Some Aspects of the Flow of Stratified Fluids: II. Experiments with a Two-Fluid System

Long, Robert R.

doi:10.1111/j.2153-3490.1954.tb01100.x

Cited by 136 publications

(102 citation statements)

References 9 publications

(3 reference statements)

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“…For a straight channel, i.e. D c = 1, Equation (4) reduces to the simpler form for a onedimensional flow over an infinitely long ridge (Long, 1954). Using data for the Zagreb profile at 12 UTC from Table II for the far-upstream condition, we derive M c = 0.37, based on F ∞ = 0.3 and D c = 1.…”

Section: Upstream Profilementioning

confidence: 99%

On the onset of bora and the formation of rotors and jumps near a mountain gap

Gohm

Mayr

Fix³

et al. 2008

Quart J Royal Meteoro Soc

125

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This study investigates the onset phase of a strong Adriatic bora windstorm that occurred on 4 April 2002. The target area is a gap about 20 km wide embedded in the coastal mountain barrier of the Dinaric Alps that favours strong jet-like winds. Airborne-aerosol back-scatter lidar measurements on board the DLR Falcon research aircraft, together with surface and upper-air observations, are used to verify high-resolution numerical experiments conducted with the mesoscale atmospheric model RAMS and a single-layer shallow-water model (SWM). Especially during the breakthrough phase of the bora, the flow at the gap exit exhibits a complex spatial structure and temporal evolution. On a transect through the centre of the gap, a hydraulic jump forms; this is located close to the coast throughout the night, and starts to propagate downstream in the early morning. On a transect through the edge of the gap, a lee-wave-induced rotor becomes established, due to boundary-layer separation. It starts to propagate downstream about two hours after the jump. This flow evolution implies that the onset of strong winds at the coast occurs several hours earlier downstream of the centre of the gap than downwind of the edge of the gap. Consequently, the wind field in the vicinity of Rijeka airport, located downwind of the gap, is strongly inhomogeneous and transient, and represents a potential hazard to aviation. Measured bora winds at the surface exceed 20 ms −1 , and the simulated wind speed in the gap wind layer exceeds 30 ms −1 . The simulated turbulent kinetic energy exceeds 10 m 2 s −2 .RAMS indicates that wave-breaking near a critical level is the dominant mechanism for the generation of the windstorm. Gap jets can be identified downstream of several mountain passes. The simulated wave pattern above the Dinaric Alps, the wave decay with height due to directional wind shear and the strong flow descent on the leeward side of the barrier are supported by measured back-scatter intensities. Basic bora flow features, including gap jets and jumps, are remarkably well reproduced by SWM simulations. The RAMS reference run captures observed flow phenomena and the temporal flow evolution qualitatively well. A cold low-level bias, an overestimated bora inversion strength, and a slightly too-early bora onset are probably related to insufficient turbulent mixing in the boundary layer. The amplitude of trapped gravity waves, the time of the bora breakthrough and the inversion strength are found to be quite sensitive to the turbulence parametrization.

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Section: Upstream Profilementioning

confidence: 99%

On the onset of bora and the formation of rotors and jumps near a mountain gap

Gohm

Mayr

Fix³

et al. 2008

Quart J Royal Meteoro Soc

125

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“…The ultimate understanding of such complicated flows will require reference to idealized models in which generic transients can be isolated and studied. In non-rotating hydraulics, Long's towing experiments (Long 1954(Long , 1955(Long , 1970 and the classical dam break problem (Stoker 1957) have provided a foundation for investigating more complex phenomena. In geophysical fluid dynamics, the classical Rossby adjustment problem (see Gill 1982) and its extension to a channel setting (Gill 1976;Hermann, Rhines & Johnson 1989;Tomasson & Melville 1992) have played a similar role.…”

Section: Introductionmentioning

confidence: 99%

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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“…Long (1954) theoretically studied the behavior of shallow fluid over a mountain and compared it with laboratory experiments. He showed that there is a definite limit to the mountain height for the existence of the steady-state solution and that the behavior of the shallow fluid can be classified by the Froude number of the approaching flow and non-dimensional mountain height into three regimes: a sub-critical flow, an unsteady flow having hydraulic jumps, and a supercritical flow.…”

Section: Introductionmentioning

confidence: 99%

Shallow Water Flow Having a Lee Hydraulic Jump over a Mountain Range in a Channel of Variable Width

Saitō¹

1992

Journal of the Meteorological Society of Japan

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Some Aspects of the Flow of Stratified Fluids: II. Experiments with a Two-Fluid System

Cited by 136 publications

References 9 publications

On the onset of bora and the formation of rotors and jumps near a mountain gap

On the onset of bora and the formation of rotors and jumps near a mountain gap

Nonlinear Rossby adjustment in a channel

Shallow Water Flow Having a Lee Hydraulic Jump over a Mountain Range in a Channel of Variable Width

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