Rotating hydraulics of strait and sill flows†

Whitehead, J. A.; Leetmaa, Ants; Knox, Robert A.

doi:10.1080/03091927409365790

Cited by 199 publications

(163 citation statements)

References 2 publications

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“…The bound is based on the anticipation that steady flow from the upstream reservoir will approach the connecting strait in a boundary layer along the left-hand wall, cross to the right-hand wall within the strait, and continue into the second reservoir as a boundary current along the right-hand wall. The above bound then follows from the geostrophic relation and the supposition that the depth difference across the boundary layer cannot be greater than The reduction in transport by rotation is a feature anticipated by steady hydraulic theories such as Whitehead et al (1974). However, this conclusion is typically reached by fixing the reservoir state upstream of a strait or sill and calculating the change in outflow rate as rotation is increased.…”

Section: Semigeostrophic and Full Numerical Solutionsmentioning

confidence: 99%

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Nonlinear Rossby adjustment in a channel

1999

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The Rossby adjustment problem for a homogeneous fluid in a channel is solved for large values of the initial depth discontinuity. We begin by analysing the classical dam break problem in which the depth on one side of the discontinuity is zero. An approximate solution for this case can be constructed by assuming semigeostrophic dynamics and using the method of characteristics. This theory is supplemented by numerical solutions to the full shallow water equations. The development of the flow and the final, equilibrium volume transport are governed by the ratio of the Rossby radius of deformation to the channel width, the only non-dimensional parameter. After the dam is destroyed the rotating fluid spills down the dry section of the channel forming a rarefying intrusion which, for northern hemisphere rotation, is banked against the right-hand wall (facing downstream). As the channel width is increased the speed of the leading edge (along the right-hand wall) exceeds the intrusion speed for the non-rotating case, reaching the limiting value of 3.80 times the linear Kelvin wave speed in the upstream basin. On the left side of the channel fluid separates from the sidewall at a point whose speed decreases to zero as the channel width approaches infinity. Numerical computations of the evolving flow show good agreement with the semigeostrophic theory for widths less than about a deformation radius. For larger widths cross-channel accelerations, absent in the semigeostrophic approximation, reduce the agreement. The final equilibrium transport down the channel is determined from the semigeostrophic theory and found to depart from the non-rotating result for channels widths greater than about one deformation radius. Rotation limits the transport to a constant maximum value for channel widths greater than about four deformation radii.The case in which the initial fluid depth downstream of the dam is non-zero is then examined numerically. The leading rarefying intrusion is now replaced by a Kelvin shock, or bore, whose speed is substantially less than the zero-depth intrusion speed. The shock is either straight across the channel or attached only to the righthand wall depending on the channel width and the additional parameter, the initial depth difference. The shock speeds and amplitudes on the right-hand wall, for fixed downstream depth, increase above the non-rotating values with increasing channel width. However, rotation reduces the speed of a shock of given amplitude below the non-rotating case. We also find evidence of resonant generation of Poincaré waves by the bore. Shock characteristics are compared to theories of rotating shocks and qualitative agreement is found except for the change in potential vorticity across the shock, which is very sensitive to the model dissipation. Behind the leading shock the flow evolves in much the same way as described by linear theory except for the generation of strongly nonlinear transverse oscillations and rapid advection down the 188 K. R. Helfrich, A. C. Kuo and L. J. Pratt rig...

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Section: Semigeostrophic and Full Numerical Solutionsmentioning

confidence: 99%

“…These flows can be strongly time-dependent, a feature which hinders interpretation in terms of rotating, hydraulic theory (e.g. Whitehead, Leetma & Knox 1974;Gill 1977). Prominent examples include deep overflows of the Denmark Strait (Smith 1976) and the Faroe Bank Channel (Cederlf, Lundberg & Sterhus 1989).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Rossby adjustment in a channel

1999

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“…A single-layer rotating channel model was introduced by Whitehead et al (1974), andGill (1974) who considered the behavior of steady flow in a rotating channel. The theory of rotating hydraulics has been further explored by Pratt (1983Pratt ( , 1984aPratt ( , 1985, and Hogg (1983) considered a two-layer rotating hydraulics problem.…”

Section: Flowsmentioning

confidence: 99%

Hydraulics and instabilities of quasi-geostrophic zonal flows

Ralph¹

1994

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“…Although on time scales of weeks the outflow path is dominated by eddies, there have been suggestions that hydraulic control governs the average outflow rate. Recent progress in understanding the effects related to the hydraulic nature of this exchange has been given by Pratt [2004] who emphasized the importance of establishing a 'weir formula' that will allow monitoring of deep overflows at the choke points as was suggested by Whitehead et al [1974] (hereinafter referred to as WLK) who applied laws of rotating hydraulics.…”

Section: Introductionmentioning

confidence: 99%

A Riccati model for Denmark Strait overflow variability

Käse

2006

Geophysical Research Letters

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[1] A controlled volume box model of the western basins of the Nordic Seas for water denser than 1027.8 kg m À3 is constructed, where accumulation in volume ( dV dt ) is driven by net imbalances between prescribed net inflow from the northern, eastern and top boundaries (Q s ) and hydraulically limited outflow through the Denmark Strait. The resulting Riccati equation is solved analytically for filling and flushing experiments with constant Q s and numerically for stochastic forcing Q s (t). For small perturbations to Q s with white noise spectrum, the overflow response is red noise with a time scale between 5 and 15 years depending on the mean interface height and area. For

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Rotating hydraulics of strait and sill flows†

Cited by 199 publications

References 2 publications

Nonlinear Rossby adjustment in a channel

Nonlinear Rossby adjustment in a channel

Hydraulics and instabilities of quasi-geostrophic zonal flows

A Riccati model for Denmark Strait overflow variability

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