|
Authors: |
Hendrik L Tolman
MMAB
Hendrik.Tolman@NOAA.gov
|
Title: | Optimum Discrete Interaction Approximations for wind waves Part 3: Generalized multiple DIAs |
Additional Bibliographic Information: | |
Year: | 2008 |
MMAB Contribution Number: | 269 |
Keywords: | Wind waves, DIA |
Status: | Published |
Abstract: | The present report is the third in a series assessing the potential of the
Discrete Interaction Approximation for representing nonlinear interactions in
wind wave models. This study addresses generalization of the DIA with multiple
representative quadruplets to arbitrary depth, and particularly focuses on
scaling behavior of this DIA with respect to depth. Major findings are that
(i) shallow water quadruplet layouts need to be considered explicitly to
assure proper conservation characteristics of a DIA, (ii) full shallow water
expressions are needed to retain realistic shallow water interaction shapes,
(iii) separate scaling functions with appropriate shallow and deep asymptotic
behavior are needed to obtain proper scaling behavior for arbitrary depth,
(iv) the choice of the underlying definition of spectral space has a notable
(numerical) impact on the resulting interactions. Experiments with numerical
optimization show that (a) an optimized generalized DIA configured like the
traditional DIA requires approximately twice the computing time of the latter,
(b) generalizing the quadruplet layout increases the costs by an additional
factor of just below two, and (c) that the costs of the optimized MDIA scales
linearly with the number of representative quadruplet realizations.
As a side note that the assessment of the generalized multiple DIA, diffusion
approaches to nonlinear interactions are addressed. It is shown that the
traditional DIA with a quadruplet layout that is not resolved by the discrete
spectral grid reduces to a simple diffusion operator that satisfies all
conservation properties of the nonlinear interactions. A high-frequency filter
based on such an approach is designed and optimized to be used in conjunction
with the generalized multiple DIA, or with Neural Network Interaction
Approximations. |
Link: | /mmab/papers/tn269/MMAB_269.pdf |
Return to index listing
Return to branch main page
|