Channel Of Parabolic Cross-section Research Articles

Computation of Normal Depth in Parabolic Cross Sections Using The Rough Model Method

A new method is applied to calculate the normal depth in an open channel of parabolic cross section. This is the rough model method whose main particularity is to ignore the flow resistance coefficients, such as Chezy’s coefficient and manning’s roughness coefficient. The method is applied to a referential rough model, whose friction coefficient is constant, which explicitly express the hydraulic and geometric characteristics of the model such as aspect ratio. By means of a non-dimensional correction factor, the normal depth is explicitly deduced. The rough model method is applicable to the entire domain of turbulent flow.

A numerical study of wave propagation and run-up in water channels

It is important to understand how water waves propagate through water channels in order to reduce inundation damages induced by surges and/or tsunami run-up. For this purpose, a two-dimensional numerical model is developed based on Nonlinear Shallow Water Equations. In order to appropriately describe the strongly nonlinear hydrodynamics, a high-order TVD scheme is implemented. Model capabilities are confirmed through comparison with existing analytical studies including the dam-break problems, run-up and back-wash on a sloping bathymetry. The model is then applied to the study on the inundation of bore propagating in a channel of parabolic cross-section from a side breach.

Comments on “Is the Faroe Bank Channel Overflow Hydraulically Controlled?”

Abstract In a recent paper Girton et al., due to what appears to be a misunderstanding, stated that a critical-flow analysis of the deep-water transport through the Faroe Bank Channel had been undertaken by Lake et al. on the basis of rotating hydraulic theory for a channel of parabolic cross section. In fact, this quoted investigation dealt with a rectangular passage. In the present comment it is demonstrated how the use of parabolic bathymetry leads to significant improvements of the Froude number results.

Is the Faroe Bank Channel Overflow Hydraulically Controlled?

Abstract The overflow of dense water from the Nordic Seas through the Faroe Bank Channel (FBC) has attributes suggesting hydraulic control—primarily an asymmetry across the sill reminiscent of flow over a dam. However, this aspect has never been confirmed by any quantitative measure, nor is the position of the control section known. This paper presents a comparison of several different techniques for assessing the hydraulic criticality of oceanic overflows applied to data from a set of velocity and hydrographic sections across the FBC. These include 1) the cross-stream variation in the local Froude number, including a modified form that accounts for stratification and vertical shear, 2) rotating hydraulic solutions using a constant potential vorticity layer in a channel of parabolic cross section, and 3) direct computation of shallow water wave speeds from the observed overflow structure. Though differences exist, the three methods give similar answers, suggesting that the FBC is indeed controlled, with a critical section located 20–90 km downstream of the sill crest. Evidence of an upstream control with respect to a potential vorticity wave is also presented. The implications of these results for hydraulic predictions of overflow transport and variability are discussed.

On the deep‐water flow through the Faroe Bank Channel

A substantial part of the Norwegian Sea deep‐water outflow into the North Atlantic takes place via the Faroe Bank Channel, the deepest passage through the Greenland‐Scotland Ridge. In order to estimate this flux of cold, low‐saline bottom water, a field survey comprising hydrographie observations as well as current measurements was carried out in the channel during May 1983. Transport calculations were undertaken for a total of four sets of observations and yielded values ranging from 1.5 to 1.9 sverdrup. The outflow is most likely subjected to hydraulic control, and consequently, a simple model has been formulated in order to determine the maximum discharge through a rotating channel of parabolic cross section. This geometry is well‐adapted to the topography of the Faroe Bank Channel, and the theoretically predicted magnitude of the transport was found to be in good agreement with the observations.

Interaction between a vertical wall and a wave propagating in a channel of parabolic cross section

The reflection of a long wave from a vertical wall is studied on the assumption that the wave travels in a channel or river of parabolic cross section. According to [11], such cross sections are found in river beds formed in noncohesive soils. Expressions describing the evolution of the height of the wave at the vertical wall are obtained on the assumption that the exponent of the parabola takes the values k=2/(2n − 1). The conditions corresponding to the formation of a bore at the vertical wall are described.

Free and forced shallow-water oscillations in a rotating channel of parabolic cross-section

Free and forced oscillations of shallow water in an infinitely long rotating channel of parabolic cross-section are analyzed. The pure cross-channel oscillations ofChrystal (1905) and solutions for zero rotation first discussed byProudman (1925) andHidaka (1932) are special asymptotic solutions for the free modes of this model. However, for increasingly large, along-shore wave number, our solutions donot uniformly approach those ofReid (1958) andBall (1967) for a single shore-line and semi-infinite ocean. A method of computing eigen frequencies and eigen functions for the general problem is described, and a sufficient number of these are exhibited graphically to permit visualization of the transitions between the asymptotic regions.