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.

Intrusive gravity currents propagating along thin and thick interfaces

2007 ◽  
Vol 586 ◽  
pp. 109-118 ◽  
Author(s):  
BRUCE R. SUTHERLAND ◽  
JOSHUA T. NAULT
Keyword(s):  
Wave Speed ◽  
Lower Layer ◽  
Finite Depth ◽  
Gravity Currents ◽  
Average Density ◽  
Constant Speed ◽  
Interfacial Wave ◽  
Mode 2 ◽  
Finite Distance ◽  
The Waves

Inviscid gravity currents released from a finite-length lock are known to propagate at a constant speed to a predicted finite distance before decelerating. By extension this should occur in a two-layer fluid with equal upper- and lower-layer depths for an intrusion having the average density of the ambient. The experiments presented here show this is not necessarily the case. The finite-depth thickness of the interface non-negligibly influences the evolution of the intrusion so that it propagates well beyond the predicted constant-speed limit; it propagates without decelerating beyond 22 lock lengths in a rectilinear geometry and beyond 6 lock radii in an axisymmetric geometry. Experiments and numerical simulations demonstrate that the intrusion speed decreases to half the two-layer speed in the circumstance in which the interface spans the domain. The corresponding long mode-2 interfacial wave speed increases rapidly with interfacial thickness, becoming comparable with the intrusion speed when the interfacial thickness is approximately one-quarter the domain height. For somewhat thinner interfacial thicknesses, the intrusion excites solitary waves that move faster than the long-wave speed. The coupling between intrusions and the waves they excite, together with reduced mixing of the current head, result in constant-speed propagation for longer times.

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.

Finite-amplitude internal wavepacket dispersion and breaking

2001 ◽  
Vol 429 ◽  
pp. 343-380 ◽  
Author(s):  
BRUCE R. SUTHERLAND
Keyword(s):  
Numerical Simulations ◽  
Internal Waves ◽  
Large Amplitude ◽  
Finite Amplitude ◽  
Critical Amplitude ◽  
Fully Nonlinear ◽  
Weakly Nonlinear ◽  
The Stability ◽  
The Waves ◽  
Horizontal Wavelength

The evolution and stability of two-dimensional, large-amplitude, non-hydrostatic internal wavepackets are examined analytically and by numerical simulations. The weakly nonlinear dispersion relation for horizontally periodic, vertically compact internal waves is derived and the results are applied to assess the stability of weakly nonlinear wavepackets to vertical modulations. In terms of Θ, the angle that lines of constant phase make with the vertical, the wavepackets are predicted to be unstable if [mid ]Θ[mid ] < Θc, where Θc = cos−1 (2/3)1/2 ≃ 35.3° is the angle corresponding to internal waves with the fastest vertical group velocity. Fully nonlinear numerical simulations of finite-amplitude wavepackets confirm this prediction: the amplitude of wavepackets with [mid ]Θ[mid ] > Θc decreases over time; the amplitude of wavepackets with [mid ]Θ[mid ] < Θc increases initially, but then decreases as the wavepacket subdivides into a wave train, following the well-known Fermi–Pasta–Ulam recurrence phenomenon.If the initial wavepacket is of sufficiently large amplitude, it becomes unstable in the sense that eventually it convectively overturns. Two new analytic conditions for the stability of quasi-plane large-amplitude internal waves are proposed. These are qualitatively and quantitatively different from the parametric instability of plane periodic internal waves. The ‘breaking condition’ requires not only that the wave is statically unstable but that the convective instability growth rate is greater than the frequency of the waves. The critical amplitude for breaking to occur is found to be ACV = cot Θ (1 + cos2 Θ)/2π, where ACV is the ratio of the maximum vertical displacement of the wave to its horizontal wavelength. A second instability condition proposes that a statically stable wavepacket may evolve so that it becomes convectively unstable due to resonant interactions between the waves and the wave-induced mean flow. This hypothesis is based on the assumption that the resonant long wave–short wave interaction, which Grimshaw (1977) has shown amplifies the waves linearly in time, continues to amplify the waves in the fully nonlinear regime. Using linear theory estimates, the critical amplitude for instability is ASA = sin 2Θ/(8π2)1/2. The results of numerical simulations of horizontally periodic, vertically compact wavepackets show excellent agreement with this latter stability condition. However, for wavepackets with horizontal extent comparable with the horizontal wavelength, the wavepacket is found to be stable at larger amplitudes than predicted if Θ [lsim ] 45°. It is proposed that these results may explain why internal waves generated by turbulence in laboratory experiments are often observed to be excited within a narrow frequency band corresponding to Θ less than approximately 45°.

