Beautiful fluids

Beautiful fluids

This is the time of year when I’m reminded of the beauty of fluids. That’s because we’re coming up to the fluid dynamics meeting of the American Physical Society (APS), which organises a headline grabbing “Gallery of Fluid Motion” photo and video competition. If you need convincing of the beauty of fluid dynamics, take a few moments to browse through past winners and entrants, here.

An image of some mini vortex rings taken from S. Morris & C.H.K Williamson’s winning poster entry (Cornell)

But why is this competition so popular? Why are fluid flows so easy on the eye? Personally, I think it’s because there is a balance between order and surprise that we see in flow patterns. They are at once intuitive and unpredictable, familiar and bizarre. Like a good film or piece of music – it satisfies us by playing by the rules that we understand, only to surprise us when it breaks them.  Ben Collyer (a past PhD student of the group) would probably say I was complicating things. I recall him saying that flows are pretty, “simply because the fields are two-times continuously differentiable”. He had an ironic sense of humour.

Anyway, with all this in mind, I decided to see if I could make my own ‘fluids art’. I thought it would be fun to be able to create viable fluid fields from photographs (of anything!). The basic technical idea is to convert the intensity of an image (how light or dark it is) into a stream function. A stream function is a simple way to define a 2D velocity field that satisfies the (incompressible) continuity equation (which most fluid flows must). So, this ensures that the flows I generate from an image look physically feasible. I then use a mathematical programming language (Matlab) to create streamlines in the velocity field.

So, like many great artists (!), I decided first to embark on a self portrait:

Hmmm… Well, undeterred by the results, I wanted to see if I could simulate the dissipation of these flow patterns in time (as you would see in the bath, say). I did this be using the velocity field as an initial condition to a numerical solution to the basic fluid equations of motion (here, the 2D unsteady incompressible laminar Navier-Stokes equations). This is what you get (note, the video below is played in reverse, then forwards, then looped).

It was stupid of me to expect that reversing the time would give the impression that my face emerges from the flow dynamics…but it’s sort of interesting to watch. You just can’t beat the real thing, though (watch from 1:30):

So, the conclusion? I’m not going to submit anything to this year’s Gallery of Fluid Motion. But you never know what might be produced in the Micro Nano Flows group for next year…