The mechanics of buoyant jet flows issuing with a general three-dimensional geometry into an unbounded ambient environment with uniform density or stable density stratification and under stagnant or steady sheared current conditions is investigated. An integral model is formulated for the conservation of mass, momentum, buoyancy and scalar quantities in the turbulent jet flow. The model employs an entrainment closure approach that distinguishes between the separate contributions of transverse shear (leading to jet, plume, or wake internal flow dynamics) and of azimuthal shear mechanisms (leading to advected momentum puff or thermal flow dynamics), respectively. Furthermore, it contains a quadratic law turbulent drag force mechanism as suggested by a number of recent detailed experimental investigations on the dynamics of transverse jets into crossflow. The model is validated in several stages: First, comparison with basic experimental data for the five asymptotic, self-similar stages of buoyant jet flows, i.e., the pure jet, the pure plume, the pure wake, the advected line puff, and the advected line thermal, support the choice and magnitude of the turbulent closure coefficients contained in the entrainment formulation. Second, comparison with many types of non-equilibrium flows support the proposed transition function within the entrainment relationship, and also the role of the drag force in the jet deflection dynamics. Third, a number of spatial limits of applicability have been proposed beyond which the integral model necessarily becomes invalid due to its parabolic formulation. These conditions, often related to the breakdown of the boundary layer nature of the flow, describe features such as terminal layer formation in stratification, upstream penetration in jets opposing a current, or transition to passive diffusion in a turbulent ambient shear flow. Based on all these comparisons, that include parameters such as trajectories, centerline velocities, concentrations and dilutions, the model appears to provide an accurate and reliable representation of buoyant jet physics under highly general flow conditions.

Integral Model for Turbulent Buoyant Jets in Unbounded Stratified Flows. Part I: Single Round Jet

A general Lagrangian jet model formulation is presented for an inclined buoyant jet in a current, with a three‐dimensional trajectory. The shear‐induced entrainment is computed as a function of the local densimetric Froude number and jet orientation, while the forced entrainment is taken as the ambient flow intercepted by the “windward” side of the buoyant jet. Model predictions are compared with both trajectory and tracer concentration data for a wide range of discharge and ambient flow conditions: horizontal buoyant jets in a coflow; vertical jets, oblique jets, and dense plumes in a cross flow; buoyant jets in a stagnant uniform or stratified fluid; and a horizontal buoyant jet in a perpendicular cross flow. The model is also consistent with the concept of asymptotic flow regimes, and reproduces the correct behavior in both the near and far field of a vertical momentum of buoyancy‐dominated jet in a cross flow. The connection of the model with traditional integral jet models is also discussed.

Generalized Lagrangian Model for Buoyant Jets in Current

It is well known that vortex rings are the dominant flow structures in the near field of a free jet, and this has led many researchers to believe that they also occur in a jet in cross flow (JICF). Previous studies have postulated that these vortex rings deform and fold as they convect downstream, which culminates in the formation of vortex loops at both the upstream and the lee-side of the jet column. In this paper, we take a fresh look at the vortical structures of JICF in water by releasing dye at strategic locations around the jet exit. The results show that there is no evidence of ring vortices in JICF, and the postulation that vortex loops are formed from the folding of the vortex rings does not reflect the actual flow behavior. The presence of a counter-rotating vortex pair (CVP) at the jet exit is found to inhibit the formation of the vortex rings. Instead, vortex loops are formed directly from the deformation of the cylindrical vortex sheet or jet column, without going through the vortex rings, in a process similar to the buoyant jet and wake structures studied by Perry and Lim [J. Fluid Mech. 88, 451 (1978)].

On the development of large-scale structures of a jet normal to a cross flow

A model developed to simulate the behavior of oil and gas accidentally released from deep water is presented This model presents major modifications to a three-dimensional model developed earlier (Yapa and Zheng, 1997) that simulate the behaviour of oil from under water accidents (shallow water) In deepwater, the ultra-high pressure and cold temperature causes phase changes in gases These combined with relatively strong currents in some deepwater regions presents extraordinary challenges to modeling jets/plumes from deepwater oil and gas blowouts The present model incorporates the phase changes of gas, associated changes in thermodynamics and its impact on the hydrodynamics of the jet/plume Hydrate formation, hydrate decomposition, gas dissolution, non-ideal behavior of the gas, and possible gas separation from the main plume due to strong cross currents are integrated with the jet/plume hydrodynamics and thermodynamics This paper presents the complete model development and testing of various comput

A model for simulating deepwater oil and gas blowouts - Part I: Theory and model formulation

DeepBlow – a Lagrangian Plume Model for Deep Water Blowouts

A recently-developed Lagrangian jet model (JETLAG) is combined with visualization technology to give virtual reality simulations of three-dimensional rosette-shaped jet groups issuing from ocean outfalls. The main features of the new entrainment formulation in the Lagrangian model, in particular the prediction of mixing in the weak-strong current transition, and the coflowing jet, are described. Representative comparisions of model predictions with experimental data are presented. The incorporation of computer graphic techniques to develop a PC-based, interactive flow visualization tool is summarized. The resulting model, VISJET, portrays the evolution and interaction of multiple buoyant jets discharged at different angles to the ambient tidal current. The model enables the determination of the degree of merging of the interacting plumes, and is capable of communicating the predicted environmental impact effectively to the stakeholders.

Lagrangian modelling and visualization of rosette outfall plumes

The mixing behavior of a 45° two‐dimensional buoyant jet in a linearly stratified fluid has been studied. Experimental data on the maximum height of rise and the concentration distribution of a tracer in the spreading layer are presented for the entire plume‐jet range. Characteristic variables are successfully correlated by dimensional analysis. Compared to vertical discharges, the 45° momentum jet spreads at a lower level; the spreading layer extends below the source elevation. However, the minimum dilution in the spreading layer remains unchanged. The present data, which complement previously reported data for vertical jets, are also compared with calculations of an integral jet model. The results can be used for outfall design or for the verification of detailed numerical models of turbulent buoyant jets in stratified fluid.

V. Cheung

Papers

Generalized Lagrangian Model for Buoyant Jets in Current

Lagrangian modelling and visualization of rosette outfall plumes

Inclined Plane Buoyant Jet in Stratified Fluid

Mixing of buoyancy-dominated jets in a weak current.

Mathematical modelling of a round buoyant jet in a current: an assessment