ...tion and for the vorticity dynamics (if any). Viscous problems. When viscosity is present, the no-flow-through kinematic condition is augmented by the no-slip condition on the body surface. Lighthill =-=[14]-=- postulated that this extra condition is consistent with the creation of new vorticity at the surface, by the flux of the vortex sheet associated with the no-flow-through condition into the adjacent f... |

10 |
The Hamiltonian structure of a twodimensional rigid circular cylinder interacting dynamically with N point vortices”.
- Shashikanth, Marsden, et al.
- 2002
(Show Context)
Citation Context ... have convincingly demonstrated that locomotion in inviscid flows is best studied within the framework of geometric mechanics, with the help of a boundary element solver to compute the potential flow =-=[10, 17, 8, 9]-=-. This approach essentially leads to a view of locomotion as a 1 natural consequence of global conservation laws for the fluid–body system, and produces an attractively clean algorithm for computing t... |

7 |
Shapechanging bodies in fluid: hovering, ratcheting, and bursting
- Spagnolie, Shelley
- 2009
(Show Context)
Citation Context ...quations is that it places no restrictions on the intrinsic mass of the bodies; in contrast, many previous formulations are challenged by special cases of massless [3, 11] or neutrally buoyant bodies =-=[1, 18]-=-. Unfortunately, the geometric mechanics framework is not readily extendible to problems of finite Reynolds number. However, we will show in this paper that the dynamical equations for a body in visco... |

5 |
Dynamically coupled fluid-body interactions in vorticity-based numerical simulations
- Eldredge
- 2008
(Show Context)
Citation Context ... inviscid locomotion problem exists within the ‘cracks’ of the full viscous problem. It should be noted that this paper condenses and refines an earlier version of the coupling algorithm presented in =-=[7]-=-. 2 Methodology This paper will focus on two-dimensional problems, but the ideas can be readily extended to threedimensional configurations. We take the density of the fluid to be unity and the genera... |

4 | Stability of a coupled body-vortex system”.
- Kanso, Oskouei
- 2008
(Show Context)
Citation Context |

2 |
2008: Self-propulsion of a deformable joukowski foil in a perfect fluid with vortex shedding
- Xiong, Kelly
(Show Context)
Citation Context ...ial flow problem is linear in the components of surface velocity – rigid body motion plus some parametrization of surface shape change – so the scalar potential can be linearly decomposed accordingly =-=[13, 9, 20]-=-. From these forms, an added mass representation can be identified, which we write generically as( P γb + P b Πγb + Πb ) = M ·U . (8) 3 In these equations, the vector U consists of the rigid body comp... |

2 |
A viscous vortex particle method for deforming bodies with application to biolocomotion
- Zhang, Eldredge
- 2008
(Show Context)
Citation Context ...t in an inviscid problem; the strength of the sheet can be determined by solving an integral equation arising from this condition, subject to the additional constraint of Kelvin’s circulation theorem =-=[21]-=-. This sheet strength can be linearly decomposed into contributions from fluid vorticity and body motion, γ = γω + γb. In other words, γω is the strength of the surface vortex sheet in reaction to amb... |