کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4642750 1632056 2007 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On frequency–amplitude dependences for surface and internal standing waves
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
On frequency–amplitude dependences for surface and internal standing waves
چکیده انگلیسی

The analytic approach proposed by Sekerzh-Zenkovich [On the theory of standing waves of finite amplitude, Dokl. Akad. Nauk USSR 58 (1947) 551–554] is developed in the present study of standing waves. Generalizing the solution method, a set of standing wave problems are solved, namely, the infinite- and finite-depth surface standing waves and the infinite- and finite-depth internal standing waves. Two-dimensional wave motion of an irrotational incompressible fluid in a rectangular domain is considered to study weakly nonlinear surface and internal standing waves. The Lagrangian formulation of the problems is used and the fifth-order perturbation solutions are determined. Since most of the approximate analytic solutions to these problems were obtained using the Eulerian formulation, the comparison of the results, as an example the analytic frequency–amplitude dependences, obtained in Lagrangian variables with the corresponding ones known in Eulerian variables has been carried out in the paper. The analytic frequency–amplitude dependences are in complete agreement with previous results known in the literature. Computer algebra procedures were written for the construction of asymptotic solutions. The application of the model constructed in Lagrangian formulation to a set of different problems shows the ability to correctly reproduce and predict a wide range of situations with different characteristics and some advantages of Lagrangian particle models (for example, the bigger radius of convergence of an expansion parameter than in Eulerian variables, simplification of the boundary conditions, parametrization of a free boundary).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 200, Issue 2, 15 March 2007, Pages 459–470
نویسندگان
, ,