High-resolution simulations of unstable cylindrical gravity currents undergoing wandering and splitting motions in a rotating system

2018 ◽  
Vol 30 (2) ◽  
pp. 026601 ◽  
Author(s):  
Albert Dai ◽  
Ching-Sen Wu
Keyword(s):  
High Resolution ◽  
Gravity Currents ◽  
Rotating System

High-resolution simulations of cylindrical gravity currents in a rotating system

2016 ◽  
Vol 806 ◽  
pp. 71-101 ◽  
Author(s):  
Albert Dai ◽  
Ching-Sen Wu
Keyword(s):  
High Resolution ◽  
Kinetic Energy ◽  
Potential Energy ◽  
Three Dimensional ◽  
Gravity Currents ◽  
The Body ◽  
Heavy Fluid ◽  
Rotating System ◽  
Maximum Radius ◽  
Inertia Forces

Cylindrical gravity currents, produced by a full-depth lock release, in a rotating system are investigated by means of three-dimensional high-resolution simulations of the incompressible variable-density Navier–Stokes equations with the Coriolis term and using the Boussinesq approximation for a small density difference. Here, the depth of the fluid is chosen to be the same as the radius of the cylindrical lock and the ambient fluid is non-stratified. Our attention is focused on the situation when the ratio of Coriolis to inertia forces is not large, namely $0.1\leqslant {\mathcal{C}}\leqslant 0.3$, and the non-rotating case, namely ${\mathcal{C}}=0$, is also briefly considered. The simulations reproduce the major features observed in the laboratory and provide more detailed flow information. After the heavy fluid contained in a cylindrical lock is released in a rotating system, the influence of the Coriolis effects is not significant during the initial one-tenth of a revolution of the system. During the initial one-tenth of a revolution of the system, Kelvin–Helmholtz vortices form and the rotating cylindrical gravity currents maintain nearly perfect axisymmetry. Afterwards, three-dimensionality of the flow quickly develops and the outer rim of the spreading heavy fluid breaks away from the body of the current, which gives rise to the maximum dissipation rate in the system during the entire adjustment process. The detached outer rim of heavy fluid then continues to propagate outward until a maximum radius of propagation is attained. The body of the current exhibits a complex contraction–relaxation motion and new outwardly propagating pulses form regularly in a period slightly less than half-revolution of the system. Depending on the ratio of Coriolis to inertia forces, such a contraction–relaxation motion may be initiated after or before the attainment of a maximum radius of propagation. In the contraction–relaxation motion of the heavy fluid, energy is transformed between potential energy and kinetic energy, while it is mainly the kinetic energy that is consumed by the dissipation. As a new pulse initially propagates outward, the potential energy in the system increases at the expense of decreasing kinetic energy, until a local maximum of potential energy is reached. During the latter part of the new pulse propagation, the kinetic energy in the system increases at the expense of decreasing potential energy, until a local minimum of potential energy is reached and another new pulse takes form. With the use of three-dimensional high-resolution simulations, the lobe-and-cleft structure at the advancing front can be clearly observed. The number of lobes is maintained only for a limited period of time before merger between existing lobes occurs when a maximum radius of propagation is approached. The high-resolution simulations complement the existing shallow-water formulation, which accurately predicts many important features and provides insights for rotating cylindrical gravity currents with good physical assumptions and simple mathematical models.

Numerical simulations of lock-exchange compositional gravity current

2009 ◽  
Vol 635 ◽  
pp. 361-388 ◽  
Author(s):  
SENG KEAT OOI ◽  
GEORGE CONSTANTINESCU ◽  
LARRY WEBER
Keyword(s):  
High Resolution ◽  
Dissipation Rate ◽  
Friction Velocity ◽  
Gravity Current ◽  
Gravity Currents ◽  
Inviscid Limit ◽  
Grashof Number ◽  
Front Speed ◽  
Initial Volume ◽  
Bed Friction

