Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-17T20:54:45.705Z Has data issue: false hasContentIssue false
  • English
  • Français

Rotating flow over shallow topographies

Published online by Cambridge University Press:  29 March 2006

Arsalan Vaziri  and
Don L. Boyer
Arsalan Vaziri
Affiliation:
Department of Civil Engineering, University of Delaware, Newark, Delaware
Don L. Boyer
Affiliation:
Department of Civil Engineering, University of Delaware, Newark, Delaware Present address: National Science Foundation, Washington, D.C.
Get access Rights & Permissions [Opens in a new window]

Abstract

The flow of a rotating homogeneous incompressible fluid over various shallow topographies is investigated. In the physical system considered, the rotation axis is vertical while the topography and its mirror image are located on the lower and upper of two horizontal plane surfaces. Upstream of the topographies and outside the Ekman layers on the bounding planes the fluid is in a uniform free-stream motion. An analysis is considered in which E [Lt ] 1, Ro ∼ E½, H/D ∼ E0, and h/D ∼ E½, where E is the Ekman number, Ro the Rossby number, H/D the fluid depth to topography width ratio and h/D the topography height-to-width ratio. The governing equation for the lowest-order interior motion is obtained by matching an interior geostrophic region with Ekman boundary layers along the confining surfaces. The equation includes contributions from the non-linear inertial, Ekman suction, and topographic effects. An analytical solution for a cosine-squared topography is given for the case in which the inertial terms are negligible; i.e. Ro [Lt ] E½. Numerical solutions for the non-linear equations are generated for both cosine-squared and conical topographies. Laboratory experiments are presented which are in good agreement with the theory advanced.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 50 , Issue 1 , 15 November 1971 , pp. 79 - 95
Copyright
© 1971 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arakawa, A. 1966 Computational design for long-term numerical integration of the equations of fluid motions: two-dimensional flow. Part 1. J. Comput. Phys. 1, 119.Google Scholar
Boyer, D. L. 1970 Flow past a right circular cylinder in a rotating frame. J. Basic Eng. A.S.M.E. D 92, 430.Google Scholar
Boyer, D. L. 1971a Rotating flow over long shallow ridges. J. Geophys. Fluid Dynamics, 2, 165.
Boyer, D. L. 1971b Rotating flow over a step. J. Fluid Mech. to be published.
Charney, J. G., Fjörtoft, R. & von Neumann, J. 1950 Numerical integration of the barotropic vorticity equation. Tellus, 2, 237.Google Scholar
Forsythe, G. E. & Wasow, W. R. 1960 Finite-Difference Methods for Partial-Differential Equations. John Wiley.
Hide, R. & Ibbetson, A. 1966 An experimental study of Taylor columns. Icarus, 5, 279.Google Scholar
Hide, R., Ibbetson, A. & Lighthill, M. J. 1968 On slow transverse flow past obstacles in a rapidly rotating fluid. J. Fluid Mech. 32, 251.Google Scholar
Ingersoll, A. P. 1969 Inertial Taylor columns and Jupiter's Great Red Spot. J. Atmos. Sci. 26, 744.Google Scholar
Jacobs, S. J. 1964 The Taylor column problem. J. Fluid Mech. 20, 581.Google Scholar
Lilly, D. K. 1965 On the computational stability of numerical solutions of time-dependent non-linear geophysical fluid dynamics problems. Mon. Weather Rev. 93, 11.Google Scholar
Miyaeoda, K. 1962 Contribution to the numerical weather prediction-computation with finite difference. Jap. J. Geophys. 3, 75.Google Scholar
Moore, D. W. & Saffman, P. G. 1969 Flow induced by the transverse motion of a thin disk in its own plane through a contained rapidly rotating viscous liquid. J. Fluid Mech. 39, 831.Google Scholar
Phillips, N. A. 1959 An example of non-linear computational instability. In The Atmosphere and Sea in Motion. Rockefeller Institute Press.
Platzman, G. W. 1954 The computational stability of boundary conditions in numerical integration of the vorticity equation. Arch. Met. Geophys. Bioklim. A 7, 29.Google Scholar
Richtmyer, R. D. & Morton, K. W. 1957 Difference Methods for Initial Value Problems. Interscience.
Taylor, G. I. 1923 Experiments on the motion of solid bodies in rotating fluids. Proc. Roy. Soc. A 104, 213.Google Scholar
Varga, R. S. 1962 Matrix Iterative Analysis. Prentice Hall.
Vaziri, A. 1971 Rotating flow over shallow topographies. Ph.D. dissertation. Department of Civil Engineering, University of Delaware.
Wachspress, E. 1966 Iterative Solution of Elliptic Systems. Prentice Hall.
Williams, G. P. 1969 Numerical integration of the three-dimensional Navier-Stokes equations for incompressible flow. J. Fluid Mech. 37, 727.Google Scholar