Author:
KLEMP JOSEPH B.,ROTUNNO RICHARD,SKAMAROCK WILLIAM C.
Abstract
According to classical hydraulic theory, the energy losses
within an external bore must occur within the expanding layer. However,
the application of this theory to describe the propagation of internal
bores leads to contradiction with accepted gravity-current behaviour in
the limit as the depth of the expanding layer ahead of the bore becomes
small. In seeking an improved expression for the propagation of
internal bores, we have rederived the steady front condition for a bore
in a two-layer Boussinesq fluid in a channel under the assumption that
the energy loss occurs within the contracting layer. The resulting
front condition is in good agreement with available laboratory data and
numerical simulations, and has the appropriate behaviour in both the
linear long-wave and gravity-current limits. Analysis of an idealized
internal bore assuming localized turbulent stresses suggests that the
energy within the expanding layer should, in fact, increase. Numerical
simulations with a two-dimensional non-hydrostatic model also reveal a
slight increase of energy within the expanding layer and suggest that
the structure of internal bores is fundamentally different from
classical external bores, having the opposite circulation and little
turbulence in the vicinity of the leading edge. However, if there is
strong shear near the interface between layers, the structure and
propagation of internal jumps may become similar to their counterparts
in classical hydraulic theory. The modified jump conditions for
internal bores produce some significant alterations in the traditional
Froude-number dependence of Boussinesq shallow-water flow over an
obstacle owing to the altered behaviour of the upstream-propagating
internal bore.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
110 articles.
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