Creator 

Abstract or Summary 
 The main result of this paper is a proof of the existence of a solution
generated by a method for the variational assimilation of observational data
into the twodimensional, incompressible Euler equations. The data are
assumed to be given by linear (measurement) functionals acting on the space
of functions representing vorticity. From a practical point of view, the data
are considered to be sparse and available on a fixed spacetime domain.
The objective of the variational assimilation is to obtain an estimate
of the vorticity which minimizes a cost functional. The cost functional is
the sum of a generalized mean squared error in the dynamics, a generalized
mean squared error in the initial condition, and a weighted squared error
in the misfit to the observed data. These generalized mean squared errors
are computed over the fixed spacetime domain containing the data. The
estimate then provides a best (generalized) least squares fit between the
model, the initial condition, and the data. A necessary condition for the estimate of vorticity to minimize the cost
functional is that it must satisfy the corresponding system of EulerLagrange
equations, which consist of a nonlinear, coupled system of partial differential
equations with an initial condition, a final condition, and boundary conditions.
Construction of a solution to the EulerLagrange equations is possible
provided they are linearized through an iterative scheme.
Analysis of one such scheme motivates a reformulation of the variational
problem in terms of an iterated linearization of the dynamics. This second
method results in a slightly different iterated system of EulerLagrange equations.
The sequence of solutions generated is shown to be bounded in the
Sobolev space W[superscrit k,p] (in spacetime). It follows from a Sobolev imbedding
theorem that the sequence contains a convergent subsequence, the limit of
which is a classical solution of the nonlinear, forced Euler equation corresponding
to the forward problem of the EulerLagrange system.
The two schemes mentioned above are compared based on formal applications
of Newton's method to the operators defining the systems. We
conclude that the two formulations of the assimilation problem are in fact
different and provide some intuitive reasons for preferring the second method,
beyond the fact that the existence proof is established.

Resource Type 

Date Available 

Date Issued 

Degree Level 

Degree Name 

Degree Field 

Degree Grantor 

Commencement Year 

Advisor 

Academic Affiliation 

NonAcademic Affiliation 

Subject 

Rights Statement 

Language 

Digitization Specifications 
 File scanned at 300 ppi (Monochrome) using Capture Perfect 3.0.82 on a Canon DR9080C in PDF format. CVista PdfCompressor 4.0 was used for pdf compression and textual OCR.

Replaces 

Additional Information 
 description.provenance : Approved for entry into archive by Patricia Black(patricia.black@oregonstate.edu) on 20100716T19:40:24Z (GMT) No. of bitstreams: 1
HagelbergerCarlR1992.pdf: 512759 bytes, checksum: c82cd0146677904116fe78dfd8680a08 (MD5)
 description.provenance : Submitted by Nitin Mohan (mohanni@onid.orst.edu) on 20100715T23:17:57Z
No. of bitstreams: 1
HagelbergerCarlR1992.pdf: 512759 bytes, checksum: c82cd0146677904116fe78dfd8680a08 (MD5)
 description.provenance : Approved for entry into archive by Patricia Black(patricia.black@oregonstate.edu) on 20100716T19:38:27Z (GMT) No. of bitstreams: 1
HagelbergerCarlR1992.pdf: 512759 bytes, checksum: c82cd0146677904116fe78dfd8680a08 (MD5)
 description.provenance : Made available in DSpace on 20100716T19:40:24Z (GMT). No. of bitstreams: 1
HagelbergerCarlR1992.pdf: 512759 bytes, checksum: c82cd0146677904116fe78dfd8680a08 (MD5)
