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 ScienceDirect Available online at www.sciencedirect.com ScienceDirect

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

Procedia Structural Integrity 40 (2022) 75–81

© 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 article discusses the selection of boundary conditions at the boundary between adjacent layers in a stratified viscous incompressible fluid. It is shown that the "continuity condition + differentiability condition" pair traditionally used in many disciplines gives physically unjustified properties of the resulting exact solution for the velocity field. Although the condition for the differentiability of velocities is close in mathematical form to the stress continuity condition (by virtue of Newton's law), in terms of physics, taking these conditions into account gives fundamentally different properties of the exact solution of the Navier-Stokes system of equations. It is shown that the consideration of the "the velocity field continuity condition + the stress field continuity condition" pair is more adequate to the physics of the process, which is consistent with the hypothesis of continuity. © 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: viscous incompressible two-layer fluid; stratified fluid; isobaric isothermal flow; shear flow; Navier-Stokes equations; exact solution; boundary conditions 15th International Conference on Mechanics, Resource and Diagnostics of Materials and Stru tures Features of selecting boundary conditions when describing flows of stratified fluids Natalya V. Burmasheva a,b *, Ekaterina A. Larina a,b , Evgeniy Yu. Prosviryakov a,b a Institute of Engineering Science UB RAS, 34 Komsomolskaya St., Ekaterinburg, 620049, Russia b B.N. Yeltsin Ural F deral University, 19 Mira St., Ekaterinburg, 620002, Russia Abstract The article discusses the selection of boundary conditions at the boundary between adjacent layers in a stratified viscous incompre sible fluid. It is shown that the "con inuity condition + differentiabi it co dition" pair traditionally used in many disciplines gives physically unjus fied properties of the resulting exact s lut on for the veloc ty field. Although the condit on for the differentiability o velociti s is cl se in mathematic l form o the stress continuity condition (by virtue of Newton's law), i terms f physics, taking these conditions int acc unt give fu damentally ifferent properties of the exact solution of the Navier-Sto es system of equations. It is shown that the consideration of the "the velocity fi ld continuity condi ion + th stress field continuity condition" pair is more ad quate to the physics of the pr ess, which is consistent with the ypothe is of continuity. © 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 scientific committe of the15th International C ference on Mechanics, Resource and Diagnostics of Materials and S ructur s. Keywords: viscous incompressible two-layer fluid; stratified fluid; isobaric isothermal flow; shear flow; Navier-Stokes equations; exact solution; boundary conditions 15th International Conference on Mechanics, Resource and Diagnostics of Materials and Structures Features of selecting boundary conditions when describing flows of stratified fluids Natalya V. Burmasheva a,b *, Ekaterina A. Larina a,b , Evgeniy Yu. Prosviryakov a,b a Institute of Engineering Science UB RAS, 34 Komsomolskaya St., Ekaterinburg, 620049, Russia b B.N. Yeltsin Ural Federal University, 19 Mira St., Ekaterinburg, 620002, Russia

* Corresponding author. Tel.: +7-343-375-3576. E-mail address: nat_burm@mail.ru * Corresponding author. Tel.: +7-343-375-3576. E-mail ad ress: nat_burm@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 re ponsibility of scientific committe of the15th Int rnational C ference o Mechanics, Resource and Diagnostics of Mate ials 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.2022.04.009