scholarly journals Gravity currents and internal waves in a stratified fluid

2008 ◽  
Vol 616 ◽  
pp. 327-356 ◽  
Author(s):  
BRIAN L. WHITE ◽  
KARL R. HELFRICH
Keyword(s):  
Internal Waves ◽  
Wave Speed ◽  
Numerical Solutions ◽  
Gravity Current ◽  
Gravity Currents ◽  
Stratified Fluid ◽  
Front Speed ◽  
Long Wave ◽  
Conjugate State ◽  
Energy Conserving

A steady theory is presented for gravity currents propagating with constant speed into a stratified fluid with a general density profile. Solution curves for front speed versus height have an energy-conserving upper bound (the conjugate state) and a lower bound marked by the onset of upstream influence. The conjugate state is the largest-amplitude nonlinear internal wave supported by the ambient stratification, and in the limit of weak stratification approaches Benjamin's energy-conserving gravity current solution. When the front speed becomes critical with respect to linear long waves generated above the current, steady solutions cannot be calculated, implying upstream influence. For non-uniform stratification, the critical long-wave speed exceeds the ambient long-wave speed, and the critical-Froude-number condition appropriate for uniform stratification must be generalized. The theoretical results demonstrate a clear connection between internal waves and gravity currents. The steady theory is also compared with non-hydrostatic numerical solutions of the full lock release initial-value problem. Some solutions resemble classic gravity currents with no upstream disturbance, but others show long internal waves propagating ahead of the gravity current. Wave generation generally occurs when the stratification and current speed are such that the steady gravity current theory fails. Thus the steady theory is consistent with the occurrence of either wave-generating or steady gravity solutions to the dam-break problem. When the available potential energy of the dam is large enough, the numerical simulations approach the energy-conserving conjugate state. Existing laboratory experiments for intrusions and gravity currents produced by full-depth lock exchange flows over a range of stratification profiles show excellent agreement with the conjugate state solutions.

The front speed of intrusions into a continuously stratified medium

2007 ◽  
Vol 594 ◽  
pp. 369-377 ◽  
Author(s):  
DIOGO BOLSTER ◽  
ALICE HANG ◽  
P. F. LINDEN
Keyword(s):  
Numerical Simulations ◽  
Gravity Current ◽  
Gravity Currents ◽  
Stratified Fluid ◽  
Stratified Medium ◽  
Fluid Density ◽  
Neutral Buoyancy ◽  
Front Speed ◽  
Predicted Values ◽  
Good Agreement

This paper examines intrusive Boussinesq gravity currents, propagating into a continuously stratified fluid. We develop a model, based on energy arguments, to predict the front speed of such an intrusive gravity current from a lock release. We find that the depth at which the intrusion occurs, which corresponds to the level of neutral buoyancy (i.e. the depth where the intrusion density equals the stratified fluid density), affects the front speed. The maximum speeds occur when the intrusion travels along the top and bottom boundaries and the minimum speed occurs at mid-depth. Experiments and numerical simulations were conducted to compare to the theoretically predicted values, and good agreement was found.

A Laboratory Study of the Velocity Structure in an Intrusive Gravity Current

2000 ◽  
Author(s):  
Ryan J. Lowe
Keyword(s):  
Particle Tracking ◽  
Laboratory Experiments ◽  
Velocity Structure ◽  
Gravity Current ◽  
Current Theory ◽  
Head Region ◽  
Front Speed ◽  
Energy Conserving ◽  
The Stability ◽  
Lock Gate

