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### A wave driver theory for vortical waves propagating across junctions with application to those between rigid and compliant walls

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Sen, P. K., Ph.D., Carpenter, P. W. (Peter William), 1942-, Hedge, S. R. and Davies, Christopher.
(2009)
*A wave driver theory for vortical waves propagating across junctions with application to those between rigid and compliant walls.*
Journal of Fluid Mechanics, Vol.625
.
pp. 1-46.
ISSN 0022-1120

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Official URL: http://dx.doi.org/10.1017/S0022112008005545

## Abstract

A theory is described for propagation of vortical waves across alternate rigid and compliant panels. The structure in the fluid side at the junction of panels is a highly vortical narrow viscous structure which is idealized as a wave driver. The wave driver is modelled as a ‘half source cum half sink’. The incoming wave terminates into this structure and the outgoing wave emanates from it. The model is described by half Fourier–Laplace transforms respectively for the upstream and downstream sides of the junction. The cases below cutoff and above cutoff frequencies are studied. The theory completely reproduces the direct numerical simulation results of Davies & Carpenter (J. Fluid Mech., vol. 335, 1997, p. 361). Particularly, the jumps across the junction in the kinetic energy integral, the vorticity integral and other related quantities as obtained in the work of Davies & Carpenter are completely reproduced. Also, some important new concepts emerge, notable amongst which is the concept of the pseudo group velocity.

Item Type: | Journal Article |
---|---|

Subjects: | Q Science > QA Mathematics Q Science > QC Physics |

Divisions: | Faculty of Science > Engineering |

Library of Congress Subject Headings (LCSH): | Vortex-motion -- Research, Wave-motion, Theory of, Laplace transformation, Fourier transformations, Fluid dynamics |

