Theoretical mean wave resistance of precursor solition generation in two-layer flow |
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Authors: | Xu Zhaoting Wu Kejian Samuel Shan-pu Shen |
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Institution: | (1) Institute of Physical Oceanography and Physical Oceanography Laboratary, Ocean University of Qingdao, 266003 Qingdao, China;(2) Department of Mathematics and Applied Mathematics Institute, University of Alberta, T6G 2G1 Edmonton, Alberta, Canada |
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Abstract: | A new concept of pseudo mean wave resistance is introduced to find theoretical mean wave resistances of the precursor soliton
generation in two-layer flow over a localized topography at near-resonance in this paper. The pseudo mean wave resistance
of the precursor soliton generation of two-layer flow is determined in terms of the AfKdV equation. From the theoretical results
it is shown that the theoretical mean wave resistance is equal to the pseudo mean wave resistance times 1/m
1, wherem
1 is the coefficient of the fKdV equation. From the regional distribution of the energy of the precursor soliton generation
at the resonant points, it is shown that ratios of the theoretical mean wave resistance and regional mean energy to the total
mean energy are invariant constants, i.e.
: (−1/2):1:1, in which
and
are the mean energy of the generating regions of the precursor solitons, of the depression and of the trailing, wavetrain
at the resonant points respectively,
and <D> are the total energy of the system and the theoretical mean wave resistance at the resonant points. A prediction of the
theoretical mean wave resistance flow over the semicircular topography is carried out in terms of the theoretical results
of the present paper. The comparison shows that the theoretical mean wave resistance is in good agreement with the numerical
calculation.
The project supported by the Foundation of The State Education Commission “The Dynamics of Upper Ocean” and the Grants of
The Physical Oceanography Laboratory of Ocean University of Qingdao |
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Keywords: | Precursor soliton Pseudo mean wave resistance Theoretical mean wave resistance Generating energy |
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