Abstract Laboratory experiments were performed in which an intrusive gravity current was observed using shadowgraph and particle tracking methods. The intrusion was generated in a two-layer fluid with a sharp interface by mixing the fluid behind a vertical lock-gate and then suddenly withdrawing the gate from the tank. The purpose of the experiments is to determine the structure of the velocity field inside the intrusion as well as the stability characteristics of the interface. Soon after the removal of the lock-gate the speed of the front of the intrusive gravity current reached a constant speed. The observed structure of the flow inside the intrusion shows a “head region” where the flow is nearly uniform, followed by a region of intense mixing and high velocities and finally followed by another region of fairly uniform velocity with a speed slightly faster than the front speed. The results show that the maximum centerline velocity is about 50% greater than the front speed and corresponds to the position in the intrusion where the strongest Kelvin- Helmholtz billows form. Closer to the front, the relative flow within the head is weak, which explains why Benjamin’s (1968) energy-conserving gravity current theory accurately predicts the behavior of dissipative gravity currents.

Gravity currents and related phenomena

1968 ◽  
Vol 31 (2) ◽  
pp. 209-248 ◽  
Author(s):  
T. Brooke Benjamin
Keyword(s):  
Salt Water ◽  
Gravity Current ◽  
Circular Cross Section ◽  
Gravity Currents ◽  
Head Wave ◽  
Physical Problems ◽  
Energy Conserving ◽  
Fluid Theory ◽  
Hydrodynamical Problem ◽  
Upper Boundary

This paper presents a broad investigation into the properties of steady gravity currents, in so far as they can be represented by perfect-fluid theory and simple extensions of it (like the classical theory of hydraulic jumps) that give a rudimentary account of dissipation. As usually understood, a gravity current consists of a wedge of heavy fluid (e.g. salt water, cold air) intruding into an expanse of lighter fluid (fresh water, warm air); but it is pointed out in § 1 that, if the effects of viscosity and mixing of the fluids at the interface are ignored, the hydrodynamical problem is formally the same as that for an empty cavity advancing along the upper boundary of a liquid. Being simplest in detail, the latter problem is treated as a prototype for the class of physical problems under study: most of the analysis is related to it specifically, but the results thus obtained are immediately applicable to gravity currents by scaling the gravitational constant according to a simple rule.In § 2 the possible states of steady flow in the present category between fixed horizontal boundaries are examined on the assumption that the interface becomes horizontal far downstream. A certain range of flows appears to be possible when energy is dissipated; but in the absence of dissipation only one flow is possible, in which the asymptotic level of the interface is midway between the plane boundaries. The corresponding flow in a tube of circular cross-section is found in § 3, and the theory is shown to be in excellent agreement with the results of recent experiments by Zukoski. A discussion of the effects of surface tension is included in § 3. The two-dimensional energy-conserving flow is investigated further in § 4, and finally a close approximation to the shape of the interface is obtained. In § 5 the discussion turns to the question whether flows characterized by periodic wavetrains are realizable, and it appears that none is possible without a large loss of energy occurring. In § 6 the case of infinite total depth is considered, relating to deeply submerged gravity currents. It is shown that the flow must always feature a breaking ‘head wave’, and various properties of the resulting wake are demonstrated. Reasonable agreement is established with experimental results obtained by Keulegan and others.

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.

A laboratory study of the velocity structure in an intrusive gravity current

2002 ◽  
Vol 456 ◽  
pp. 33-48 ◽  
Author(s):  
RYAN J. LOWE ◽  
P. F. LINDEN ◽  
JAMES W. ROTTMAN
Keyword(s):  
Velocity Field ◽  
Velocity Structure ◽  
Fluid Velocity ◽  
Gravity Current ◽  
Maximum Speed ◽  
Wake Region ◽  
Tail Region ◽  
Front Speed ◽  
Energy Conserving ◽  
Lock Gate

Laboratory experiments were performed in which an intrusive gravity current was observed using shadowgraph and particle tracking methods. The intrusion was generated in a two-layer fluid with a sharp interface by mixing the fluid behind a vertical lock gate and then suddenly withdrawing the gate from the tank. The purpose of the experiments was to determine the structure of the velocity field inside the intrusion and the stability characteristics of the interface. Soon after the removal of the lock gate, the front of the intrusive gravity current travelled at a constant speed close to the value predicted by theory for an energy-conserving gravity current. The observed structure of the flow inside the intrusion can be divided into three regions. At the front of the intrusion there is an energy-conserving head region in which the fluid velocity is nearly uniform with speed equal to the front speed. This is followed by a dissipative wake region in which large billows are present with their associated mixing and in which the fluid velocity is observed to be non-uniform and have a maximum speed approximately 50% greater than the front speed. Behind the wake region is a tail region in which there is very little mixing and the velocity field is nearly uniform with a speed slightly faster than the front speed.

