Turbulence Theory:  Bounds and Higher-Order Statistics
{'Code': '06020102', 'Directorate': {'Abbreviation': 'GEO', 'LongName': 'Directorate For Geosciences'}, 'Division': {'Abbreviation': 'AGS', 'LongName': 'Div Atmospheric & Geospace Sciences'}}
{'SignBlockName': 'Robert W. Taylor'}
The objective of this research is the development of                    turbulence approximations which provide upper and lower bounds on               quantities of physical interest. This work is in the spirit of                  the bounding theory of Howard and Busse but proceeds from a                     decimation scheme in which only a subset of the modes of the flow               system are treated explicitly.  The remaining, implicit modes are               represented by stochastic forcing terms which are subject to an                 in infinite set of moment constraints taken from the exact                      dynamics.  To find bounds, it is proposed to seek solutions which               extremalize the chosen quantities under a restricted subset of                  these constraints, imposed together with realizability                          inequalities.  Since the constraints are exact, bounds so                       constructed would be rigorous. Fourth.order statistics play an                  essential role in the development of bounds.  These statistics                  are additionally important because of recent Navier.Stokes                      simulation studies which show interesting behavior of mean.square               helicity and the mean square of the total nonlinear term.  It is                proposed to study 4th.order statistics by the decimation scheme.                The complexity of the work can be reduced by using integral                     rather than detailed forms of 4th.order moment constraints.
{'FirstName': 'Robert', 'LastName': 'Kraichnan', 'EmailAddress': None, 'StartDate': '06/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Robert H Kraichnan Inc', 'CityName': 'Dublin', 'ZipCode': '03444', 'PhoneNumber': None, 'StreetAddress': None, 'CountryName': 'United States', 'StateName': 'New Hampshire', 'StateCode': 'NH'}
[{'Code': '1266', 'Text': 'APPLIED MATHEMATICS'}, {'Code': '1522', 'Text': 'PHYSICAL METEOROLOGY'}, {'Code': '5730', 'Text': 'GLOBAL ATMOSPHERIC RESEARCH'}, {'Code': '5740', 'Text': 'Climate & Large-Scale Dynamics'}]
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