Fully nonlinear structures, wave trains, and solitary waves in vortex filaments
Abstract
Solutions for incompressible, inviscid flows have been obtained representing flow structures in vortices with strong axial accelerations. The fluid is assumed to be confined to cylindrical tubes or annuli of either finite or infinite length. The solutions are axially-symmetric static bifurcations from columnar vortices constructed by either a monotone iteration procedure, or by various continuation schemes. One class of solutions represents fully nonlinear periodic wavetrains of permanent form generalizing weakly nonlinear cnoidal waves. As the wavelength increases indefinitely, these solutions pass over to the fully nonlinear generalization of the weakly nonlinear (Korteweg-deVries) solitary wave. Other classes of solutions are described also, one of which sheds light on numerical (Navier-Stokes) simulations of vortex breakdown. The inviscid solutions to be discussed are characterized by axial decelerations which can lead to stagnation points and regions of reversed axial flow.
- Publication:
-
Nonlinear Wave Interactions in Fluids
- Pub Date:
- 1987
- Bibcode:
- 1987nwif.proc...67L
- Keywords:
-
- Incompressible Flow;
- Inviscid Flow;
- Solitary Waves;
- Vortex Filaments;
- Wave Packets;
- Annular Flow;
- Cnoidal Waves;
- Navier-Stokes Equation;
- Pipe Flow;
- Fluid Mechanics and Heat Transfer