流体流动由偏微分方程的复杂非线性系统控制。在许多感兴趣的情况下，流量跨度范围很大
Modern society has been shaped by a long tradition of mutual inspiration and enrichment between Mathematics and the Sciences. In this tradition, the Department of Applied Mathematics offers its graduate students opportunities for study in the areas of Control Theory and Dynamical Systems, Fluid Mechanics, Mathematical Medicine and Biology, Mathematical Physics, and Scientific Computation. Our students' research projects involve cutting-edge applications of mathematical theory in a broad range of fundamental and applied sciences. These applications include, for instance, cancer therapy optimization, control of shape memory alloys, fractal image processing, quantum computing, and the study of climate variability, inflationary cosmology, and nanotechnology. The Department of Applied Mathematics is one of five units that comprise the Faculty of Mathematics at the University of Waterloo, which was ranked 20th worldwide in the 2015 QS University Rankings for mathematics. Graduate students in the department benefit from our close links with the Faculties of Science and Engineering, the Centre for Mathematical Medicine, the Centre for Theoretical Neuroscience, the Institute for Quantum Computing, the Perimeter Institute for Theoretical Physics, the Waterloo Institute for Nanotechnology, the Water Institute, and the Centre for Computational Mathematics in Industry and Commerce. We offer both Master's and PhD programs. Our thesis-based Master's of Mathematics (MMath) program normally takes two years to complete. Many of the graduates of this program subsequently pursue PhD degrees, others are successful in obtaining rewarding positions in industry or government. Our PhD program generally takes four years to complete. Most of our PhD graduates find employment in university research. Others take on positions in research and development in industry, government, or commerce.<br><br>Fluid flow is governed by complicated nonlinear systems of partial differential equations. In many situations of interest the flow spans a huge range of length scales, with the nonlinearity of the governing equations resulting in the transfer of energy from one length scale to another. Because of this complexity, the field of fluid mechanics has been the birth place of many important ideas in mathematics. It continues to stimulate work in areas such as partial differential equations, asymptotics and perturbation theory, computational methods, and nonlinear waves, including solitons, instability theory, chaos, and stochastic processes.