9411212 Tough The flow of superfluid helium is limited at high velocities by a random tangle of quantized vortex lines that fills the fluid. In uniform flows, when the tangle is homogeneous, this state of turbulence is well understood both experimentally and theoretically. A fundamental microscopic theory, supported by computer simulations, gives many properties of the tangle in excellent agreement with experiments. It was therefore surprising when preliminary experiments on weakly inhomogeneous superfluid turbulence gave results that cannot be understood as a simple extension of the homogeneous case. This experimental project extensive new data on the static and dynamic properties of superfluid turbulence in nonuniform flows where the tangle is inhomogeneous. % % % % Understanding and controlling turbulence in the flow of fluids is an important and long-standing problem in science. From the behavior of aircracts and ships, to predicting the weather and increasing the efficiency of flow through pipelines, turbulence plays a critical role. Enormous progress has been made recently in understanding a kind of turbulence in the simplest fluid: superfluid turbulence in liquid helium. A fundamental theory gives results in excellent agreement with experimental observations as long as the turbulence is the same in every part of the fluid. When the turbulence is inhomogeneous however, there are surprising discrepancies. The experimental project will produce extensive new data on the properties of inhomogeneous superfluid turbulence, proving a rigorous test of our theoretical; understanding. ***