Jet In Shallow Water Research Articles

Entrainment and mixing in plane turbulent jets in shallow water

Plane jets in shallow water are often encountered in geophysical flows and engineering applications. The present investigation shows that depending on the distance from the origin scaled by depth, the jets can be divided into three fields with distinct behaviour. A model is then presented allowing discussion of the conditions related to the observed increase or decrease of momentum flux in the vicinity of the orifice. The influence of skin-friction on spreading and entrainment is studied on the basis of existing experimental evidence including the one in the present work.

Line momentum source in cross-flow

A series of jets in shallow water is represented as a line source of momentum in a two-dimensional flow. The flow field produced in the presence of cross-current is determined by a finite element solution to the governing shallow water equations. The effects of shoreline boundary and the magnitude of the cross-current are studied and the results are compared satisfactorily with experiments. The global flow features and the induced flow at the line source are in general well predicted. While in the case of strong cross-current the fine flow features around the source cannot be reproduced due to its three-dimensional nature.

Horizontal Round Buoyant Jet in Shallow Water

A common outfall configuration in practice involves a buoyant discharge through a horizontal circular pipe into a shallow body of water. A detailed experimental study of the near‐field flow and mixing characteristics is presented. The proximity of the bed and the free surface has a significant influence on the flow pattern. Experimental results are adequately represented by length and buoyancy scales defined by source momentum and source buoyancy flux. Jet path, centerline dilution and horizontal and vertical half widths are compared with an integral model in an unconfined environment.

Experiments on vertical plane buoyant jets in shallow water

The paper reports on measurements of the flow generated by a plane buoyant jet discharging vertically into shallow water. The study comprises visualization experiments, mean-velocity and turbulence measurements with a two-channel laser-Doppler anemometer and temperature measurements with thermistor probes. According to the previous investigation of Jirka & Harleman (1979) (JH) the flow may be either stable with the heated discharge water leaving the near field in a warm water layer adjacent to the surface, or unstable with flow recirculation and re-entrainment of heated water into the jet. The stable situation usually involves an internal hydraulic jump associated with a roller. Both stable and unstable situations were investigated, the limiting case of a non-buoyant jet representing the unstable one. In order that a roller representing an internal hydraulic jump developed in the relatively short test channel in the buoyant situations, a strong downstream control had to be imposed by inserting a slightly submerged weir. Most experiments were carried out at a depth-to-discharge-width ratio of 100, and in this case the strong upstream control caused the hydraulic jump to be flooded for both of the densimetric Froude numbers studied (F = 9.9 and 21). In each case, a thick upper layer of nearly uniform temperature developed, with a larger layer thickness for F = 21. Below this layer was a relatively thin interface with temperature gradients and below this a counterflow of cold ambient water. For both Froude numbers, the flow was stable in the sense of JH, but only marginally so in the higher-Froude-number case. The observed trends of the flow behaviour follow the stability analysis of JH, but the dilution of the heated water, which was determined from the temperature measurements, is different from that predicted by the JH mixing analysis. The dilution is much lower in the present case with the flooded jump than in the JH analysis and experiments without specific downstream control and with a much longer test channel and thus no flooded jump.

Experimental Measurements of Multiple‐Jet Induced Flow

Experimental results are confirmed for theoretical predictions of a vortex model for the two-dimensional inviscid flow generated by a line of submerged, turbulent, shallow water jets in a coflowing current. The experiments are performed in a large shallow water basin in which a strong uniform current can be produced and boundary effects are negligible. The vortex model is validated against detailed velocity measurements at and downstream of the momentum source line. Observations of surface flow patterns show that, depending only on the ambient current to ultimate slipstream velocity ratio, distinct flow regimes ranging from a strong inwardly directed sink flow to a smooth contracting slipstream can result.

Comparison of Two River Diffuser Models

The effect of lateral boundaries on the mechanics of mixing multiple shallow water jets in a coflowing current is studied. Two exact inviscid solutions of the momentum-induced flow are examined: A model that accounts for the finite width of the receiving water is compared with a model that neglects lateral confinement. A parametric study reveals remarkably little difference in the key predictions of the velocity and contraction of the ultimate slipstream—especially with reference to a related recent study of boundary effects on multiple submerged jets. The conclusions are corroborated by detailed velocity measurements in a systematic set of experiments covering a wide range of induced flows.

BOUNDARY EFFECTS ON A SUBMERGED JET GROUP

A vortex model is employed to calculate the flow induced by a line group of submerged high velocity shallow water jets discharging in proximity to a shoreline boundary. Based on an inviscid flow model, a kinematic and dynamic boundary condition are formulated along the unknown lines of velocity discontinuity downstream of the multiple jets. This results in two governing nonlinear integral equations in terms of the unknown circulation strength along the unknown slip streamlines. The numerically computed two dimensional momentum-induced flow shows that, as the jet group is placed closer to the boundary, the contraction of the slipstream becomes stronger, resulting in a decrease of the induced flow. All of the features predicted by the theory are in good agreement with experimental results of this and previous investigations.

Closure to “ Vertical Round Buoyant Jet in Shallow Water ” by Joseph H. W. Lee and Gerhard H. Jirka (December, 1981)

Closure to “ <i>Vertical Round Buoyant Jet in Shallow Water</i> ” by Joseph H. W. Lee and Gerhard H. Jirka (December, 1981)

Discussion of “ Vertical Round Buoyant Jet in Shallow Water ” by Joseph H. W. Lee and Gerhard H. Jirka (December, 1981)

Discussion of “ <i>Vertical Round Buoyant Jet in Shallow Water</i> ” by Joseph H. W. Lee and Gerhard H. Jirka (December, 1981)

Vertical Round Buoyant Jet in Shallow Water

The stability and bulk mixing characteristics of an axisymmetric turbulent buoyant jet discharging vertically into a stagnant waterbody of large horizontal extent is studied theoretically and experimentally. A stable discharge configuration is defined as one in which a buoyant surface layer is formed which spreads radially from the source and does not communicate with the initial buoyant jet region. On the other hand, the discharge configuration is unstable when recirculation cells exist around the jet efflux. A semi-empirical theory shows the discharge stability is only dependent on the dynamic interaction of three near-field regions—the buoyant jet region, surface impingement region, and radial internal hydraulic jump region. A series of laboratory experiments were performed with a half-jet, using heat as source of buoyancy, and inserting a plane of symmetry in a large model basin. The experimental results are in good agreement with the theoretical predictions, both as regards the stability criterion and the near field mixing characteristics.

Two-Dimensional Heated Jets in Shallow Water

The flow field induced by a two-dimensional heated jet in shallow stagnant water is analyzed. The governing partial differential equation is reduced to ordinary differential equations by integrating over the depth with assumed distributions of temperature and velocity. A multiple regression analysis applied to numerical results yielded simple expressions for the near-field dilution and the far-field length of the surface layer. A few experiments were conducted which guided the mathematical analysis. A reasonable agreement is obtained between the experimental results and numerical calculations.