Laminar free-surface flow around emerging obstacles: Role of the obstacle elongation on the horseshoe vortex

Abstract

Abstract An emerging rectangular obstacle placed in a laminar boundary layer developing under a free-surface generates three vortical structures: a horseshoe vortex (HSV) in front of the obstacle, a wake downstream and two lateral recirculation zones at its sides. The present work investigates, through PIV measurements, the effect of the obstacle elongation (length over width ratio L ∕ W ) on the HSV, which is partly indirect through the modification of the two other vortical structures. Horizontal velocity fields in the near-bottom region show that an increase of the obstacle elongation leads to a higher adverse pressure gradient in front of the obstacle, and in consequence, to the longitudinal extension of the HSV. This modification of geometry, in turn, impacts the vortex dynamics of the HSV. On top of that, maps of spectra and oscillation direction obtained from velocity fields indicate that each of the three structures (HSV, wake and lateral recirculation zones) exhibits a proper oscillation frequency. As the oscillation associated to the wake is energetically dominant and is strong enough to travel upstream, it impacts the HSV dynamics for sufficiently short obstacles.