Rotational flows over obstacles in the forced Korteweg-de Vries framework

• V. Flamarion, Marcelo ^[1]
  1. [1] Universidade Federal de Pernambuco

     Universidade Federal de Pernambuco

     Brasil

     
• Localización: Selecciones Matemáticas, ISSN-e 2411-1783, Vol. 8, Nº. 1, 2021 (Ejemplar dedicado a: Enero-Julio), págs. 125-130
• Idioma: inglés
• DOI: 10.17268/sel.mat.2021.01.12
• Títulos paralelos:
  • Flujo rotacional sobre obstáculos para la ecuación forzada de Korteweg-de Vries
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• Resumen
  • español

    En este trabajo investigamos ondas rotacionales provocadas resonantemente por un obstáculo sumergido en un canal cizallado de aguas poco profundas con vorticidad constante. En el régimen débilmente no lineal y el débilmente dispersivo, el problema se formula desde la ecuación forzada de Korteweg-de Vries. Calculamos numéricamente la solución del problema de valor inicial para esta ecuación usando un método pseudoespectral de Fourier con factor de integración. La superficie del agua se toma inicialmente en reposo, y una vez que la corriente es liberada, ondas se generan inmediatamente en la superficie libre. Identificamos los principales efectos de la corriente variable en las ondas generadas como, por ejemplo, ondas solitarias rotacionales que se propagan río arriba y ondas con crestas agudas.

  • English

    In this work we investigate rotational waves resonantly excited by a submerged obstacle in a sheared shallow water channel with constant vorticity. In the weakly nonlinear, weakly dispersive regime, the problem is formulated in the forced Korteweg-de Vries framework. We compute the solution of the initial value problem for this equation numerically using a Fourier pseudospectral method with integrating factor. The water surface is initially taken at rest, and once the current is turned on, waves are immediately generated in the free surface. We identify the main effects of sheared current in the generated waves such as rotational solitary waves propagating upstream and sharp crested waves being generated.

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