Marner, F. and Gaskell, P. H. and Scholle, M. (2017) 'A complex-valued first integral of Navier-Stokes equations : unsteady Couette flow in a corrugated channel system.', Journal of mathematical physics., 58 (4). 043102.
For a two-dimensional incompressible viscous flow, a first integral of the governing equations of motion is constructed based on a reformulation of the unsteady Navier-Stokes equations in terms of complex variables and the subsequent introduction of a complex potential field; complementary solid and free surface boundary conditions are formulated. The methodology is used to solve the challenging problem of unsteady Couette flow between two sinusoidally varying corrugated rigid surfaces utilising two modelling approaches to highlight the versatility of the first integral. In the Stokes flow limit, the results obtained in the case of steady flow are found to be in excellent agreement with corresponding investigations in the open literature. Similarly, for unsteady flow, the results are in accord with related investigations, exploring material transfer between trapped eddies and the associated bulk flow, and vice versa. It is shown how the work relates to the classical complex variable method for solving the biharmonic problem and perspectives are provided as to how the first integral may be further utilised to investigate other fluid flow features.
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|Publisher Web site:||https://doi.org/10.1063/1.4980086|
|Publisher statement:||© 2017 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Marner, F., Gaskell, P. H. and Scholle, M. (2017) 'A complex-valued first integral of Navier-Stokes equations: unsteady Couette flow in a corrugated channel system.', Journal of mathematical physics., 58 (4): 043102 and may be found at https://doi.org/10.1063/1.4980086|
|Date accepted:||30 March 2017|
|Date deposited:||30 June 2017|
|Date of first online publication:||19 April 2017|
|Date first made open access:||30 June 2017|
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