PSI - Issue 40

ScienceDirect Structural Integrity Procedia 00 (2022) 000 – 000 Structural Integrity Procedia 00 (2022) 000 – 000 Available online at www.sciencedirect.com Available online at www.sciencedirect.com Sci nceDirect Available online at www.sciencedirect.com ScienceDirect

www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia

Procedia Structural Integrity 40 (2022) 171–179

© 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the15th International Conference on Mechanics, Resources and Diagnostics of Materials and Structures. Abstract The paper studies a Couette – Poiseuille exact solution for describing inhomogeneous steady-state flows of a viscous incompressible vertical vortex fluid. The fluid moves in an infinite horizontal layer, this motion being conditioned by the displacement of the lower boundary and the specification of the pressure gradient. An exact solution to the hydrodynamics equations describing the three-dimensional inhomogeneous Couette – Poiseuille shear flow is obtained. It is polynomial in all the coordinates, and it belongs to the Lin – Sidorov – Aristov family. Consideration of the inhomogeneity of the velocity field leads to the recording of counterflows. Pressure variation along the horizontal coordinates results in an additional stationary stagnation point as compared to the isobaric flow of a viscous incompressible fluid. © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the15th International Conference on Mechanics, Resource and Diagnostics of Materials and Structures. Keywords: exact solution, Navier-Stokes equation, incompressibility equation, overdetermined system, isobaric flow, gradient flow, vertical vortex 1. Introduction Searching for exact solutions to the Navier – Stokes equations complemented by the incompressibility equation is an important task for today’s hydrodynamics of isothermal fluids (Ershkov et al., 2021; Aristov et al., 2009; Drazin e al., 2006; Pukhnachev et al., 2006). The quadratic nonlinearity of fluid motion equations makes their qualitative and quantitative analysis extremely difficult; therefore, to understand the features of the Navier – Stokes equations, it is 15th International Conference on Mechanics, Resource and Diagnostics of Materials and Stru tures Inhomogeneous Couette – Poiseuille shear flow Larisa S. Goruleva, Evgeniy Yu. Prosviryakov * Institute of Engineering Science UB RAS, 34, Komsomolskaya St., Ekaterinburg, 620049, Russia Abstract The paper studies a Couette – Poiseuille exact solution for describing inhomogeneous steady-state flows of a viscous incompressible v rtical v rtex fluid. Th fluid moves i an infinite horizo tal lay r, this motion being conditioned by the displacement of the lower boundary and the specification of the pr ssu e gradient. An exact solution to the hydro ynamics equations describing the three-dimensio al inhomogeneous Couette – Poi euille sh ar flow is ob ained. It is polynomial in ll the coord nates, and t belongs to the Li – Sidorov – Aristov family. Consideration of the inhomogeneity of the velocity f e d le ds to the ecording of counterflows. Pressure va iation al ng the horiz tal coordinates results in a additional stationary stagnation point as compared to the is baric flow of a v sc us incompr ssible fluid. © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review u der re ponsibility of scientific committe of the15th Int rnational C nference on Mechanics, Resource and Diagnostics of Materials and S ructur s. Keywords: exact solution, N vier-Stokes equation, incompressibility equation, overdetermined system, isobaric flow, gradient flow, vertical vortex 1. Introduction Searching for exact solutions to the Navier – Stokes equations complemented by the incompressibility equation is an importa t task for today’s hydr dynamics of is thermal fluid (Ershkov et al., 2021; Aristov t al., 2009; Drazin e l., 2006; Pukhnachev et al., 2006). The quadrat c nonlinearity of fluid motion equations makes heir qualitative a d quantitative analysis ex remely difficult; therefore, to u derstand the features of the Navier – Stok s equa ions, it is 15th International Conference on Mechanics, Resource and Diagnostics of Materials and Structures Inhomogeneous Couette – Poiseuille shear flow Larisa S. Goruleva, Evgeniy Yu. Prosviryakov * Institute of Engineering Science UB RAS, 34, Komsomolskaya St., Ekaterinburg, 620049, Russia

* Corresponding author. Tel.: +7-982-654-5223; E-mail address: evgen_pros@mail.ru * Corresponding author. Tel.: +7-982-654-5223; E-mail address: evgen_pros@mail.ru

2452-3216 © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the15th International Conference on Mechanics, Resource and Diagnostics of Materials and Structures. 2452-3216 © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review u der responsibility of t scientific committe of the15th Int rnational Conference on Mechanics, Resource and Diagnostics of Materials and Structures.

2452-3216 © 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the15th International Conference on Mechanics, Resources and Diagnostics

of Materials and Structures. 10.1016/j.prostr.2022.04.023