Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session L35: Geophysical Fluid Dynamics: General
4:05 PM–6:41 PM,
Monday, November 19, 2018
Georgia World Congress Center
Room: B407
Chair: Alfredo Pinelli, City University London
Abstract ID: BAPS.2018.DFD.L35.4
Abstract: L35.00004 : Gravity current in a channel of general cross-section with open top surface
4:44 PM–4:57 PM
Presenter:
Marius Ungarish
(Technion Haifa Israel)
Author:
Marius Ungarish
(Technion Haifa Israel)
Consider the idealized steady-state gravity current of height h and density ρ1 that propagates into an ambient motionless fluid of height H and density ρ2 (< ρ1) in a channel of general cross-section (rectangle, triangle, semi-circle, trapezoid, etc.) with an upper surface open to the atmosphere (open channel) at high Reynolds number. The current propagates with speed U and causes a depth decrease χ of the top surface. This is a significant extension of the solution for the fixed-top channel χ = 0. Here the determination of χ is a part of the problem. For a given cross-section geometry, the dimensionless parameters of the problem are a=h/H and r = ρ2/ρ1. We show that a control-volume analysis determines χ/H and Fr = U/(g' h)½ as functions of a and r, where g' = (1/r -1)g is the reduced gravity. The system satisfies balance of volume and momentum (explicitly), and vorticity (implicitly). We present solutions and insights for various cross-section geometries. For a Boussinesq system with r ≈ 1, we obtain χ/H ≈ 0 , and the present Fr and dissipation results differ only slightly from the fixed-top predictions, as expected.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2018.DFD.L35.4
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