PROPAGATING HOLMBOE WAVES AT THE INTERFACE BETWEEN 2 IMMISCIBLE FLUIDS

The instability of the surface of discontinuity separating two streams of immiscible constant-density fluids is studied experimentally and t heoretically near onset when surface tension effects are significant. Following Thorpe's original idea, a tube filled with two immiscible fl uids is tilted at an angle and returned to its horizontal position to produce a nearly constant velocity difference between both streams tha t can be varied continuously across threshold. In order to control the wavenumber near onset, the flow is spatially forced by periodically d istributing small obstacles on the upper side of the tank. When the ki nematic viscosities of each fluid are nearly equal, ones observes two counter-propagating waves of equal amplitude, which cannot be explaine d from a vortex sheet model. A linear stability analysis of a density discontinuity embedded within a piecewise-linear velocity profile demo nstrates that such waves are Holmboe modes associated with the diffusi ve layers above and below the interface. Good agreement is obtained be tween the measured and predicted values of the critical velocity diffe rence, propagation velocity and growth factors of the waves. The insta bility analysis of the asymmetric velocity profile reveals that the br eaking of reflectional symmetry gives rise to a single propagating wav e near onset. When the kinematic viscosities of each fluid differ, the first destabilized wave is observed to propagate in the same directio n as the less-viscous fluid, in agreement with the theoretical results , and the dominant direction of propagation can be manipulated by adju sting the viscosities accordingly.