Title: Near-critical turbulent open-channel flows over bumps andramps
Authors: Schneider, Wilhelm 
Müller, Markus 
Yasuda, Youichi 
Category: Original Research Article
Issue Date: 2018
Journal: Acta Mechanica 
ISSN: 0001-5970
Steady two-dimensional turbulent free-surface flow in a channel with a slightly uneven bottom is considered. The shape of the unevenness of the bottom can be in the form of a bump or a ramp of very small height. The slope of the channel bottom is assumed to be small, and the bottom roughness is assumed to be constant. Asymptotic expansions for very large Reynolds numbers and Froude numbers close to the critical value Fr=1, respectively, are performed. The relative order of magnitude of two small parameters, i.e. the bottom slope and (Fr−1), is defined such that no turbulence modelling is required. The result is a steady-state version of an extended Korteweg–de Vries equation for the surface elevation. Other flow quantities, such as pressure, flow velocity components, and bottom shear stress, are expressed in terms of the surface elevation. An exact solution describing stationary solitary waves of the classical shape is obtained for a bottom of a particular shape. For more general shapes of ramps and bumps, stationary solitary waves of the classical shape are also obtained as a first approximation in the limit of small, but nonzero, dissipation. With the exception of an eigensolution for a ramp, an outer region has to be introduced. The outer solution describes a ’tail’ that is attached to the stationary solitary wave. In addition to the solutions of the solitary-wave type, solutions of smaller amplitudes are obtained both numerically and analytically. Experiments in a water channel confirm the existence of both types of stationary single waves.
Keywords: flow; free surface; Free Surface Flow
DOI: 10.1007/s00707-018-2230-3
Organisation: E322 - Institut für Strömungsmechanik und Wärmeübertragung 
License: CC BY 4.0 CC BY 4.0
Publication Type: Article
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