Numerical investigation of the collision of a vortex pair upon a solid wavy wall

Abstract

The vortex dynamics produced by the collision of a vortex pair with a solid wavy wall are examined numerically using a proposed high-order vortex particle method. The influences of the Reynolds number (ReΓ) of the vortex pair, the wavelength (λw), and the wave amplitude (Aw) of the wall on the induced vortex structures, interactions among vortices, and the instability and reconnection of secondary vortices are discussed. The boundary layers at the top of ripples separate first to form the secondary vortices moving around the primary tubes. Meanwhile, the boundary layers at the bottom of ripples detach late, move vertically upward, and then form incomplete vortex loops due to an unsuccessful reconnection of the secondary vortices. The ReΓ effects cause the appearance of various vortex structures, such as incomplete primary vortex loops from the bottom of ripples at ReΓ=1000, secondary vortex loops due to interactions of the first loops with the wall at ReΓ=2000, and hairpin vortices at ReΓ=4000. The wavelength of the wall induces instability in the secondary vortex tubes. This instability on the secondary tubes appears at the top of ripples at λw=2r0, while it spreads over the whole secondary vortices at λw=4r0, where r0 is the initial spacing between the primary vortex tubes. This instability results in various wavy tubes that robustly interact with the primary tubes. Due to the effects of Aw, the primary vortex tubes significantly decay with time compared to those in the flat wall case.