Separation in fluid flows

In recent years we have studied several hydrodynamic phenomena, where flow separation is a major mechanism for structure formation. The term separation is used in fluid mechanics to describe the situ­ation, where part of a flow has a direction opposite to the mean flow. In the case of a flow past a cylinder at low flow ve­lo­ci­ties a small zone of re­ver­sed flow -a separation bubble - is created on the lee side as shown (flow comes from the left).

 

 

 

The figures to the left show other cases, where separation is important: formation of sand dunes in the desert (in particular “Barchen dunes”), sand ripples under oscillating currents, blood flow, where sepa­ra­tion is an im­por­tant fac­tor in the cre­ation of ar­terio­scle­ro­sis and the se­pa­ration be­hind an air­plane wing leading to stall, when the angle of attack becomes too large.

 

 

The theoretical problem to overcome in the description of separating flows is the so-called Goldstein-Landau singularity occurring generically at separation in the boundary layer approximation, which is the standard approach to such flows.

 

In one case: the strongly non-linear stationary surface waves called hydraulic jumps, created when a fluid jet e.g. from a faucet in the kitchen sink, impinges on a flat surface, we have been able to overcome this problem by means of an averaging approach (a classical approach going back to von Karman and Pohlhausen). and the resulting flow is shown below (From S. Watanabe, V. Putkaradze and T. Bohr: Journal of  Fluid Mechanics 480, 233 (2004))

 

Sand ripples is another case that we have studied. The figure to the left shows the cross section of a sand ripple formed under oscillating flow. The picture is taken when the water moves to the right and a separation vortex forms to the lee side of the crest. This limits the sand flux and creates motion of the sand grains against the mean flow, thereby giving rise to the peaked structure of the ripples. We are currently developing a so-called “amplitude equation” to describe this situation and we are preparing an experiment in which the sand is replaced by a viscoelastic fluid which doesn’t mix with water and therefore doesn't enter into the flow. This is an important check on the importance of long-distance grain motion for sand-ripples.