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On hydraulic falls of single-layer flow

Acta Oceanologica Sinica 1996年第1期15卷 19-30页

作者： Xu Zhaoting Tian Jiwei lou shunli andsamuel shan pn shen Institute of Physical Oceanography Physical Oceanography Laboratory Ocean University of Qingdao Qingdao 266003 China Department of Mathematics Institute of Applied Mathematics University of Alberta Edmonton Alta. T6G 2G1 Canada

Hydraulic falls of single-layer now are determined theoretically in terms of a time-dependent averaged fKdV equation(AfKdV equation)in phase coordinate. From the theory of the present paper it was known that difference of the asymptotic mean levels upstream and downsream at the subcritical cutoff points is just equal to a subcritical value of the AfKdV equation An experiment is carried out to examine the theoretical results. From comparison between theoreticaland experimental results, it was shown that they are in good *** the same time, it should be pointed out that the theory of the present paper is agreement with the experimental and numerical results of Forbes and can be employed to find the generating properties of the precursor solitons at near-resonance.

关键词： Hydraulic fall fKdV equation subcritical cutoff point single-layer flow

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On hydraulic falls of two-layer flow

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Acta Oceanologica Sinica 1996年第2期15卷 179-191页

作者： Xu Zhaoting lou shunli Tian Jiwei and Samuel shan pn shen(Institute of Physical Deeanopaphy and Physical oceanography Laboratory, Ocean University Of Qngdao, Qngdao266003, China Department of Mathematics and Applied Mathematics institute, University of A Institute of Physical Oceanography Physical Oceanography Laboratory Ocean University of Qingdao Qingdao 266003 China Department of Mathematics Applied Mathematics Institute University of Alberta Edmonton Alta. T6G 2G1 Canada

Hydraulic falls and asymptotic mean levels of two-layer flow are determined by means of AfKdV equation in phase coordinate theoretically. By present theory, the hydraulic falls Hf depend on a characteristic value of the MfKdV equation at the subcritical cutoff points It is proved that the differences of the asymptotic mean levels upstream and downstream at the subcritical cutoff points are equal to 2 A relation between and the asymptotic mean levels at the subcritical cutoff points is also found in terms of the solution of the hydraulic falls. Because the AfKdV equation is derived based on the small topography assumption, for semicircular topography the valid region of this theory is α< 0. 35, in which α is radius of the semicircular topography. An experiment is carried out to examine the theory of the present paper. From comparisons between the theoretical and experimental results. it is shown that they are in better agreement. Under conditions of different stratified parameters, the hydraulic falls of two-layer flow are predicted theoretically. This work was supered by the Foundation of the State Education COmmission 'The dynamics of upper ocean'.

关键词： fKdV equation hydraulic fall two-layer flow subcritical cutoff point

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