Journal or Publication Title: | Journal of Fluid Mechanics |

Publisher: | Cambridge University Press |

ISSN: | 0022-1120 |

Date: | April 2009 |

Volume: | Vol.625 |

Page Range: | pp. 1-46 |

Identification Number: | 10.1017/S0022112008005545 |

Status: | Peer Reviewed |

Access rights to Published version: | Restricted or Subscription Access |

References: | Ashpis, D. E. & Reshotko, E. 1990 The vibrating ribbon problem revisited. J. Fluid Mech. 213, 531–547. Billingham, J. & King, A. C. 2000 Wave Motion. Cambridge University Press. Carpenter, P. W. & Garrad, A. D. 1985 The hydrodynamic stability of flow over Kramer-type compliant surfaces. Part 1. Tollmien–Schlichting instabilities. J. Fluid Mech. 155, 465–510. Carpenter, P. W. & Morris, P. J. 1990 The effect of anisotropic wall compliance on boundary-layer stability and transition. J. Fluid Mech. 218, 171–223. Carpenter, P. W. & Sen, P. K. 2003 Propagation of waves across junctions between rigid and flexible walls. In Flow Past Highly Compliant Boundaries and in Collapsible Tubes (ed. P. W. Carpenter & T. J. Pedley), pp. 147–166. Kluwer. Carpenter, P. W., Sen, P. K., Hegde, S. & Davies, C. 2002 Wave propagation in flows across junctions between rigid and flexible walls. ASME Paper IMECE 2002–32202. Davies, C. & Carpenter, P. W. 1997 Numerical simulation of the evolution of Tollmien–Schlichting waves over finite compliant panels. J. Fluid Mech. 335, 361–392. Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press. Gaster, M. 1965 On the generation of spatially growing waves in a boundary layer. J. Fluid Mech. 22, 433–441. Grotberg, J. B. & Jensen, O. E. 2004 Biofluid mechanics in flexible tubes. Annu. Rev. Fluid Mech. 36, 121–147. Hegde, S. 2002 Study of small disturbance waves across alternate rigid and compliant panels, with analytical jump conditions at the junctions. PhD thesis, Indian Institute of Technology, Delhi. Heil, M. & Jensen, O. E. 2003 Flow in deformable tubes and channels. In Flow Past Highly Compliant Boundaries and in Collapsible Tubes (ed. P. W. Carpenter & T. J. Pedley), pp. 15–49, Kluwer. Henningson, D. S. & Schmid, P. J. 1992 Vector eigenfunction-expansions for plane channel flows. Stud. Appl. Math. 87, 15–43. Hill, D. C. 1995 Adjoint systems and their role in receptivity problem for boundary layers. J. Fluid Mech. 292, 183–204. Howe, M. S. 1998 Acoustics of Fluid-Structure Interactions. Cambridge University Press. Ince, E. L. 1926 Ordinary Differential Equations. Longmans, Green and Co. Kramer, M. O. 1960 Boundary-layer stabilization by distributed damping. J. Am. Soc. Nav. Engrs. 72, 25–33. Landahl, M. T. 1962 On the stability of a laminar incompressible boundary layer over a flexible surface. J. Fluid Mech. 13, 609–632. Lighthill, J. 1978 Waves in Fluids. Cambridge University Press. Lucey, A. D., Sen, P. K. & Carpenter, P. W. 2003 Excitation and evolution of waves on an inhomogeneous flexible surface in a mean flow. J. Fluids Struct. 18, 251–267. Luo, X. Y. & Pedley, T. J. 1995 A numerical simulation of steady flow in a 2-D collapsible channel. J. Fluids Struct. 9, 149–174. Luo, X. Y. & Pedley, T. J. 1996 A numerical simulation of unsteady flow in a 2-D collapsible channel. J. Fluid Mech. 314, 191–225. Manuilovich, S. V. 1992 Passage of an instability wave through a channel section of variable width (in Russian). Izv. Ros. Akad Nauk, Mekh. Zhidk. Gaza, No. 2, 34–41 (Translation in Fluid Dyn. 27, 177–182). Manuilovich, S. V. 2001 Propagation of Tollmien–Schlichting wave in a boundary layer over flexible path of a wall. In book of abstracts for IUTAM Symposium on Flow in Collapsible Tubes and Past Other Highly Compliant Boundaries, University of Warwick. Manuilovich, S. V. 2003 Propagation of perturbations in plane Poiseuille flow between walls of nonuniform compliance. Fluid Dyn. 38, 529–544. Manuilovich, S. V. 2004a Transformation of the instability wave under an abrupt change. Dokl. Phys. 49, 342–346. Manuilovich, S. V. 2004b Propagation of Tollmien–Schlichting waves over the junction between stiff and flexible panels (in Russian). Mekh. Zhidk. i Gaza, No. 5, 31–48. Nguyen, V. B., Pa¨ıdoussis, M. P. & Misra, A. K. 1994 A CFD-based model for the study of the stability of cantilevered coaxial cylindrical shells. J. Sound Vib. 176, 105–125. Noble, B. 1958 Methods Based on the Wiener–Hopf Technique. Pergamon Press. Pa¨ıdoussis, M. P. 1998 Fluid-Structure Interactions: Slender Structures and Axial Flow. vol. 1, Academic Press. Pedrizzetti, G. 1998 Fluid flow in a tube with an elastic membrane insertion. J. Fluid Mech. 375, 39–64. Schmid, P. J. & Henningson, D. S. 2001 Stability and Transtion in Shear Flows. Springer. Sen, P. K. & Arora, D. S. 1988 On the stability of laminar boundary layer flow over a flat plate with a compliant surface. J. Fluid Mech. 197, 201–240. Sen, P. K., Hegde, S. & Carpenter, P. W. 2002 Simulation of small disturbance waves over alternate rigid and compliant panels. Indian J. Engng Mater. Sci. 9, 409–413. Sen, P. K., Hegde, S. & Carpenter, P. W. 2003 Propagation of small disturbance waves in a fluid flow across junctions between rigid and compliant panels. Def. Sci. J. 53, 189–198. Wiplier, O. & Ehrenstein, U. 2000 Numerical simulation of linear and nonlinear disturbance evolution in a boundary layer with compliant walls. J. Fluids Struct. 14, 157–182. |

URI: | http://wrap.warwick.ac.uk/id/eprint/2576 |

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