Self-similarity in incompressible Navier-Stokes equations

Date

2015-12-01

Author

Ercan, Ali
Kavvas, M. Levent

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The self-similarity conditions of the 3-dimensional (3D) incompressible Navier-Stokes equations are obtained by utilizing one-parameter Lie group of point scaling transformations. It is found that the scaling exponents of length dimensions in i = 1, 2, 3 coordinates in 3-dimensions are not arbitrary but equal for the self-similarity of 3D incompressible Navier-Stokes equations. It is also shown that the self-similarity in this particular flow process can be achieved in different time and space scales when the viscosity of the fluid is also scaled in addition to other flow variables. In other words, the self-similarity of Navier-Stokes equations is achievable under different fluid environments in the same or different gravity conditions. Self-similarity criteria due to initial and boundary conditions are also presented. Utilizing the proposed self-similarity conditions of the 3D hydrodynamic flow process, the value of a flow variable at a specified time and space can be scaled to a corresponding value in a self-similar domain at the corresponding time and space. (C) 2015 AIP Publishing LLC.

URI

https://hdl.handle.net/11511/100965

Journal

CHAOS

DOI

https://doi.org/10.1063/1.4938762

Collections

Department of Civil Engineering, Article

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Citation Formats

A. Ercan and M. L. Kavvas, “Self-similarity in incompressible Navier-Stokes equations,” CHAOS, vol. 25, no. 12, pp. 0–0, 2015, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/100965.