Flow pattern analysis of linear gradient flow distribution

doi:10.1007/s10483-015-1920-9

Applied Mathematics and Mechanics (English Edition) ›› 2015, Vol. 36 ›› Issue (1): 81-106.doi: https://doi.org/10.1007/s10483-015-1920-9

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Flow pattern analysis of linear gradient flow distribution

Da-ming LI¹, Xiao-yu LI^1,2, Yan-qing LI³, R. J. FARAHANI²

1. School of Civil Engineering & Key Laboratory of Harbor & Ocean Engineering Ministry of Education, Tianjin University, Tianjin 300072, P. R. China;
2. Civil and Environmental Engineering, Johns Hopkins University, Baltimore 21218, U. S. A.;
3. Civil Engineering, The University of Adelaide, Adelaide 5005, Australia

Received:2014-04-02 Revised:2014-09-19 Online:2015-01-01 Published:2015-01-01
Supported by:
Project supported by the National Natural Science foundation of China (No. 51079095) and the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (No. 51021004)

Abstract

Abstract: This paper uses the Oseen transformation to solve the differential equations governing motion of the vertical linear gradient flow distribution close to a wall surface. The Navier-Stokes equations are used to consider the inertia term along the flow direction. A novel contour integral method is used to solve the complex Airy function. The boundary conditions of linear gradient flow distribution for finite problems are determined. The vorticity function, the pressure function, and the turbulent velocity profiles are provided, and the stability of particle trajectories is studied. An L_x-function form of the third derivative circulation is used to to simplify the solution. Theoretical results are compared with the experimental measurements with satisfactory agreement.

Key words: contour integral, linear gradient distribution flow, stability analysis, Oseen transformation, Airy function

2010 MSC Number:

Da-ming LI;Xiao-yu LI;Yan-qing LI;R. J. FARAHANI. Flow pattern analysis of linear gradient flow distribution. Applied Mathematics and Mechanics (English Edition), 2015, 36(1): 81-106.

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Flow pattern analysis of linear gradient flow distribution

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