Rotational Steady Waves in a Low-pressure Region

M. V. Flamarion

Abstract


Nonlinear steady rotational waves in a low-pressure region are investigated. The problem is formulated in a simplified canonical domain through the use of a conformal mapping, which flattens the free surface. Steady waves are computed numerically using a Newton’s method and classified into three types. Besides, our results indicate that there is a region in which steady waves do not exist. The thickness of this region is compared with the one predicted by the weakly nonlinear, weakly dispersive regime.


Keywords


Steady waves; rotational waves; shear flow; Euler equations.

Full Text:

PDF

References


Akylas, TR. 1984 On the excitation of long nonlinear water waves by a moving pressure distributions. J Fluid Mech. 141, 455-466

Baines, P. 1995 Topographic effects in stratified flows. Cambridge University

Press.

Binder, BJ., Blyth. M., Balasuriya, S. 2014 Non-uniqueness of steady

free-surface flow at critical Froude number, EPL. 105 44003-1-44003-6

Boyd, J. 1991 Weakly non-local solitons for capillary-gravity waves: Fifth- degree Korteweg-de Vries equation. Physica D: Nonlinear Phenomena 48 (1), 12–146

Choi, W. 2009 Nonlinear surface waves interacting with a linear shear current. Math Comput Simul., 80, 29-36.

Dyachenko. AL., Zakharov. VE., Kuznetsov. EA. 1996 Nonlinear dy- namics of the free surface of an ideal fluid, Plasma Phys. 22, 916-928.

Flamarion, M. V. & Milewski, P. A. & Nachbin A. 2019 Rotational waves generated by current-topography interaction. Stud Appl Math, 142, 433- 464.

Fracius, M., Hsu, H-C., Kharif, C. & Montalvo, P. 2016 Gravity- capillary waves in finite depth on flows of constant vorticity. Proc. R. Soc. Lond. A, 472, 20160363.

Grimshaw, R. & Smyth, N. 1986 Resonant flow of a stratified fluid over topography in water of finite depth. J. Fluid Mech., 169, 429-464.

Grimshaw, R. & Maleewong, M. 2013 Stability of steady gravity waves generated by a moving localized pressure disturbance in water of finite depth. Phys Fluids, 25.

Grimshaw, R. & Malewoong, M. 2016 Transcritical flow over two obstacles: forced Korteweg-de Vries framework J. Fluid Mech., 809, 918-940.

Grimshaw, R. & Malewoong, M. 2019 Transcritical flow over obstacles and holes: forced Korteweg-de Vries framework J. Fluid Mech., 881, 660-678.

Johnson, R. S. 2012 Models for the formation of a critical layer in water wave propagation. Phil. Trans. R. Soc. A 370, 1638-1660.

Joseph. A. 2016 Investigating Seaflaws in the Oceans New York: Elsevier.

Milewski, P. A. 2004 The Forced Korteweg-de Vries Equation as a Model for Waves Generated by Topography. CUBO A mathematical Journal 6 (4), 33-51.

Gao, T., Wang, Z. & Milewski, P. A. 2019 Nonlinear hydroelastic waves on a linear shear current at finite depth. J. Fluid Mech., 876, 55-86.

Pratt, LJ. 1984 On nonlinear flow with multiple obstructions. J. Atmos. Sci. 41 , 1214-1225.

Peyrard, M. 1994 Nonlinear excitations in biomolecules Berlim: Springer.

Trefethen, L. N. 2001 Spectral Methods in MATLAB. Philadelphia: SIAM..

Wu, T. Y. 1987 Generation of upstream advancing solitons by moving distur- banks J Fluid Mech 184 , 75-99.

Wu. DM & Wu. T. Y. 1982 Three-dimensional nonlinear long waves due to moving surface pressure. In: Proc. 14th. Symp. on Naval Hydrodynamics Nat. Acad. Sci., Washington, DC, 103-25.




DOI: https://doi.org/10.5540/tcam.2022.023.02.00273

Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM

Refbacks

  • There are currently no refbacks.


Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)

 

Indexed in:

                       

         

 

Desenvolvido por:

Logomarca da Lepidus Tecnologia