Mathematical Sciences: Nonlinear Partial Differential       Equations from Hydrodynamics
{'Code': '03040102', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'John V. Ryff', 'PO_EMAI': None, 'PO_PHON': None}
Work to be done on this project will concentrate on                        nonlinear problems arising in hydrodynamics.  Particular                        emphasis will be placed on the propagation of waves in                          stratified media.  These waves, arising from density                            stratification due to changes in salinity or temperature have                   been investigated analytically for several decades.  Much of                    the internal wave phenomena which has been observed                             experimentally, remains to be clarified.                                             Mathematical models for stratified wave motion are given                   by nonlinear partial differential equations for the                             pseudostream function.  Computing this, together with the                       wave speed, is one of the primary goals of the project.                         Current work has focused on equations with smooth densities                     in which there is a gradual density change in an ocean                          thermocline.  In cases where there are abrupt changes, work                     will proceed on the question of how much streamlines steepen                    along solution branches.                                                             Other work has considered surges in two-fluid systems.                     No rigorous analytic studies of this type of internal wave                      have been presented in the literature before.  A dynamical                      systems approach to the corresponding elliptic problem and a                    center manifold to model the behavior of small waves has now                    been developed.  The question of global behavior of surges is                   quite open and attention will be given to this issue by using                   global bifurcation methods.                                                          Numerical studies on the multitude of internal wave                        structures will also be carried out.  Initial work was                          carried out on periodic progressing gravity waves between                       immiscible fluids.  Present investigations are also analyzing                   a new phenomenon of overhanging waves.  In addition, a study                    is being continued on the limiting behavior of solitary waves                   in a two-fluid system with upper and lower fixed horizontal                     walls.  This models ocean flows under ice caps.                                      Applications of this research to the understanding of                      important wave phenomena are manifest.
{'FirstName': 'Robert E', 'LastName': 'Turner', 'PI_MID_INIT': 'L', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Robert E L Turner', 'EmailAddress': None, 'NSF_ID': '000156077', 'StartDate': '05/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Wisconsin-Madison', 'CityName': 'MADISON', 'ZipCode': '537151218', 'PhoneNumber': '6082623822', 'StreetAddress': '21 North Park Street', 'StreetAddress2': 'Suite 6301', 'CountryName': 'United States', 'StateName': 'Wisconsin', 'StateCode': 'WI', 'CONGRESSDISTRICT': '02', 'CONGRESS_DISTRICT_ORG': 'WI02', 'ORG_DUNS_NUM': '161202122', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF WISCONSIN SYSTEM', 'ORG_PRNT_DUNS_NUM': '041188822'}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8721771.xml'}