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Waves over Curved Bottom: The Method of Composite Conformal Mapping
Journal of Experimental and Theoretical Physics ( IF 1.0 ) Pub Date : 2020-07-03 , DOI: 10.1134/s1063776120040081 V. P. Ruban
中文翻译:
波浪在弯曲的底部上方:复合共形映射的方法
更新日期:2020-07-03
Journal of Experimental and Theoretical Physics ( IF 1.0 ) Pub Date : 2020-07-03 , DOI: 10.1134/s1063776120040081 V. P. Ruban
Abstract
A compact and efficient numerical method is described for studying plane flows of an ideal fluid with a smooth free boundary over a curved and nonuniformly moving bottom. Exact equations of motion in terms of the so-called conformal variables are used. In addition to the previously known applications for shear flows with constant (including zero) vorticity, here a generalization is made to the case of potential flows in uniformly rotating coordinate systems, where centrifugal and Coriolis forces are added to the gravity force. A brief review is given of previous results obtained by this method in a number of physically interesting problems such as modeling of tsunami waves caused by the movement of nonuniform bottom, the dynamics of Bragg (gap) solitons over a spatially periodic bottom profile, the Fermi–Pasta–Ulam (FPU) recurrence phenomenon for waves in a finite pool, the formation of anomalous waves in an opposing nonuniform curent, and the propagation of a solitary wave in a shear current and its runup on a depth difference. In addition, a number of new numerical results are presented concerning the nonlinear dynamics of a free boundary in closed rotating containers partially filled with a fluid—centrifuges of complex shape. In this case, the equations of motion differ in some essential details from those of x-periodic systems.中文翻译:
波浪在弯曲的底部上方:复合共形映射的方法