# Research Contributions

Most of my research is concerned with flows of gasses or liquids. These keep airplanes in the air, but also add greatly to the U.S. fuel requirements. `Boundary layers' are thin layers of gas or fluid that a moving vehicle drags along. They form at the surface of the vehicle and become a major nuisance if they `separate' from the surface and go their own merry way. It can cause an airplane to crash (`stall' or `spin') and it adds greatly to the aerodynamic resistance, or `drag', of a vehicle. Regrettably, we still don't understand very well how boundary layers separate.

The initial separation: discovery (2D).
The numerical discovery of the initial separation process. This is my most well known contribution. It was initially very controversial. (With Shan-fu Shen).
The initial separation: structure (2D).
The description of the structure of the initial separation process. It proved to have some unexpected properties. (With Shan-fu Shen).
Pictures of an initial separation.
Here are some color pictures of the initial separation process around a wire in a wind gust. Computed by the great Shankar Subramaniam.
Separation moving to the front
A description of the flow structure near the position where a boundary layer separates from a solid surface. In this case the position of separation is moving towards the front of the vehicle. (With Shan-fu Shen).
Separation moving to the rear
A study of the flow structure near the position where a boundary layer separates from a solid surface. In this case the position of separation is moving towards the rear of the vehicle. An unsolved, very controversial case. (With Shan-fu Shen).
Separation at rest
A study of the flow structure near the position where a boundary layer separates from a solid surface. In this case the position of separation is at rest compared to the vehicle. Not much of a contribution. (With Shan-fu Shen).
Boundary layer development at the leeward side of an obstacle such as a wire, leg of an oil rigg, etcetera. (With Shan-fu Shen).
Thrust augmentation
Study of the possibility to augment the thrust of a jet engine by enclosing it within a duct. (With Norm Whitley and Yulu Krothapalli).
Fast velocity determination
Numerical tricks to allow the computation of flows to be done much faster. (With Elke Rundensteiner).
Pictures of Stalling Wing Cross Sections
When the wings of planes get under too large an angle, the boundary layer separates. The result is that the wing loses its lift and the plane falls. Recovery can be achieved by pushing the nose of the plane first down, then up. Here are some pictures of the boundary layer separating. (With Szu-Chuan Wang).
Decay of counter-rotating vortices
Vortices can be tought of as idealized tornados. This study examines how two of them, rotating in opposite directions, kill each other off. (With Shankar Subramaniam).
Numerical simulation of diffusion
Vorticity is angular rotation of fluids or gasses induced by an obstacle. It tends to move in complex ways, requiring some cleverness to compute it well.
Possible mechanics of turbulence
Turbulence means random fluctuations in the flow of a fluid or gas. We still do not really understand exactly how the fluid fluctuates. This studies some possible processes that might occur.