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.

scholarly journals The evolution of mode-2 nonlinear internal waves over the northern Heng-Chun Ridge south of Taiwan

2015 ◽  
Vol 22 (4) ◽  
pp. 413-431 ◽  
Author(s):  
S. R. Ramp ◽  
Y. J. Yang ◽  
D. B. Reeder ◽  
M. C. Buijsman ◽  
F. L. Bahr
Keyword(s):  
Internal Waves ◽  
High Frequency ◽  
Velocity Structure ◽  
Primary Study ◽  
Turbulent Dissipation ◽  
Nonlinear Internal Waves ◽  
Mode 2 ◽  
Sill Depth ◽  
The Waves ◽  
Very High

Abstract. Two research cruises were conducted from the R/V OCEAN RESEARCHER 3 during 05–16 August 2011 to study the generation and propagation of high-frequency nonlinear internal waves (NLIWs) over the northern Heng-Chun Ridge south of Taiwan. The primary study site was on top of a smaller ridge about 15 km wide by 400 m high atop the primary ridge, with a sill depth of approximately 600 m. A single mooring was used in conjunction with shipboard observations to sample the temperature, salinity and velocity structure over the ridge. All the sensors observed a profusion of mode-2 NLIWs. Some of the waves were solitary, while others had as many as seven evenly spaced waves per packet. The waves all exhibited classic mode-2 velocity structure with a core near 150–200 m and opposing velocities in the layers above and below. At least two and possibly three most common propagation directions emerged from the analysis, suggesting multiple generation sites near the eastern side of the ridge. The turbulent dissipation due to overturns in the wave cores was very high at order 10−4–10−3 W kg−1. The energy budget suggests that the waves cannot persist very far from the ridge and likely do not contribute to the South China Sea transbasin wave phenomenon.

Internal wave excitation from stratified flow over a thin barrier

1998 ◽  
Vol 377 ◽  
pp. 223-252 ◽  
Author(s):  
BRUCE R. SUTHERLAND ◽  
PAUL F. LINDEN
Keyword(s):  
Internal Wave ◽  
Numerical Simulations ◽  
Internal Waves ◽  
Wavelet Transforms ◽  
Large Amplitude ◽  
Internal Gravity Waves ◽  
Wave Excitation ◽  
Mean Flow ◽  
Propagating Waves ◽  
The Waves

We perform laboratory experiments in a recirculating shear flow tank of non-uniform salt-stratified water to examine the excitation of internal gravity waves (IGW) in the wake of a tall, thin vertical barrier. The purpose of this study is to characterize and quantify the coupling between coherent structures shed in the wake and internal waves that radiate from the mixing region into the deep, stationary fluid. In agreement with numerical simulations, large-amplitude internal waves are generated when the mixing region is weakly stratified and the deep fluid is sufficiently strongly stratified. If the mixing region is unstratified, weak but continuous internal wave excitation occurs. In all cases, the tilt of the phase lines of propagating waves lies within a narrow range. Assuming the waves are spanwise uniform, their amplitude in space and time is measured non-intrusively using a recently developed ‘synthetic schlieren’ technique. Using wavelet transforms to measure consistently the width and duration of the observed wavepackets, the Reynolds stress is measured and, in particular, we estimate that when large-amplitude internal wave excitation occurs, approximately 7% of the average momentum across the shear depth and over the extent of the wavepacket is lost due to transport away from the mixing region by the waves.We propose that internal waves may act back upon the mean flow modifying it so that the excitation of waves of that frequency is enhanced. A narrow frequency spectrum of large-amplitude waves is observed because the feedback is largest for waves with phase tilt in a range near 45°. Numerical simulations and analytic theories are presented to further quantify this theory.

