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Effects of Bottom-Height Changes on Maximal Exchange-Flow Estimates in Channels with Quadratic- Shape Cross Sections

Author(s): Janek Laanearu; Peter A. Davies; T. Iit Koppel

Linked Author(s): Janek Laanearu, Peter A. Davies

Keywords: Estuary; Sill; Exchange flow; Froude number; Critical flow

Abstract: This study is mot ivated by the difficult ies in applying internal hydraulics theory to density-driven exchange flows in the river estuary condit ions. River estuary has usually complex morphodynamic character in bottom shape and applicat ion of hydraulic model for density-driven exchange is not straightforward due to unique bottom geometry and roughness elements. The geometrical problem arising from natural channels is that the cross-sect iona l perimeters do not, in general, have analyt ical relationships between width and depth changes. In this study the internal regimes o f two-layer flow are presented for non-rectangular channels with sill and without surface-width changes and constant shape. The internal regimes of exchange flow over sills in rectangular channel are employed for comparison. Hydraulic regimes are quant ified in terms o f a shape parameter x represent ing the ratio o f the crosssect ional area o f the chosen channel section to that of the bank-full area. The internal flow solut ions are parameterized by densimetric Froude numbers of two-layer flow, formulated in terms o f this parameter x (Laanearu and Davies, 2007). For density-driven exchange over sills, two or three control po ints G2 = 1 solut ions can be found. One control is located at the sill section and other controls at the exit sect ion in the side of dense-water pool. The solut ion with three control po ints is presented for the net flow case in the non-rectangular channel. The exchange flow problem without net flow is so lved by the equat ions describing the flow at the two control points at the sill and channel exit. The internal-energy funct ion and internal flux equation for the quadratic channel are used to present parameterized solut ions in the interna l Froude numbers space. In part icular, two features of a maximal exchange flows in the quadratic channels are determined; 1) the dependence of interface posit ion and transport on sill height changes and 2) locations of controls in the Froude-number plane.


Year: 2007

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