New studies in vortex dynamics: Incompressible and compressible vortex reconnection, core dynamics, and coupling between large and small scales
- 130 Downloads
Coherent structure dynamics in turbulent flows are explored by direct numerical simulations of the Navier-Stokes equations for idealized vortex configurations. For this purpose, two dynamically significant coherent structure interactions are examined: (i) incompressible and compressible vortex reconnection and (ii) core dynamics (with and without superimposed small-scale turbulence). Reconnection is studied for two antiparallel vortex tubes at a Reynolds number (Re) of 103. Incompressible reconnection consists of three distinct phases: inviscid advection, bridging and threading. The key mechanism, bridging, involves the ‘cutting’ of vortex lines by viscous cross diffusion and their subsequent reconnection in front of the advancing vortex dipole. We conjecture that reconnection occurs in successive bursts and is a physical mechanism of cascade to smaller scales.
Compressible reconnection is seen to be significantly affected by the choice of pressure and density initial conditions. We propose a polytropic initial condition which is consistent with experimental results and low-Mach number asymptotic theories. We also explain how compressibility initiates an early reconnection due to shocklet formation, but slows down the circulation transfer at late times. Thus, the reconnection timescale increases with increasing Mach number.
Motivated by the important role of helical vortex lines in the reconnected vortices (bridges), we focus our attention on the dynamics of an axisymmetric vortex column with axial variation of core size. The resulting core dynamics is first explained via coupling between swirl and meridional flows. We then show that core dynamics can be better understood by applying a powerful analytical tool —helical wave decomposition — which extracts vorticity wave packets, thereby providing a simple explanation of the dynamics. The increase in core size variation with increasing Re in such a vortex demonstrates the limitation of the prevalent vortex filament models which assume constant core size. By studying the columnar vortex with superimposed small-scale, homogeneous, isotropic turbulence, we address the mutual interactions between large and small scales in turbulent flows. At its boundary the columnar vortex organizes the small scales, which, if Re is sufficiently high, induce bending waves on the vortex which further organize the small scales. Such backscatter from small scales cannot be modelled by an eddy viscosity. Based on the observation of such close coupling between large and small scales, we question the local isotropy assumption and conjecture a fractal vortex model for high Re turbulent flows.
KeywordsVortex dynamics vortex reconnection compressible vortex dynamics core dynamics helical wave decomposition coherent structures large-scale/small-scale interaction coherent structure/small-scale turbulence coupling
Unable to display preview. Download preview PDF.
- Bridges J, Husain H, Hussain F 1989 Whither coherent structures? InWhither turbulence? Turbulence at the crossroads (ed.) J Lumley (Berlin: Springer-Verlag)Google Scholar
- Erlebacher G, Hussaini M, Kreiss H, Sarkar S 1990 The analysis and simulation of compressible turbulence.icase Rep. No. 90–15Google Scholar
- Feiereisen W, Reynolds W, Ferziger J 1981 Numerical simulation of a compressible homogeneous, turbulent shear flow. Report No.tf-13, StandfordGoogle Scholar
- Greene J M 1990 Vortex nulls and magnetic nulls. InTopological fluid mechanics (eds) H K Moffatt, A Tsinober (Cambridge: University Press)Google Scholar
- Hussain F 1981 Role of coherent structures in turbulent shear flows.Proc. Indian Acad. Sci. (Eng. Sci.) 4: 129–175Google Scholar
- Hussain F 1984 Coherent structures and incoherent turbulence. InTurbulence and chaotic phenomena in fluids (ed.) T Tatsumi (Amsterdam: North-Holland)Google Scholar
- Kerr R N, Hussain F 1989 Simulation of vortex reconnection.Physica D37: 474–484Google Scholar
- Lee S, Lele S, Moin P 1991 Eddy shocklets in decaying compressible turbulence.Phys. Fluids A3: 657–664Google Scholar
- Mandella M 1987Experimental and analytical studies of compressible vortices, Ph D thesis, Stanford University, StanfordGoogle Scholar
- Meiron D I, Shelley M J, Ashurst W T, Orszag S A 1989 Numerical studies of vortex reconnection. InMathematical aspects of vortex dynamics (ed.) R Caflish (SIAM)Google Scholar
- Melander M V, Hussain F 1988 Cut-and-connect of two antiparallel vortex tubes. Report-S88, 257–286, Stanford University: also, 1989Phys. Fluids A1: 633–636Google Scholar
- Melander M V, Hussain F 1990 Topological aspects of vortex reconnection. InTopological fluid mechanics (eds) H K Moffatt, A Tsinober (Cambridge: University Press)Google Scholar
- Melander M V, Hussain F 1993a Topological vortex dynamics in axisymmetriv viscous flows.J. Fluid Mech. (in press)Google Scholar
- Melander M V, Hussain F, Basu A 1991 Breakdown of a circular jet into turbulence.Turbulent Shear Flows 8, Munich, pp. 15.5.1–15.5.6Google Scholar
- Narasimha R 1989 The utility and drawbacks of traditional approaches. InWhither turbulence? Turbulence at the crossroads (ed.) J Lumley (Berlin: Springer-Verlag)Google Scholar
- Schwarz K 1985 Three-dimensional vortex dynamics in superfluid4He: Line-line and line-boundary interactions.Phys. Rev. B31: 5782–5803Google Scholar
- Stanaway S, Shariff K, Hussain F 1988 Head-on collision of viscous vortex rings.NASA reportctr S-88, 287Google Scholar
- Takaki R, Hussain F 1985 Recombination of vortex filaments and its role in aerodynamic noise.Turbulent Shear Flows V, Cornell University, 3.19–3.25Google Scholar
- Truesdell C 1954The kinematics of vorticity, Indiana University Publications Science Series, No. 19Google Scholar
- Van Dyke M 1988An album of fluid motion (Stanford,CA: Parabolic Press)Google Scholar