The instability of a vortex ring impinging on a free surface

Abstract

Direct numerical simulation is used to study the development of a single laminar vortex ring as it impinges on a free surface directly from below. We consider the limiting case in which the Froude number approaches zero and the surface can be modelled with a stress-free rigid and impermeable boundary. We find that as the ring expands in the radial direction close to the surface, the natural Tsai–Widnall–Moore–Saffman (TWMS) instability is superseded by the development of the Crow instability. The Crow instability is able to further amplify the residual perturbations left by the TWMS instability despite being of differing radial structure and alignment. This occurs through realignment of the instability structure and shedding of a portion of its outer vorticity profile. As a result, the dominant wavenumber of the Crow instability reflects that of the TWMS instability, and is dependent upon the initial slenderness ratio of the ring. At higher Reynolds number a short-wavelength instability develops on the long-wavelength Crow instability. The wavelength of the short waves is found to vary around the ring dependent on the local displacement of the long waves.

Flow visualization of a vortex ring interaction with porous surfaces

“…The study of vortex rings is well documented and includes: formation, 1-4 transport, [5][6][7] and interaction with solid walls [8][9][10][11] or free surfaces. [12][13][14][15] In most interaction experiments, the vortex ring is allowed to interact with solid or interfacial surfaces. [8][9][10][11][12][13][14][15] These interactions show that for non-permeable surfaces the vortex ring/boundary interaction can produce a range of dynamics depending on the strength of the vortex ring.…”

“…[12][13][14][15] In most interaction experiments, the vortex ring is allowed to interact with solid or interfacial surfaces. [8][9][10][11][12][13][14][15] These interactions show that for non-permeable surfaces the vortex ring/boundary interaction can produce a range of dynamics depending on the strength of the vortex ring. If a vortex is sufficiently strong, it will form a boundary layer on the surface that separates forming secondary vortex rings that orbit the primary vortex and then convect away from the wall.…”

Numerical Study of the Instability and Flow Transition in a Vortex-Ring/Wall Interaction

“…The vortex rings are initially placed at H = 6R 0 . Following the previous treatment (Swearingen et al 1995;Archer et al 2010), periodic boundary conditions are used in the x-and y-directions. The computational domain chosen in the present study is sufficiently large to ensure that the effects of the periodicity are very small.…”

“…The experimental study (Walker et al 1987) has revealed that the primary vortex ring no longer remains stable as it approaches the wall at high Reynolds number. When the Reynolds number is high enough, the interaction can lead to the breakdown of vortex rings and transition to turbulent state (Orlandi and Verzicco 1993;Archer et al 2010). Thus, the instability of vortex rings and transition to turbulence need to be investigated for a vortex ring impinging on a wall in the high-Reynolds-numberregime.…”

“…Orlandi and Verzicco (1993) numerically analysed the azimuthal instabilities at Re = 1250 by imposing an initial azimuthal perturbation on the primary vortex ring and identifie a response perturbation in the secondary ring. Archer et al (2010) then studied a laminar vortex ring impacting a free surface using direct numerical simulation (DNS) and found that the instability transfers from short-wavelength instability to long-wavelength instability. The transfer happens through the rotation of wavy inner core structure and the shedding of outer core vorticity.…”