5 results
Barotropically induced interfacial waves in two-layer exchange flows over a sill
- M. ELETTA NEGRETTI, DAVID Z. ZHU, GERHARD H. JIRKA
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- Journal:
- Journal of Fluid Mechanics / Volume 592 / 10 December 2007
- Published online by Cambridge University Press:
- 14 November 2007, pp. 135-154
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Two-layer exchange flows are observed in the channels/straits connecting two water bodies of different densities. This study examines the nature of the barotropic forcing and its effect on the interfacial waves in two-layer exchange flows over a smooth/break underwater sill. Experiments were conducted with different initial conditions, distinguishing the case of hydrostatic disequilibrium and the case of a global pressure-balanced state. The experiments demonstrate that the baroclinic exchange flow is dominated by the barotropic-forcing-induced oscillations. A simplified barotropic model is developed to predict the period of the barotropic oscillation with an excellent agreement with experimental measurements. Detailed velocity and flow-rate measurements also indicate the importance of the barotropic forcing in exchange flows. The effect of the superimposed barotropic forcing on the interfacial wave characteristics is also investigated. Large two-dimensional surge-like structures are observed during the experiments, whose generation is shown to be related to the flow-rate oscillations. The length scales of these structures is comparable with the total water depth and is shown to increase with increasing Reynolds numbers.
Near-surface turbulence in a grid-stirred tank
- Blair H. Brumley, Gerhard H. Jirka
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- Journal:
- Journal of Fluid Mechanics / Volume 183 / October 1987
- Published online by Cambridge University Press:
- 21 April 2006, pp. 235-263
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In order to elucidate the turbulent structure below a shear-free gas-liquid interface, turbulence measurements were made in a 50 cm square by 40 cm deep tank stirred by a vertically oscillating grid well below the surface, using a split-film anemometer probe rotating in a horizontal circle. This instrument is able to measure both vertical and horizontal velocity fluctuations to within 0.4 mm of the surface, from which spatial spectra and profiles of r.m.s. velocity fluctuations and integral lengthscales can be calculated. The turbulent structure is affected by the presence of the surface within a ‘surface-influenced layer’ roughly one integral scale, or ten per cent of the distance from the surface to the centre of the grid stroke, in thickness. The shapes of the spectra and profiles within the surface-influenced layer are predicted to a good first approximation by the source theory of Hunt & Graham (1978), which treats the turbulent structure as the superposition of homogeneous turbulence with an irrotational velocity field driven by a source distribution at the surface which cancels the vertical velocity fluctuations there. The magnitudes (as opposed to the shapes) of the profiles scale according to the values that would otherwise occur in the vicinity of the surface-influenced layer were the surface not present. These magnitudes are adequately predicted by the bulk relations determined by Hopfinger & Toly (1976) and Thompson & Turner (1975), with no apparent dependence on turbulent Reynolds number. There are some minor discrepancies between the measured profiles and those of Hunt & Graham. A thin layer of reduced velocity fluctuations below what would be expected from the theory was observed near the surface. Also, anisotropy in the velocity spectra at depths within the surface-influenced layer extended well into the inertial subrange, whereas the Hunt & Graham theory predicts no anisotropy at high wavenumbers.
Density currents or density wedges: boundary-layer influence and control methods
- Gerhard H. Jirka, Masamitsu Arita
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- Journal:
- Journal of Fluid Mechanics / Volume 177 / April 1987
- Published online by Cambridge University Press:
- 21 April 2006, pp. 187-206
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Density currents and density wedges are two observed manifestations of interactions between an ambient flow and a horizontal buoyant intrusion. In a density current the buoyant pressure force is primarily balanced by the local form drag of the current head which has a blunt shape and abrupt depth change. In a density wedge a distributed interfacial drag is the primary balancing force, leading to a stretched-out shape and long-distance intrusions. A perturbation analysis of the approach flow to the inclined front of a density current shows that slight momentum changes caused by viscous effects in the ambient flow determine which of these two flow types is established. In a uniform ambient channel flow, any momentum deficit relative to the inviscid case will lead to a local flattening of the front and ultimate breakdown into a density wedge. On the other hand, a momentum surplus will support a steady-state density current. Several exploratory experiments on control of the ambient boundary layer through local non-uniformities were performed with the objective of achieving stable density-current forms with limited intrusion lengths. These methods include a small step, a barrier and suction and are applied for intrusions at either the bottom or surface of an ambient water flow. In all cases, good agreement is found with the force balances predicted by Benjamin's (1968) theory and its extension by Britter & Simpson (1978) which accounts for entrainment in the wake zone of the head.
