THE DYNAMIC EARTH: A BLOG ABOUT GEOLOGY AND THE EARTH SCIENCES

## Wednesday, October 1, 2008

### Kinematic Theory of Unsteady Seperation

One of the problems with so much of our understanding of hydrodynamics (and, more broadly, all Earth Processes) is that we have to make so many damn generalizations and simplifications. Of course these are important first steps in developing greater insight into the world, but sometimes, you just want to have a firm grasp on what the hell is going on, you know?

Two recent papers, Weldon et al. 2008 and Lekien and Haller 2008, have made some impressive advances in our ability to describe and predict flow separation under unsteady conditions; the ramifications of this are pretty big, and if you've got a secret love of hydrodynamics (like me), it's pretty exciting stuff!

Fundamentally, flow separation occurs where a fluid is moving away from a solid boundary of some sort. In sedimentology, this is commonly illustrated by the behavior of a fluid flowing over a bedform, such as a dune in a river. While we have always had a general, qualitative appreciation of the effects of flow separation on bedform dynamics (i.e., back-flow eddies in the lee-sides of dunes, Kelvin-Helmholz instabilities in turbidity currents, etc), a quantitative description of the behavior has been lacking; as such, modeling these systems is difficult, and requires some arm-waving.

In fact, the nearest thing we've had to a kinematic solution for flow separation was Prandtl 1904. Using some mind-bogglingly complex math, ol' Prandtl was able to come up with a solution for laminar boundary separation in steady 2-D flows. Sentences like the previous one make sedimentologists involuntarily twitch: "laminar" and "steady" are both exceedingly rare in the natural world, making Prandtl's work useful for gross generalizations, but frustratingly weak in unsteady and turbulent flows.

Now, however, Weldon et al. and Lekien and Haller have both shown numerical and -most importantly- EXPERIMENTAL data that advances a kinematic theory of unsteady separation, allowing us to accurately predict separation points in unsteady flows. Furthermore, part of Weldon et al. (2008)'s work has shown that their kinematic theory accurately predicts flow separation in flows that are kinematically equivalent to turbulent flows.

Lekien and Haller (2008) also apply this particular kinematic theory to boundary separation models of the North Atlantic geostrophic current AND to boundary current separation and reattachment in Monteray Bay, based on field data collected from real live currents.

The public take on this (see here for MIT's own press release on the research) is focused on larger, non-geologic issues, such as increasing fuel efficiency by decreasing shear drag on cars. However, for selfish reasons, it will be particularly exciting to see where this sort of research leads to in the sed realm. We might finally start to home in on some robust models of mixing layer dynamics in sediment laden flows, or even (bestill my heart!) start being able to really interrogate bedform morphodynamics and evolution under realistically complex flow conditions!

WORKS CITED:

Weldon, M., Peacock, T., Jacobs, G.B., Helu, M., and Haller, G., 2008, Experimental and numerical investigation of the kinematic theory of unsteady separation: Journal of Fluid Mechanics, v. 611, p. 1 - 11.

Lekien, F., and Haller, G., 2008, Unsteady flow separation on slip boundaries: Physics of Fluids, v. 20