Numerical study of the collapse of an axisymmetric mixed region in a pycnocline

Terez, Dmitry; Knio, Omar M.

doi:10.1063/1.869666

Cited by 5 publications

(2 citation statements)

References 13 publications

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“…During the adjustment process the isopycnals overshoot their equilibrium positions, and this results in the generation of internal waves, clearly illustrated by the elongated, inclined ω θ -andρ-patches at t = 2. Similar adjustment processes to localized perturbations of the density distribution of a stratified fluid have been reported by Wu (1969), Hartman & Lewis (1972) and Terez & Knio (1998). These papers describe the response of a stratified fluid to the presence of a region with partially mixed or homogeneous fluid.…”

Section: Initial Conditionssupporting

confidence: 69%

Dynamics of pancake-like vortices in a stratified fluid: experiments, model and numerical simulations

et al. 2001

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The dynamics and the three-dimensional structure of vortices in a linearly stratified, non-rotating fluid are investigated by means of laboratory experiments, an analytical model and through numerical simulations. The laboratory experiments show that such vortices have a thin pancake-like appearance. Due to vertical diffusion of momentum the strength of these vortices decreases rapidly and their thickness increases in time. Also it is found that inside a vortex the linear ambient density profile becomes perturbed, resulting in a local steepening of the density gradient. Based on the assumption of a quasi-two-dimensional axisymmetric flow (i.e. with zero vertical velocity) a model is derived from the Boussinesq equations that illustrates that the velocity field of the vortex decays due to diffusion and that the vortex is in so-called cyclostrophic balance. This means that the centrifugal force inside the vortex is balanced by a pressure gradient force that is provided by a perturbation of the density profile in a way that is observed in the experiments. Numerical simulations are performed, using a finite difference method in a cylindrical coordinate system. As an initial condition the three-dimensional vorticity and density structure of the vortex, found with the diffusion model, are used. The influence of the Froude number, Schmidt number and Reynolds number, as well as the initial thickness of the vortex, on the evolution of the flow are investigated. For a specific combination of flow parameters it is found that during the decay of the vortex the relaxation of the isopycnals back to their undisturbed positions can result in a stretching of the vortex. Potential energy of the perturbed isopycnals is then converted into kinetic energy of the vortex. However, when the stratification is strong enough (i.e. for small Froude numbers), the evolution of the vortex can be described almost perfectly by the diffusion model alone.

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Section: Initial Conditionssupporting

confidence: 69%

Dynamics of pancake-like vortices in a stratified fluid: experiments, model and numerical simulations

et al. 2001

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“…A number of numerical simulations have reported on gravity currents. Many of these computation have focused on two‐dimensional models of planar current [ Daly and Pracht , 1968; Droegemeier and Wilhelmson , 1986, 1987; Terez and Knio , 1998b, 1998a; Hallworth et al , 2001; Choi and García , 2002; Özgökmen and Chassignet , 2002; Ungarish and Zemach , 2003; Birman et al , 2005]. At sufficiently large Reynolds numbers, gravity currents are strongly three‐dimensional and fully turbulent, and in such situations two‐dimensionality of the current is only in a statistical sense.…”

Section: Introductionmentioning

confidence: 99%

Turbulent structures in planar gravity currents and their influence on the flow dynamics

Cantero¹,

Balachandar²,

García³

et al. 2008

J. Geophys. Res.

107

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[1] Direct numerical simulations (DNS) of planar gravity current in the Boussinesq limit have been conducted with the objective of identifying, visualizing, and describing turbulent structures and their influence on the flow dynamics. The simulations are performed for Reynolds numbers of Re = 8950 and Re = 15,000 with 31-and 131-million grid point resolutions, respectively. This range of Reynolds numbers ensures fully developed turbulent gravity currents, which have never been simulated before using DNS. The flow develops zones with different turbulence characteristics, which eventually interact with each other. The near-wall bottom flow resembles boundary layer flow with several hairpin-like vortices oriented in the direction of the flow and preferential patterns of low-and high-speed streaks. The separation between low-speed streaks at the front scales with the lobe size, which is about 200 wall units for Re = 15,000. Upstream of the front, the separation between low-speed streaks scales with the well-accepted value of 100 wall units for turbulent boundary layers. These patterns have associated regions of low and high bottom shear stresses with implications for sediment erosion and bed load transport. Most of the erosive power of the flow is found in the gravity current front. The interface between heavy and light fluids rolls up by baroclinic generation of KelvinHelmholtz vortices, which undergo sudden breakup and decay to small-scale turbulence. The effect of turbulence and three-dimensionality on the flow dynamics is addressed by comparing two-and three-dimensional simulations. Three-dimensional simulations present active mechanisms that undermine the strong flow coherence, comparing well with experimental observations.

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On the front velocity of gravity currents

et al. 2007

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Highly resolved three-dimensional and two-dimensional simulations of gravity currents in planar and cylindrical configurations are presented. The volume of release of the heavy fluid is varied and the different phases of spreading, namely acceleration, slumping, inertial and viscous phases, are studied. The incompressible Navier–Stokes equations are solved assuming that the Boussinesq approximation is valid for small density difference. The simulations are performed for three different Reynolds numbers (Re): 895, 3450 and 8950 (this particular choice corresponds to values of Grashof number: 105, 1.5 × 106 and 107, respectively). Following their sudden release, the gravity currents are observed to go through an acceleration phase in which the maximum front velocity is reached. As the interface of the current rolls up, the front velocity slightly decreases from the maximum and levels off to a nearly constant value. At higher Re, three-dimensional disturbances grow rapidly and the currents become strongly turbulent. In contrast, in two-dimensional simulations, the rolled-up vortices remain coherent and very strong. Depending on the initial Re of the flow and on the size of the release, the current may transition from the slumping to the inertial phase, or directly to the viscous phase without an inertial phase. New criteria for the critical Re are introduced for the development of the inertial phase. Once the flow transitions to the inertial or viscous phase, it becomes fully three-dimensional. During these phases of spreading, two-dimensional approximations underpredict the front location and velocity. The enhanced vortex coherence of the two-dimensional simulations leads to strong vortex interaction and results in spurious strong time variations of the front velocity. The structure and dynamics of the three-dimensional currents are in good agreement with previously reported numerical and experimental observations.

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Numerical study of the collapse of an axisymmetric mixed region in a pycnocline

Cited by 5 publications

References 13 publications

Dynamics of pancake-like vortices in a stratified fluid: experiments, model and numerical simulations

Dynamics of pancake-like vortices in a stratified fluid: experiments, model and numerical simulations

Turbulent structures in planar gravity currents and their influence on the flow dynamics

On the front velocity of gravity currents

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