Stability and mixing of a vertical plane buoyant jet in confined depth
- Gerhard H. Jirka, Donald R. F. Harleman
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- Journal:
- Journal of Fluid Mechanics / Volume 94 / Issue 2 / 25 September 1979
- Published online by Cambridge University Press:
- 19 April 2006, pp. 275-304
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A plane turbulent buoyant jet discharging vertically into a two-dimensional channel of confined depth is considered. The channel opens at both ends into a large outside reservoir, thus defining a steady symmetrical flow field within the channel. The analysis is aimed at two aspects, the stability and the bulk mixing characteristics of the discharge. A stable discharge configuration is defined as one in which a buoyant surface layer is formed which spreads horizontally and does not communicate with the initial buoyant jet region. On the other hand, the discharge configuration is unstable when a recirculating cell exists on both sides of the jet efflux.
It is shown that discharge stability is only dependent on the dynamic interaction of three near-field regions, a buoyant jet region, a surface impingement region and an internal hydraulic jump region. The buoyant jet region is analysed with the assumption of a variable entrainment coefficient in a form corresponding to an approximately constant jet-spreading angle as confirmed by different experimental sources. The properties of surface impingement and internal jump regions are determined on the basis of control volume analyses. Under the Boussinesq approximation, only two dimensionless parameters govern the near-field interaction; these are a discharge densimetric Froude number and a relative depth. For certain parameter combinations, namely those implying low buoyancy and shallow depth, there is no solution to the conjugate downstream condition in the hydraulic jump which would satisfy both momentum and energy conservation principles. Arguments are given which interpret this condition as one which leads to the establishment of a near-field recirculation cell and, thus, discharge instability.
The far-field boundary conditions, while having no influence on discharge stability, determine the bulk mixing characteristics of the jet discharge. The governing equations for the two-layered counterflow system in the far field are solved. The strength of the convective transport, and hence the related dilution ratio, is governed by another non-dimensional parameter, the product of the relative channel length and the boundary friction coefficient.
Experiments in a laboratory flume, covering a range of the governing parameters, are in excellent agreement with the theoretical predictions, both the stability criterion and the bulk mixing characteristics.
Absolute and convective instabilities of plane turbulent wakes in a shallow water layer
- DAOYI CHEN, GERHARD H. JIRKA
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- Journal:
- Journal of Fluid Mechanics / Volume 338 / 10 May 1997
- Published online by Cambridge University Press:
- 10 May 1997, pp. 157-172
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In shallow turbulent wake flows (typically an island wake), the flow patterns have been found experimentally to depend mainly on a shallow wake parameter, S=cfD/h in which cf is a quadratic-law friction coefficient, D is the island diameter and h is water depth. In order to understand the dependence of flow patterns on S, the shallow-water stability equation (a modified Orr–Sommerfeld equation) has been derived from the depth-averaged equations of motion with terms which describe bottom friction. Absolute and convective instabilities have been investigated on the basis of wake velocity profiles with a velocity deficit parameter R. Numerical computations have been carried out for a range of R-values and a stability diagram with two dividing lines was obtained, one defining the boundary between absolute and convective instabilities Sca, and another defining the transition between convectively unstable and stable wake flow Scc. The experimental measurements (Chen & Jirka 1995) of return velocities in shallow wakes were used to compute R-values and two critical values, SA=0.79 and SC=0.85, were obtained at the intersections with lines Sca and Scc. Through comparison with transition values observed experimentally for wakes with unsteady bubble (recirculation zone) and vortex shedding, SU and SV respectively, the sequence SC>SA> SU>SV shows vortex shedding to be the end product of absolute instability. This is analogous to the sequence of critical Reynolds numbers for an unbounded wake of large spanwise extent. Experimental frequency characteristics compare well with theoretical results. The observed values of SU and SV for different flow patterns correspond to the velocity profile with R=−0.945, which is located at the end of the wake bubble, and it provides the dominant mode.