### Abstract

The flow induced by an impermeable flat surface executing orthogonal stretching and orthogonal shearing in a rotating fluid system is investigated. Both the stretching and shearing are linear in the coordinates. An exact similarity reduction of the Navier–Stokes equations gives rise to a pair of nonlinearly-coupled ordinary differential equations governed by three parameters. In this study we set one parameter and analyze the problem which leads to flow for an impermeable surface with shearing and stretching due to velocity u along the x-axis of equal strength a while the shearing and stretching due to velocity v along the y-axis of equal strength b. These solutions depend on two parameters—a Coriolis (rotation) parameter (Formula presented.) and a stretching/shearing ratio (Formula presented.). A symmetry in solutions is found for (Formula presented.). The exact solution for (Formula presented.) and the asymptotic behavior of solutions for (Formula presented.) are determined and compared with numerical results. Oscillatory solutions are found whose strength increases with increasing values of (Formula presented.). It is shown that these solutions tend to the well-known Ekman solution as (Formula presented.).

Original language | English |
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Pages (from-to) | 1-11 |

Number of pages | 11 |

Journal | Meccanica |

DOIs | |

Publication status | Accepted/In press - 6 Aug 2016 |

### Fingerprint

### Keywords

- Exact solution of Navier–Stokes equations
- Rotating system
- Stretching and shearing membrane
- Three-parameter family of solutions

### ASJC Scopus subject areas

- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering

### Cite this

*Meccanica*, 1-11. https://doi.org/10.1007/s11012-016-0507-y

**Biorthogonal stretching and shearing of an impermeable surface in a uniformly rotating fluid system.** / Weidman, Patrick D.; Mansur, Syahira; Mohd Ishak, Anuar.

Research output: Contribution to journal › Article

*Meccanica*, pp. 1-11. https://doi.org/10.1007/s11012-016-0507-y

}

TY - JOUR

T1 - Biorthogonal stretching and shearing of an impermeable surface in a uniformly rotating fluid system

AU - Weidman, Patrick D.

AU - Mansur, Syahira

AU - Mohd Ishak, Anuar

PY - 2016/8/6

Y1 - 2016/8/6

N2 - The flow induced by an impermeable flat surface executing orthogonal stretching and orthogonal shearing in a rotating fluid system is investigated. Both the stretching and shearing are linear in the coordinates. An exact similarity reduction of the Navier–Stokes equations gives rise to a pair of nonlinearly-coupled ordinary differential equations governed by three parameters. In this study we set one parameter and analyze the problem which leads to flow for an impermeable surface with shearing and stretching due to velocity u along the x-axis of equal strength a while the shearing and stretching due to velocity v along the y-axis of equal strength b. These solutions depend on two parameters—a Coriolis (rotation) parameter (Formula presented.) and a stretching/shearing ratio (Formula presented.). A symmetry in solutions is found for (Formula presented.). The exact solution for (Formula presented.) and the asymptotic behavior of solutions for (Formula presented.) are determined and compared with numerical results. Oscillatory solutions are found whose strength increases with increasing values of (Formula presented.). It is shown that these solutions tend to the well-known Ekman solution as (Formula presented.).

AB - The flow induced by an impermeable flat surface executing orthogonal stretching and orthogonal shearing in a rotating fluid system is investigated. Both the stretching and shearing are linear in the coordinates. An exact similarity reduction of the Navier–Stokes equations gives rise to a pair of nonlinearly-coupled ordinary differential equations governed by three parameters. In this study we set one parameter and analyze the problem which leads to flow for an impermeable surface with shearing and stretching due to velocity u along the x-axis of equal strength a while the shearing and stretching due to velocity v along the y-axis of equal strength b. These solutions depend on two parameters—a Coriolis (rotation) parameter (Formula presented.) and a stretching/shearing ratio (Formula presented.). A symmetry in solutions is found for (Formula presented.). The exact solution for (Formula presented.) and the asymptotic behavior of solutions for (Formula presented.) are determined and compared with numerical results. Oscillatory solutions are found whose strength increases with increasing values of (Formula presented.). It is shown that these solutions tend to the well-known Ekman solution as (Formula presented.).

KW - Exact solution of Navier–Stokes equations

KW - Rotating system

KW - Stretching and shearing membrane

KW - Three-parameter family of solutions

UR - http://www.scopus.com/inward/record.url?scp=84982993796&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84982993796&partnerID=8YFLogxK

U2 - 10.1007/s11012-016-0507-y

DO - 10.1007/s11012-016-0507-y

M3 - Article

AN - SCOPUS:84982993796

SP - 1

EP - 11

JO - Meccanica

JF - Meccanica

SN - 0025-6455

ER -