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Hydraulic jumps in a channel

Published online by Cambridge University Press:  10 January 2009

DANIEL BONN ,
ANDERS ANDERSEN  and
TOMAS BOHR
DANIEL BONN
Affiliation:
van der Waals-Zeeman Institute, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands
ANDERS ANDERSEN*
Affiliation:
Department of Physics and Center for Fluid Dynamics, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
TOMAS BOHR
Affiliation:
Department of Physics and Center for Fluid Dynamics, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
*
†Email address for correspondence: aanders@fysik.dtu.dk
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Abstract

We present a study of hydraulic jumps with flow predominantly in one direction, created either by confining the flow to a narrow channel with parallel walls or by providing an inflow in the form of a narrow sheet. In the channel flow, we find a linear height profile upstream of the jump as expected for a supercritical one-dimensional boundary layer flow, but we find that the surface slope is up to an order of magnitude larger than expected and independent of flow rate. We explain this as an effect of turbulent fluctuations creating an enhanced eddy viscosity, and we model the results in terms of Prandtl's mixing-length theory with a mixing length that is proportional to the height of the fluid layer. Using averaged boundary-layer equations, taking into account the friction with the channel walls and the eddy viscosity, the flow both upstream and downstream of the jump can be understood. For the downstream subcritical flow, we assume that the critical height is attained close to the channel outlet. We use mass and momentum conservation to determine the position of the jump and obtain an estimate which is in rough agreement with our experiment. We show that the averaging method with a varying velocity profile allows for computation of the flow-structure through the jump and predicts a separation vortex behind the jump, something which is not clearly seen experimentally, probably owing to turbulence. In the sheet flow, we find that the jump has the shape of a rhombus with sharply defined oblique shocks. The experiment shows that the variation of the opening angle of the rhombus with flow rate is determined by the condition that the normal velocity at the jump is constant.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 618 , 10 January 2009 , pp. 71 - 87
Copyright
Copyright © Cambridge University Press 2008

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References

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