Dynamics of Two-Dimensional Turbulent Bottom Gravity Currents

In light of previous numerical studies demonstrating a strong sensitivity of the strength of thermohaline circulation to the representation of overflows in ocean general circulation models, the dynamics of bottom gravity currents are investigated using a two-dimensional, nonhydrostatic numerical model. The model explicitly resolves the Kelvin‐Helmholtz instability, the main mechanism of mixing in nonrotating bottom gravity currents. A series of experiments were conducted to explore the impact of density difference and slope angle on the dynamics of bottom gravity currents in a nonrotating and homogeneous environment. The features of the simulated currents; that is, a characteristic head at the leading edge and lumped vortices in the trailing fluid, agree qualitatively well with those observed in laboratory experiments. Quantitative comparisons of speed of descent indicate that laboratory results remain valid at geophysical scales. Two distinct regimes of entrainment of ambient fluid into bottom gravity currents are identified: (i) the laminar entrainment regime is associated with the initial growth of the characteristic head due to the drag exerted by the fresh fluid in front and (ii) the turbulent entrainment is associated with the Kelvin‐Helmholtz instabilities. The turbulent entrainment is found to be much stronger than the laminar entrainment, and entrainment in the turbulent regime is less sensitive to the slope angle than that in the laminar regime. The entrainment is quantified as a function of basic parameters of the system, the buoyancy flux and the slope angle, for the purpose of parameterizing the mixing induced by bottom gravity currents.

[1]  Lin Jiang,et al.  Three-Dimensional Simulations of Overflows on Continental Slopes , 1996 .

[2]  G. M. Corcos,et al.  The mixing layer: deterministic models of a turbulent flow. Part 1. Introduction and the two-dimensional flow , 1984, Journal of Fluid Mechanics.

[3]  Lin Jiang,et al.  A numerical study of three-dimensional dense bottom plumes on a Southern Ocean continental slope , 1995 .

[4]  Smith.  Maximization of vortex entropy as an organizing principle in intermittent, decaying, two-dimensional turbulence. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[5]  M. Lozier,et al.  The climatology of the North Atlantic , 1995 .

[6]  E. Chassignet,et al.  On the Connection between the Mediterranean Outflow and the Azores Current , 2001 .

[7]  G. V. Heijst,et al.  Interacting two-dimensional vortex structures: Point vortices, contour kinematics and stirring properties , 1994 .

[8]  G. Marmorino.  Observations of Small-Scale Mixing Processes in the Seasonal Thermocline, Part II: Wave Breaking , 1987 .

[9]  Gerard V. Middleton,et al.  Experiments on density and turbidity currents, I.Motion of the head , 1966 .

[10]  Stuart B. Dalziel,et al.  Mixing in lock-release gravity currents , 1996 .

[11]  Harry L. Bryden,et al.  Ocean heat transport across 24゜ N in the Pacific , 1991 .

[12]  T. Özgökmen,et al.  A numerical study of layer formation due to fingers in double-diffusive convection in a vertically-bounded domain , 1998 .

[13]  H. Huppert.  The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface , 1982, Journal of Fluid Mechanics.

[14]  Glen Gawarkiewicz,et al.  A numerical study of dense water formation and transport on a shallow, sloping continental shelf , 1995 .

[15]  J. Backhaus,et al.  Application of a transient reduced gravity plume model to the Denmark Strait Overflow , 1994 .

[16]  Jean-Marc Molines,et al.  Circulation characteristics in three eddy-permitting models of the North Atlantic , 2001 .

[17]  Asymmetric salt fingers induced by a nonlinear equation of state , 1998 .

[18]  G. Johnson,et al.  Mediterranean Outflow Mixing and Dynamics , 1993, Science.

[19]  J. Rasmussen,et al.  Formation and temporal evolution of the Lamb-dipole , 1997 .

[20]  P. Killworth.  Mixing of the Weddell Sea continental slope , 1977 .

[21]  J. Gazdag.  Time-differencing schemes and transform methods , 1976 .

[22]  Rex Britter,et al.  The dynamics of the head of a gravity current advancing over a horizontal surface , 1979, Journal of Fluid Mechanics.

