ISSN:
1420-9039
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Summary The relation between classical hydraulics and modern turbulence modelling is discussed for the case of two-dimensional open channel flow down an inclined plane. A second order turbulence model describing the flow is treated asymptotically for the parameter rangeF≥O(1),δ≪1,β≪1, andδ=O(β 2), whereF is the Froude number,δ is the aspect ratio, andβ is the square root of a characteristic drag coefficient. The Chezy law formulation of mathematical hydraulics is derived as the lowest order approximation to the solution for the flow outside bore regions, and the transverse variation of the longitudinal velocity component is determined at the next stage of the analysis. It is shown that flow discontinuities calculated using the equations of mathematical hydraulics are resolved in bore regions of transverse length scaleO(H o), whereH o is the characteristic fluid depth. The bore structure is found to consist of a highly turbulent outer region with transverse length scaleO(H o) in which the turbulence intensity isO(1), and a bottom boundary layer of transverse length scaleO(β 2 H o), in which the turbulent stresses decrease rapidly to satisfy the bottom boundary conditions. The jump conditions of mathematical hydraulics at flow discontinuities are verified, and it is inferred that classical hydraulics provides an acceptable approximation to the flow outside bore regions for the parameter range considered in the theory.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00945957
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