Rotational gravity-capillary waves generated by a moving disturbance

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

     Universidade Federal Rural de Pernambuco

     Brasil

     
• Localización: Selecciones Matemáticas, ISSN-e 2411-1783, Vol. 8, Nº. 2, 2021 (Ejemplar dedicado a: August - December), págs. 228-234
• Idioma: inglés
• DOI: 10.17268/sel.mat.2021.02.02
• Títulos paralelos:
  • Ondas rotacionales de gravedad-capilaridad generadas por el paso de una perturbación
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    Se estudian ondas no lineales de gravedad-capilaridad generadas por el paso de una distribución de presión sobre un canal cizallado con vorticidad constante. El problema es modelado usando las ecuaciones de Euler. La parte harmónica del campo de velocidades es formulada en un dominio canónico a través de la representación conforme, que aplana el dominio del fluido en una franja. El número de Froude es considerado casi crítico y el número de Bond crítico. El efecto de la vorticidad cambia radicalmente el patrón de las ondas generadas para tiempos largos. Adicionalmente, dependiendo da la intensidad de la vorticidad, las soluciones pueden tornarse más suaves y con pequeñas amplitudes.

  • English

    Nonlinear gravity-capillary waves generated by the passage of a pressure distribution over a sheared channel with constant vorticity are investigated. The problem is modeled using the full Euler equations. The harmonic part of the velocity field is formulated in a canonical domain through the use of the conformal mapping, which flattens the fluid domain onto a strip. The Froude number is considered to be nearly-critical and the Bond number critical. The shear effect changes drastically the pattern of the generated waves for large times. Moreover, depending on the intensity of the vorticity, the wave solutions can become smoother with small amplitudes.

• Referencias bibliográficas
  • Akylas TR. On the excitation of long nonlinear water waves by a moving pressure distributions. J Fluid Mech. 1984; 141:455-466. DOI: 10.1017/S0022112084000926.
  • Baines P. Topographic effects in stratified flows. Cambridge: Cambridge University Press; 1995.
  • Johnson RS. Models for the formation of a critical layer in water wave propagation. Phil Trans R Soc A. 2012; 370:1638-1660. DOI: 10.1098/rsta.2011.0456.
  • Dyachenko AL, Zakharov VE, Kuznetsov EA. Nonlinear dynamics of the free surface of an ideal fluid. Plasma Phys. 1996; 22:916-928.
  • Falcon E, Laroche C, Fauve S. Observation of depression solitary surface waves on a thin fluid layer Phys Rev Lett. 2002;89:204501-1-204501-4.
  • Flamarion MV, Ribeiro-Jr R. An iterative method to compute conformal mappings and their inverses in the context of water waves over topographies...
  • Flamarion MV, Milewski PA, Nachbin A. Rotational waves generated by current-topography interaction. Stud Appl Math. 2019; 142: 433-464. DOI:...
  • Flamarion MV. Rotational flows over obstacles in the forced Korteweg-de Vries framework. Selecciones Matematicas. 2021; 8(1):125-130. DOI:...
  • Flamarion MV, Ribeiro-Jr R. Gravity-capillary flows over obstacles for the fifth-order forced Korteweg-de Vries equation. J. Eng Math. 2021;...
  • Fracius M, Hsu HC. Kharif C, Montalvo P. Gravity-capillary waves in finite depth on flows of constant vorticity. Proc R Soc Lond A. 2016;...
  • Grimshaw R, Maleewong M. Stability of steady gravity waves generated by a moving localized pressure disturbance in water of finite depth....
  • Hanazaki H, Hirata M, Okino S. Radiation of short waves from the resonantly excited capillary-gravity waves. J. Fluid Mech. 2010;810: 5-24....
  • Milewski, PA, Vanden-Broeck JM. Time dependent gravity-capillary flows past an obstacle Wave Motion. 1999; 29:63-79.
  • Milewski PA. The Forced Korteweg-de Vries equation as a model for waves generated by topography. CUBO A mathematical Journal. 2004; 6:33-51.
  • Pratt LJ. On nonlinear flow with multiple obstructions. J Atmos Sci. 1984; 41:1214-1225. DOI: 10.1175/1520-0469.
  • Trefethen LN. Spectral Methods in MATLAB. Philadelphia: SIAM; 2001.
  • Wu TY. Generation of upstream advancing solitons by moving disturbances. J. Fluid Mech. 1987; 184: 75-99. DOI:10.1017/S0022112087002817.