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Non-Stationary Helical Flows for Incompressible Couple Stress Fluid

Author

Listed:
  • Sergey V. Ershkov

    (Department of Scientific Researches, Plekhanov Russian University of Economics, Scopus Number 60030998, 36 Stremyanny Lane, 117997 Moscow, Russia)

  • Evgeniy Yu. Prosviryakov

    (Institute of Engineering Science UB RAS, 620049 Ekaterinburg, Russia
    Academic Department of Information Technologies and Control Systems, Ural Federal University, 620075 Ekaterinburg, Russia)

  • Mikhail A. Artemov

    (Department of Applied Mathematics, Informatics and Mechanics, Voronezh State University, 394018 Voronezh, Russia)

  • Dmytro D. Leshchenko

    (Odessa State Academy of Civil Engineering and Architecture, 65029 Odessa, Ukraine)

Abstract

We explored here the case of three-dimensional non-stationary flows of helical type for the incompressible couple stress fluid with given Bernoulli -function in the whole space (the Cauchy problem). In our presentation, the case of non-stationary helical flows with constant coefficient of proportionality α between velocity and the curl field of flow is investigated. In the given analysis for this given type of couple stress fluid flows, an absolutely novel class of exact solutions in theoretical hydrodynamics is illuminated. Conditions for the existence of the exact solution for the aforementioned type of flows were obtained, for which non-stationary helical flow with invariant Bernoulli -function satisfying to the Laplace equation was considered. The spatial and time-dependent parts of the pressure field of the fluid flow should be determined via Bernoulli -function if components of the velocity of the flow are already obtained. Analytical and numerical findings are outlined, including outstanding graphical presentations of various types of constructed solutions, in order to elucidate dynamic snapshots that show the timely development of the topological behavior of said solutions.

Suggested Citation

  • Sergey V. Ershkov & Evgeniy Yu. Prosviryakov & Mikhail A. Artemov & Dmytro D. Leshchenko, 2023. "Non-Stationary Helical Flows for Incompressible Couple Stress Fluid," Mathematics, MDPI, vol. 11(24), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:24:p:4999-:d:1302410
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    References listed on IDEAS

    as
    1. Ershkov, Sergey V., 2016. "About existence of stationary points for the Arnold–Beltrami–Childress (ABC) flow," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 379-383.
    2. Qammar Rubbab & Itrat Abbas Mirza & Imran Siddique & Saadia Irshad, 2017. "Unsteady Helical Flows of a Size-Dependent Couple-Stress Fluid," Advances in Mathematical Physics, Hindawi, vol. 2017, pages 1-10, February.
    3. Ershkov, Sergey V., 2016. "Non-stationary helical flows for incompressible 3D Navier–Stokes equations," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 611-614.
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