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|Title: ||Transcritical flow of a stratified fluid over topography: analysis of the forced Gardner equation|
|Authors: ||Kamchatnov, A.M.|
Grimshaw, Roger H.J.
|Keywords: ||Internal waves|
|Issue Date: ||2013|
|Publisher: ||© Cambridge University Press|
|Citation: ||KAMCHATNOV, A.M. ... et al, 2013. Transcritical flow of a stratified fluid over topography: analysis of the forced Gardner equation. Journal of Fluid Mechanics, 736, pp.495-531.|
|Abstract: ||Transcritical flow of a stratified fluid past a broad localised topographic obstacle is studied
analytically in the framework of the forced extended Korteweg–de Vries (eKdV), or
Gardner, equation. We consider both possible signs for the cubic nonlinear term in the
Gardner equation corresponding to different fluid density stratification profiles. We identify
the range of the input parameters: the oncoming flow speed (the Froude number)
and the topographic amplitude, for which the obstacle supports a stationary localised
hydraulic transition from the subcritical flow upstream to the supercritical flow downstream.
Such a localised transcritical flow is resolved back into the equilibrium flow
state away from the obstacle with the aid of unsteady coherent nonlinear wave structures
propagating upstream and downstream. Along with the regular, cnoidal undular
bores occurring in the analogous problem for the single-layer flow modeled by the forced
KdV equation, the transcritical internal wave flows support a diverse family of upstream
and downstream wave structures, including kinks, rarefaction waves, classical undular
bores, reversed and trigonometric undular bores, which we describe using the recent
development of the nonlinear modulation theory for the (unforced) Gardner equation.
The predictions of the developed analytic construction are confirmed by direct numerical
simulations of the forced Gardner equation for a broad range of input parameters.|
|Description: ||This paper was accepted for publication in the Journal of Fluid Mechanics and the definitive version is available at: http://dx.doi.org/10.1017/jfm.2013.556|
|Version: ||Accepted for publication|
|Publisher Link: ||http://dx.doi.org/10.1017/jfm.2013.556|
|Appears in Collections:||Published Articles (Maths)|
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