The distortion of short internal waves produced by a long wave, with application to ocean boundary mixing

1989 ◽  
Vol 208 ◽  
pp. 395-415 ◽  
Author(s):  
S. A. Thorpe
Keyword(s):  
Density Gradient ◽  
Internal Waves ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Finite Amplitude ◽  
Constant Density ◽  
Boundary Mixing ◽  
Short Waves ◽  
Long Wave ◽  
Boussinesq Fluid

The propagation of a train of short, small-amplitude, internal waves through a long, finite-amplitude, two-dimensional, internal wave is studied. An exact solution of the equations of motion for a Boussinesq fluid of constant density gradient is used to describe the long wave, and its distortion of the density gradient as well as its velocity field are accounted for in determining the propagation characteristics of the short waves. To illustrate the magnitude of the effects on the short waves, particular numerical solutions are found for short waves generated by an idealized flow induced by a long wave adjacent to sloping, sinusoidal topography in the ocean, and the results are compared with a laboratory experiment. The theory predicts that the long wave produces considerably distortion of the short waves, changing their amplitudes, wavenumbers and propagation directions by large factors, and in a way which is generally consistent with, but not fully tested by, the observations. It is suggested that short internal waves generated by the interaction of relatively long waves with a rough sloping topography may contribute to the mixing observed near continental slopes.

scholarly journals Lifecycle of a Submesoscale Front Birthed from a Nearshore Internal Bore

2021 ◽  
Author(s):  
Sean R. Haney ◽  
Alexandra J. Simpson ◽  
Jacqueline M. McSweeney ◽  
Amy F. Waterhouse ◽  
Merrick C. Haller ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Wave Speed ◽  
Gravity Current ◽  
Gravity Currents ◽  
Coastal Ocean ◽  
Rossby Number ◽  
Lateral Shear ◽  
Turbulent Dissipation ◽  
Shear Instabilities ◽  
Internal Bore

AbstractThe ocean is home to many different submesoscale phenomena, including internal waves, fronts, and gravity currents. Each of these processes entail complex nonlinear dynamics, even in isolation. Here we present shipboard, moored, and remote observations of a submesoscale gravity current front created by a shoaling internal tidal bore in the coastal ocean. The internal bore is observed to flatten as it shoals, leaving behind a gravity current front that propagates significantly slower than the bore. We posit that the generation and separation of the front from the bore is related to particular stratification ahead of the bore, which allows the bore to reach the maximum possible internal wave speed. After the front is calved from the bore, it is observed to propagate as a gravity current for ≈4 hours, with associated elevated turbulent dissipation rates. A strong cross-shore gradient of along-shore velocity creates enhanced vertical vorticity (Rossby number ≈ 40) that remains locked with the front. Lateral shear instabilities develop along the front and may hasten its demise.

