Nonlinear Problems in Optics and Fluid Mechanics
Abstract
Abstract/Objectives Nonlinear Problems in Optics and Fluid Mechanics This proposal is aimed at exploring two unrelated classes of nonlinear problems in (nonlinear) optics and in uid mechanics. The rst class of problems concerns the propagation of lasers in a turbulent atmo- sphere. This problem is totally new to us, and we believe that it has not yet been studied in the mathematical literature. It is a classical and essential problem in other areas of science, as e.g. astrophysics but the scales are not at all the same. We want to explore the physics and engineering literatures, to try to formulate the equations describing the phenomena, and see if some of the problems are amenable to mathematical treatment. The second problem, more familiar to the PI, is the study of two layers of inviscid shallow water ows, and the motion of a body (e.g. a boat) on such water. In the long range the purpose is to study the two-layers of water ows as in e.g. an estuary where one can nd fresh water above the saline water. There are some indications that the resistance to advancement for ships is higher in this context than on only fresh water or only saline water. The PI and his collaborator Madalina Petcu named in this proposal have studied shallow water ows for one or two layers of uid in space dimension one and the ow of one layer of uid in space dimension two. We will start to investigate the two-layer ows in space dimension two as well as some computational issues to be addressed in the medium to long range.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 12, 2016
- Source ID
- N000141512385
Entities
People
- Roger Meyer
Organizations
- Indiana University
- Office of Naval Research
- United States Navy