Compositional gravity current flows produced by the instantaneous release of a finite-volume, heavier lock fluid in a rectangular horizontal plane channel are investigated using large eddy simulation. The first part of the paper focuses on the evolution of Boussinesq lock-exchange gravity currents with a large initial volume of the release during the slumping phase in which the front of the gravity current propagates with constant speed. High-resolution simulations are conducted for Grashof numbers $\sqrt {Gr}$ = 3150 (LGR simulation) and $\sqrt {Gr}$ = 126000 (HGR simulation). The Grashof number is defined with the channel depth h and the buoyancy velocity ub = $\sqrt {g'h}$ (g′ is the reduced gravity). In the HGR simulation the flow is turbulent in the regions behind the two fronts. Compared to the LGR simulation, the interfacial billows lose their coherence much more rapidly (over less than 2.5h behind the front), which results in a much faster decay of the large-scale content and turbulence intensity in the trailing regions of the flow. A slightly tilted, stably stratified interface layer develops away from the two fronts. The concentration profiles across this layer can be approximated by a hyperbolic tangent function. In the HGR simulation the energy budget shows that for t > 18h/ub the flow reaches a regime in which the total dissipation rate and the rates of change of the total potential and kinetic energies are constant in time. The second part of the paper focuses on the study of the transition of Boussinesq gravity currents with a small initial volume of the release to the buoyancy–inertia self-similar phase. When the existence of the back wall is communicated to the front, the front speed starts to decrease, and the current transitions to the buoyancy–inertia phase. Three high-resolution simulations are performed at Grashof numbers between $\sqrt {Gr}$ = 3 × 104 and $\sqrt {Gr}$ = 9 × 104. Additionally, a calculation at a much higher Grashof number ($\sqrt {Gr}$ = 106) is performed to understand the behaviour of a bottom-propagating current closer to the inviscid limit. The three-dimensional simulations correctly predict a front speed decrease proportional to t−α (the time t is measured from the release time) over the buoyancy–inertia phase, with the constant α approaching the theoretical value of 1/3 as the current approaches the inviscid limit. At Grashof numbers for which $\sqrt {Gr}$ > 3 × 104, the intensity of the turbulence in the near-wall region behind the front is large enough to induce the formation of a region containing streaks of low and high streamwise velocities. The streaks are present well into the buoyancy–inertia phase before the speed of the front decays below values at which the streaks can be sustained. The formation of the velocity streaks induces a streaky distribution of the bed friction velocity in the region immediately behind the front. This distribution becomes finer as the Grashof number increases. For simulations in which the only difference was the value of the Grashof number ($\sqrt {Gr}$ = 4.7 × 104 versus $\sqrt {Gr}$ = 106), analysis of the non-dimensional bed friction velocity distributions shows that the capacity of the gravity current to entrain sediment from the bed increases with the Grashof number. Past the later stages of the transition to the buoyancy–inertia phase, the temporal variations of the potential energy, the kinetic energy and the integral of the total dissipation rate are logarithmic.

Topographic effects on the dynamics of gravity currents in a rotating system

2005 ◽  
Vol 39 (3-4) ◽  
pp. 227-249 ◽  
Author(s):  
David Rivas ◽  
O.U. Velasco Fuentes ◽  
José Ochoa
Keyword(s):  
Gravity Currents ◽  
Topographic Effects ◽  
Rotating System

High-resolution numerical simulations of resuspending gravity currents: Conditions for self-sustainment

2005 ◽  
Vol 110 (C12) ◽  
Author(s):  
F. Blanchette ◽  
M. Strauss ◽  
E. Meiburg ◽  
B. Kneller ◽  
M. E. Glinsky
Keyword(s):  
High Resolution ◽  
Numerical Simulations ◽  
Gravity Currents

scholarly journals High Resolution Simulations of Particle-Driven Gravity Currents

2005 ◽  
Author(s):  
Eckart Meiburg ◽  
F. Blanchette ◽  
M. Strauss ◽  
B. Kneller ◽  
M. E. Glinsky ◽  
...  
Keyword(s):  
High Resolution ◽  
Particle Concentration ◽  
Slope Angle ◽  
Fluid Motion ◽  
Spectral Element ◽  
Gravity Currents ◽  
Turbidity Currents ◽  
Clear Fluid ◽  
Small Density ◽  
Element Technique

High-resolution simulations of particle-driven gravity currents are presented. The study concentrates on dilute flows with small density differences between particle-laden and clear fluid. Moreover, particles are considered which have negligible inertia, and which are much smaller than the smallest length scales of the buoyancy-induced fluid motion. The governing equations are integrated numerically with a high-order mixed spectral/spectral-element technique. In the analysis of the results, special emphasis is placed on the sedimentation and resuspension of the particles, and on their feedback on the flow dynamics. Resuspension is modeled as a diffusive flux of particles through the bottom boundary. The conditions under which turbidity currents may become self-sustaining through particle entrainment are investigated as a function of slope angle, current and particle size, and particle concentration.

On the formation and propagation of nonlinear internal boluses across a shelf break

2007 ◽  
Vol 577 ◽  
pp. 137-159 ◽  
Author(s):  
SUBHAS K. VENAYAGAMOORTHY ◽  
OLIVER B. FRINGER
Keyword(s):  
High Resolution ◽  
Gravity Waves ◽  
Three Dimensional ◽  
Internal Gravity Waves ◽  
Gravity Currents ◽  
Interaction Process ◽  
Shelf Break ◽  
Ambient Fluid ◽  
Dense Fluid ◽  
Incident Waves

High-resolution two- and three-dimensional numerical simulations are performed of first-mode internal gravity waves interacting with a shelf break in a linearly stratified fluid. The interaction of nonlinear incident waves with the shelf break results in the formation of upslope-surging vortex cores of dense fluid (referred to here as internal boluses) that propagate onto the shelf. This paper primarily focuses on understanding the dynamics of the interaction process with particular emphasis on the formation, structure and propagation of internal boluses onshelf. A possible mechanism is identified for the excitation of vortex cores that are lifted over the shelf break, from where (from the simplest viewpoint) they essentially propagate as gravity currents into a linearly stratified ambient fluid.

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