The interaction of von Kármán vortices with the solitons of the complex Ginzburg-Landau equation


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Farazande S., Bayındır C.

ICAME 2021, Balıkesir, Turkey, 1 - 03 September 2021, no.33, pp.1-6

  • Publication Type: Conference Paper / Full Text
  • City: Balıkesir
  • Country: Turkey
  • Page Numbers: pp.1-6

Abstract

The complex Ginzburg-Landau (GL) equation is a well-known equation in various areas of physics that is also widely used to model vortex shedding phenomena occurring around a bluff body in a flow field, which is named as von Kármán vortex street [1-2]. In addition, it describes nonlinear waves, second-order phase transitions, superconductivity, superfluidity, Bose-Einstein condensation, liquid crystals, and strings in field theory, etc. [3]. Moreover, the GL equation can be utilized to find soliton solutions of many nonlinear systems [4]. Solitons are self-localized, solitary, nonlinear waves that emerge from a collision with a similar pulse having an unchanged shape and speed [5]. Most of its applications lie in the domains of optics and fluid mechanics, which are attained by solutions of some familiar partial differential equations as Korteweg-de-Vries, modified Korteweg-de-Vries, Sine-Gordon, and nonlinear Schrödinger equations [6], apart from GL equation. In the present study, we aim to analyze the interaction of the soliton solutions of the GL equation with the von Kármán vortex street. For this purpose, we solve the GL equation via a spectral scheme that uses FFT routines for the space derivative and a 4th order Runge-Kutta time-stepping method to simulate vortices. Subsequently, we use the soliton solutions of GL constructed using analytical techniques and investigate their effects on Von Kármán vortices. We investigate how the vortex structure and stability are affected and whether the vortex fluctuations are reduced by the solitons. We discuss our findings and their possible usage in controlling the vortices by solitons for structural damage prevention and resonating for energy harvesting.