Stability of Shallow Flows: a Weakly Nonlinear Approach

AIP Conference Proceedings: ICNPAA 2016 World Congress: 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences 2017
Andrejs Koliškins, Vladislavs Kremeņeckis

Linear and weakly nonlinear analysis of shallow mixing layers with free surface is performed in the present paper. It is assumed that the resistance force is not constant in the transverse direction of the flow. Linear stability problem is solved numerically for different values of the parameters of the problem. Assuming that the bed friction number is slightly smaller than the critical value we derive an amplitude evolution equation for the most unstable mode. It is shown that the amplitude equation is the complex Schrödinger equation.

Keywords
weakly nonlinear models, amplitude evolution equation, linear stability
DOI
10.1063/1.4972673
Hyperlink
http://aip.scitation.org/doi/abs/10.1063/1.4972673

Koliškins, A., Kremeņeckis, V. Stability of Shallow Flows: a Weakly Nonlinear Approach. In: AIP Conference Proceedings: ICNPAA 2016 World Congress: 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, France, La Rochelle, 4-8 July, 2016. Melville: American Institute of Physics, 2017, pp.020081-020085. ISBN 978-073541464-8. ISSN 0094-243X. Available from: doi:10.1063/1.4972673

Publication language
English (en)