Summary & Conclusions

Unsteady density current confluences are studied in this work, where two identical density currents initiated by lock-exchange combine in a horizontal, asymmetrical junction before continuing downstream as a combined current. The study focuses on simulations which are validated experimentally. Findings are assessed in terms of the initial conditions including the initial density difference, depth of the channel, and junction angle.

The unsteady phenomena was studied through numerical simulation using the continuum mechanics toolbox, OpenFOAM. The solver,twoLiquidMixingFoam, solves the unsteady, incompressible Navier-Stokes equations. Turbulence modeling was handled with a large-eddy-simulation approach and Smagorinsk-Lilly subgrid scale clo- sure. In addition to the Navier-Stokes equations, the solver evaluated the species continuity equation to conserve mass of a dissolved species or heat in a separate con- servation equation. The species concentration determines the bulk density of each cell in the computational grid which drives density current flows.

The governing equations were solved using the PIMPLE algorithm which merges the PISO and SIMPLE algorithms. PIMPLE takes advantage of the implicit predictor- explicit corrector steps of PISO while incorporating relaxation factors from the SIM- PLE algorithm for smooth solution convergence. To solve discretized equations, the GAMG and Gauss-Seidel smooth solvers were used. Time discretization was handled using the first-order accurate Euler scheme.

The 45◦ junction flume was equipped with a gate along each upstream reach of the channel network with salt water (density = 1035 kg/m3_{) in each lock to a prescribed} depth and ambient water downstream of the lock gates. Three experiments were run: two experiments involved a full-depth lock-exchange test with equal initial conditions to verify repeatability of the experiments, and the third test was a partial-depth release with the dense fluid equal to half the depth of ambient fluid. Numerical simulation of the conditions of the physical experiments matchethe results well, thus it was concluded that the numerical model is capable of capturing the flow phenomena in terms of the bulk properties. To ensure the proposed solution grid accurately captured the flow phenomena, the numerical simulations were retested with a refined grid. When plotted together, little difference was observed in the bulk property results between the base grid and refined grid.

Once the numerical model and proposed grid were validated, the numerical model was applied to the case of 45◦junction angles with variable initial density and channel depth. Nine cases of full-depth density currents and three cases of partial-depth density currents were tested. It was observed that when the two currents reach the junction zone, the front velocity and thickness of the current increase in all cases. Once the combined current continues downstream, an elevated plume of dense fluid remains in the junction zone for the full-depth cases, whereas the thickest part of the current is always close to the front position for the partial-depth cases.

When the bulk property results are nondimensionalized, no dependence on initial density was observed. The channel depth does play a role in the bulk properties; specifically, the front position is further downstream with increasing channel depth. Additionally, the thickest part of the current remained further behind the nose of the current with higher channel depth.

junction. The post-confluence constant front velocity approaches a constant value of 0.56 at large initial Reynolds numbers, but decreases at lower values of Re.

The study of density current confluences is extended to cases of variable junction angle. Along with varying initial density and channel depth, five junction angles are tested for a total of 45 simulations. The trends in the bulk properties at each junction angle are similar to those observed for the 45◦ case with little dependence on initial density. The most apparent effect of increasing the junction angle is a higher peak front velocity during reacceleration, and larger front thickness in the junction zone.

A parameter is proposed to combine the initial density, channel depth, and junction angle which gives a representation of the inertia entering the junction in the main-channel downstream direction. It is defined as ˆRe0 = Re0[1 +cos(θ)]. The peak current and plume thicknesses both are indirectly correlated to ˆRe0, and trend lines are fit to the results. The peak horizontal velocity associated with the influx of energy from the side channel and the peak horizontal velocity associated with con- finement of the combined mass of dense fluid to the width of the downstream channel both decrease with increasing ˆRe0. At high values of ˆRe0, the peak nose height and constant downstream nose height both are constant, and downstream front velocity also becomes constant. At lower values of ˆRe0, the nose heights increase, and the constant downstream froude number decreases.

Combining the observations from this work results in several general properties of the role of the confluence in the pre- and post-confluence density currents which can be summarized as follows.

• In all cases, the junction causes reacceleration of the front as well as an increase in current thickness; both the peak front velocity and peak current thickness increase at higher junction angles.

junction point.

• For the range of densities tested, the effect of the junction is independent of the initial density difference when bulk properties are nondimensionalized by the initial conditions.

• The only major distinction between the full-depth and partial-depth cases is that the latter does not leave an elevated plume in the junction zone, thus the front is the thickest part of the current at all times.

• The peak current thickness and peak near-bed horizontal velocity both decrease at larger values of ˆRe0. This should be expected since ˆRe0 increases with decreasing junction angle where the competition in the junction zone is less or- thogonal, thus horizontal velocity components from the main- and side-channels are superimposed.

• The effect of the initial conditions on the confluence behavior is only local at high Reynolds numbers which is demonstrated by the peak Froude number being dependent on channel depth and junction angle in the junction, but the constant post-confluence downstream front velocity remains unchanged with Reynolds number. Furthermore, the near-bed horizontal velocity converges to a single value in the downstream reach regardless of initial conditions.

The work presented here gives a deeper understanding of the role of the junction and initial conditions on the confluence of unsteady density current fronts. With the conclusions and understanding presented in terms the general behavior of the currents and bulk properties, further studies can now be conducted to assess specific problems related to the flow phenomena. These can include detailed studies of mixing in the junction, confluences of steady density current flows, cases with sloping and erodible

other than the constant velocity phase. With this and further studies, the findings can be applied to specific observations of density currents in natural systems such as salt-wedge flows into coastal channel networks and turbidity current confluences in submarine channel systems.

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