scholarly journals The wave instability pathway to turbulence

2013 ◽  
Vol 724 ◽  
pp. 1-4 ◽  
Author(s):  
Bruce R. Sutherland
Keyword(s):  
Internal Waves ◽  
Large Scale ◽  
Laboratory Experiments ◽  
Wave Beam ◽  
Small Scale ◽  
Monochromatic Wave ◽  
Wave Instability ◽  
Analysis Techniques ◽  
Parametric Subharmonic Instability ◽  
The Waves

AbstractOne way that large-scale oceanic internal waves transfer their energy to small-scale mixing is through parametric subharmonic instability (PSI). But there is a disconnect between theory, which assumes the waves are periodic in space and time, and reality, in which waves are transient and localized. The innovative laboratory experiments and analysis techniques of Bourget et al. (J. Fluid Mech., vol. 723, 2013, pp. 1–20) show that theory can be applied to interpret the generation of subharmonic disturbances from a quasi-monochromatic wave beam. Their methodology and results open up new avenues of investigation into PSI through experiments, simulations and observations.

scholarly journals The evolution of Mode-2 nonlinear internal waves over the northern Heng-Chun ridge south of Taiwan

2015 ◽  
Vol 2 (1) ◽  
pp. 243-296 ◽  
Author(s):  
S. R. Ramp ◽  
Y. J. Yang ◽  
D. B. Reeder ◽  
M. C. Buijsman ◽  
F. L. Bahr
Keyword(s):  
Internal Waves ◽  
High Frequency ◽  
Velocity Structure ◽  
Primary Study ◽  
Turbulent Dissipation ◽  
Nonlinear Internal Waves ◽  
Mode 2 ◽  
Sill Depth ◽  
The Waves ◽  
Very High

Abstract. Two research cruises were conducted from the R/V OCEAN RESEARCHER 3 during 5–16 August 2011 to study the generation of high-frequency nonlinear internal waves (NLIW) over the northern Heng-Chun Ridge south of Taiwan. The primary study site, centered near 21°34' N, 120°54' E, was on top of a smaller ridge about 15 km wide by 400 m high atop the primary ridge, with a sill depth of approximately 600 m. The bottom slope was steep over both sides of the ridge, supercritical with respect to both diurnal and semidiurnal tides. The key result of the experiments is that a profusion of mode-2 NLIW were observed by all the sensors. Some of the waves were solitary while others had as many as seven evenly-spaced waves per packet. The waves all exhibited classic mode-2 velocity structure with a core near 150–200 m and opposing velocities in the layers above and below. At least two and possibly three most common propagation directions emerged from the analysis, suggesting multiple generation sites near the east side of the ridge. The turbulent dissipation due to overturns in the wave cores was very high at order 10−4–10−3 W kg−1. The energy budget suggests that the waves cannot persist very far from the ridge and likely do not contribute to the South China Sea transbasin wave phenomenon.

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.

scholarly journals Large amplitude internal solitary waves over a shelf

2011 ◽  
Vol 11 (1) ◽  
pp. 17-25 ◽  
Author(s):  
N. Gavrilov ◽  
V. Liapidevskii ◽  
K. Gavrilova
Keyword(s):  
Internal Waves ◽  
Solitary Waves ◽  
Large Amplitude ◽  
Numerical Scheme ◽  
Laboratory Experiments ◽  
Open Channel ◽  
Internal Solitary Waves ◽  
Open Channel Flows ◽  
Mode 2 ◽  
The Mathematical Model

Abstract. Dynamics of large amplitude internal waves in two-layers of shallow water is considered. It is demonstrated that in laboratory experiments the subsurface waves of depression over a shelf may be simulated by internal symmetric solitary waves of the mode 2 ("lump-like" waves). The mathematical model describing the propagation and decaying of large internal waves in two-layer fluid is introduced. It is a variant of Choi-Camassa equations with hydrostatic pressure distribution in one of the layers. It is shown that the numerical scheme developed for the Green-Naghdi equations in open channel flows may be applied for the description of large amplitude internal waves over a shelf.

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