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Rotating flow over shallow topographies

  • Arsalan Vaziri (a1) and Don L. Boyer (a1) (a2)


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, RoE½, H/DE0, and h/DE½, 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.



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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.
Boyer, D. L. 1970 Flow past a right circular cylinder in a rotating frame. J. Basic Eng. A.S.M.E. D 92, 430.
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.
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.
Hide, R., Ibbetson, A. & Lighthill, M. J. 1968 On slow transverse flow past obstacles in a rapidly rotating fluid. J. Fluid Mech. 32, 251.
Ingersoll, A. P. 1969 Inertial Taylor columns and Jupiter's Great Red Spot. J. Atmos. Sci. 26, 744.
Jacobs, S. J. 1964 The Taylor column problem. J. Fluid Mech. 20, 581.
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.
Miyaeoda, K. 1962 Contribution to the numerical weather prediction-computation with finite difference. Jap. J. Geophys. 3, 75.
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.
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.
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.
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.
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Rotating flow over shallow topographies

  • Arsalan Vaziri (a1) and Don L. Boyer (a1) (a2)


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