Intrusive gravity currents from finite-length locks in a uniformly stratified fluid

2009 ◽  
Vol 635 ◽  
pp. 245-273 ◽  
Author(s):  
J. R. MUNROE ◽  
C. VOEGELI ◽  
B. R. SUTHERLAND ◽  
V. BIRMAN ◽  
E. H. MEIBURG
Keyword(s):  
Numerical Simulations ◽  
Internal Waves ◽  
Laboratory Experiments ◽  
Wave Speed ◽  
Gravity Currents ◽  
Fluid Density ◽  
Ambient Fluid ◽  
Experimental Conditions ◽  
Mode 2 ◽  
The Waves

Gravity currents intruding into a uniformly stratified ambient are examined in a series of finite-volume full-depth lock-release laboratory experiments and in numerical simulations. Previous studies have focused on gravity currents which are denser than fluid at the bottom of the ambient or on symmetric cases in which the intrusion is the average of the ambient density. Here, we vary the density of the intrusion between these two extremes. After an initial adjustment, the intrusions and the internal waves they generate travel at a constant speed. For small departures from symmetry, the intrusion speed depends weakly upon density relative to the ambient fluid density. However, the internal wave speed approximately doubles as the waves change from having a mode-2 structure when generated by symmetric intrusions to having a mode-1 structure when generated by intrusions propagating near the bottom. In the latter circumstance, the interactions between the intrusion and internal waves reflected from the lock-end of the tank are sufficiently strong and so the intrusion stops propagating before reaching the end of the tank. These observations are corroborated by the analysis of two-dimensional numerical simulations of the experimental conditions. These reveal a significant transfer of available potential energy to the ambient in asymmetric circumstances.

scholarly journals Gravity current propagation up a valley

2014 ◽  
Vol 762 ◽  
pp. 417-434 ◽  
Author(s):  
Catherine S. Jones ◽  
Claudia Cenedese ◽  
Eric P. Chassignet ◽  
P. F. Linden ◽  
Bruce R. Sutherland
Keyword(s):  
Numerical Simulations ◽  
Laboratory Experiments ◽  
Rectangular Channel ◽  
Gravity Current ◽  
Gravity Currents ◽  
Momentum Transport ◽  
Front Speed

AbstractThe advance of the front of a dense gravity current propagating in a rectangular channel and V-shaped valley both horizontally and up a shallow slope is examined through theory, full-depth lock–release laboratory experiments and hydrostatic numerical simulations. Consistent with theory, experiments and simulations show that the front speed is relatively faster in the valley than in the channel. The front speed measured shortly after release from the lock is 5–22 % smaller than theory, with greater discrepancy found in upsloping V-shaped valleys. By contrast, the simulated speed is approximately 6 % larger than theory, showing no dependence on slope for rise angles up to ${\it\theta}=8^{\circ }$. Unlike gravity currents in a channel, the current head is observed in experiments to be more turbulent when propagating in a V-shaped valley. The turbulence is presumably enhanced due to the lateral flows down the sloping sides of the valley. As a consequence, lateral momentum transport contributes to the observed lower initial speeds. A Wentzel–Kramers–Brillouin like theory predicting the deceleration of the current as it runs upslope agrees remarkably well with simulations and with most experiments, within errors.

A note on the propagation speed of a weakly dissipative gravity current

2007 ◽  
Vol 574 ◽  
pp. 393-403 ◽  
Author(s):  
EUGENY V. ERMANYUK ◽  
NIKOLAI V. GAVRILOV
Keyword(s):  
Gravity Current ◽  
Propagation Speed ◽  
Front Propagation ◽  
Gravity Currents ◽  
Minor Role ◽  
Rigid Boundary ◽  
Inviscid Flows ◽  
First Case ◽  
Energy Conserving ◽  
A Minor

This paper presents an experimental study on the propagation speed of gravity currents at moderate values of a gravity Reynolds number. Two cases are considered: gravity currents propagating along a rigid boundary and intrusive gravity currents. For the first case, a semi-empirical formula for the front propagation speed derived from simple energy arguments is shown to capture well the effect of flow deceleration because of viscous dissipation. In the second case, the propagation speed is shown to agree with the one predicted for energy-conserving virtually inviscid flows (Shin, Dalziel & Linden, J. Fluid Mech. vol. 521, 2004, p. 1), which implies that the losses due to vorticity generation and mixing at the liquid–liquid interface play only a minor role in the total balance of energy.

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