Lock-exchange flows in sloping channels

Abstract

Two-dimensional variable-density Navier-Stokes simulations have been conducted in order to investigate the effects of a slope on the classical lock-exchange flow. Simulations of full lock releases show that the flow goes through an initial quasisteady phase that is characterized by a constant front velocity. This quasi-steady front velocity has a maximum for slope angles around 40• , and it persists up to a dimensionless time of the order of 10. The flow subsequently undergoes a transition to a second phase with a larger, unsteady, front velocity. These computational findings were confirmed by experimental observations of lock-exchange flows in a tube of circular cross-section.The reason for the observed transition from a quasi-steady front velocity to a larger, unsteady, value is found in the continuous acceleration of the stratified fluid layers connecting the two fronts by the streamwise component of the gravity vector. This acceleration leads to a situation where the fluid layers behind the current front move faster than the front itself. Initially the resulting addition of fluid to the current front from behind affects only the size of the front, while its velocity remains unchanged. Eventually, the current front is unable to absorb more fluid from behind and its velocity has to increase, thereby triggering the transition to the second, unsteady, phase. The transition time is determined as a function of the slope and the density ratio of the two fluids. For increasing density contrast, the transition is seen to occur earlier for the denser current.Conceptually simple models based on the analysis by Thorpe (1968) are compared with simulation results for the flow in the region connecting the fronts. For the early stages of the flow a two-layer stratification model is found to be appropriate, while the later stages require a three-layer stratification model, owing to the intense mixing in the central part of the channel cross-section. These models are employed to estimate the time after which the accelerating stratified fluid layers will affect the velocities of the current fronts. They provide upper and lower estimates for the transition time which are in good agreement with the simulation results.

TURBINS: An immersed boundary, Navier–Stokes code for the simulation of gravity and turbidity currents interacting with complex topographies

“…13. Sketch of the grid alignment employed in the two gravity current simulations in a sloping channel, (a) present study, based on immersed boundary approach; (b) the configuration used by [4], in which the gravity vector is rotated by h, so that the coordinate directions are aligned with the container walls.…”

“…This flow configuration was investigated in detail by Birman et al [4], who performed Navier-Stokes simulations to study the effect of the slope angle h on lock-exchange gravity currents. Those authors employed a Cartesian grid that was aligned with the container walls in the x-and y-directions, so that the gravity vector g contributed to both the x-and the y-momentum equations.…”

“…Comparison of the gravity current concentration fields (white corresponds to c = 0 and black to c = 1) in a sloping channel with h = 15 o and Re = 750, obtained via two different numerical approaches, (a) present immersed boundary approach, (b) coordinates aligned with container walls ([4]). Good agreement is observed even for the small scales of the concentration field.…”

Miscible displacement flows in near-horizontal ducts at low Atwood number

“…There are also many general studies of buoyancy-driven flows of miscible Newtonian fluids over near-horizontal surfaces in oceanographic, meteorological and geophysical contexts, e.g. Benjamin (1968); Hoult (1972); Didden & Maxworthy (1982); Simpson (1997); Shin et al (2004); Birman et al (2005Birman et al ( , 2007.…”

Experimental and numerical investigations of flow structure and momentum transport in a turbulent buoyancy-driven flow inside a tilted tube

“…Here we are specifically interested in steady turbulent mixing flows observed in this geometry at small tilt angles with respect to the vertical in presence of a significant density contrast. 8 More specifically we perform lock-exchange laboratory experiments and computations, [9][10][11] in which each fluid initially fills one-half of the tube length and is set in contact with the other fluid at a time t =0 ͑see Fig. 1͒.…”