[23]  J. Turner,et al.  Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows , 1986, Journal of Fluid Mechanics.

[24]  W. Rockwell Geyer,et al.  Gravity currents: In the environment and the laboratory , 1989 .

[25]  Eric P. Chassignet,et al.  Emergence of inertial gyres in a two-layer quasigeostrophic ocean model , 1998 .

[26]  Harry L. Bryden,et al.  Steady two-layer exchange through the Strait of Gibraltar , 1991 .

[27]  W. Johns,et al.  Direct observations of seasonal exchange through the Bab el Mandab Strait , 1997 .

[28]  G. Flierl,et al.  The physical significance of modons: Laboratory experiments and general integral constraints , 1983 .

[29]  Rex Britter,et al.  The motion of the front of a gravity current travelling down an incline , 1980, Journal of Fluid Mechanics.

[30]  Herbert E. Huppert,et al.  Entrainment into two-dimensional and axisymmetric turbulent gravity currents , 1996, Journal of Fluid Mechanics.

[31]  M. Baringer,et al.  Momentum and Energy Balance of the Mediterranean Outflow , 1997 .

[32]  J. Simpson,et al.  Gravity currents in the laboratory, atmosphere, and ocean , 1982 .

[33]  Roland W. Garwood,et al.  Effects of topographic steering and ambient stratification on overflows on continental slopes: A model study , 1998 .

[34]  J. Simpson,et al.  A comparison between laboratory and atmospheric density currents , 1969 .

[35]  A. Arakawa.  Computational design for long-term numerical integration of the equations of fluid motion: two-dimen , 1997 .

[36]  E. Hopfinger,et al.  Gravity currents moving along a lateral boundary in a rotating fluid , 1983, Journal of Fluid Mechanics.

[37]  Yanli Jia.  Formation of an Azores Current Due to Mediterranean Overflow in a Modeling Study of the North Atlantic , 2000 .

[38]  P. Swarztrauber.  THE METHODS OF CYCLIC REDUCTION, FOURIER ANALYSIS AND THE FACR ALGORITHM FOR THE DISCRETE SOLUTION OF POISSON'S EQUATION ON A RECTANGLE* , 1977 .

[39]  M. Baringer,et al.  Mixing and Spreading of the Mediterranean Outflow , 1997 .

[40]  A. Watson,et al.  Deep-water renewal in the northern North Atlantic , 1990, Nature.

[41]  J. Turner,et al.  Turbulent entrainment in stratified flows , 1959, Journal of Fluid Mechanics.

[42]  Andrew Kos,et al.  Gravity currents descending a ramp in a stratified tank , 1999, Journal of Fluid Mechanics.

[43]  Molly O. Baringer,et al.  Outflows and deep water production by marginal seas , 1994 .

[44]  Geoffrey Ingram Taylor,et al.  Turbulent gravitational convection from maintained and instantaneous sources , 1956, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[45]  J. Turner,et al.  The ‘starting plume’ in neutral surroundings , 1962, Journal of Fluid Mechanics.

[46]  Robert Hallberg,et al.  Simulation of Density-Driven Frictional Downslope Flow in Z-Coordinate Ocean Models , 1998 .

[47]  J. Price,et al.  Marginal Sea Overflows for Climate Simulations , 1998 .

[48]  R. W. Griffiths.  Gravity Currents in Rotating Systems , 1986 .

[49]  Eric P. Chassignet,et al.  Impact of wind forcing, bottom topography, and inertia on midlatitude jet separation in a quasigeostrophic model , 1997 .

[50]  Rex Britter,et al.  Experiments on the dynamics of a gravity current head , 1978, Journal of Fluid Mechanics.

[51]  Peter C. Smith,et al.  A streamtube model for bottom boundary currents in the ocean , 1975 .

[52]  P. Lundberg,et al.  On the deep‐water flow through the Faroe Bank Channel , 1988 .

[53]  T. Kao,et al.  Inflows, density currents, and fronts , 1978 .

[54]  Andrew J. Watson,et al.  Evidence for slow mixing across the pycnocline from an open-ocean tracer-release experiment , 1993, Nature.