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 The lifecycle of axisymmetric internal solitary waves

2010 ◽  
Vol 17 (5) ◽  
pp. 443-453 ◽  
Author(s):  
J. M. McMillan ◽  
B. R. Sutherland
Keyword(s):  
Solitary Waves ◽  
Wave Amplitude ◽  
Lower Layer ◽  
Average Density ◽  
Constant Speed ◽  
Supporting Evidence ◽  
Linear Dispersion ◽  
Long Wave ◽  
Mode 2 ◽  
Head Height

Abstract. The generation and evolution of solitary waves by intrusive gravity currents in an approximate two-layer fluid with equal upper- and lower-layer depths is examined in a cylindrical geometry by way of theory and numerical simulations. The study is limited to vertically symmetric cases in which the density of the intruding fluid is equal to the average density of the ambient. We show that even though the head height of the intrusion decreases, it propagates at a constant speed well beyond 3 lock radii. This is because the strong stratification at the interface supports the formation of a mode-2 solitary wave that surrounds the intrusion head and carries it outwards at a constant speed. The wave and intrusion propagate faster than a linear long wave; therefore, there is strong supporting evidence that the wave is indeed nonlinear. Rectilinear Korteweg-de Vries theory is extended to allow the wave amplitude to decay as r-p with p=½ and the theory is compared to the observed waves to demonstrate that the width of the wave scales with its amplitude. After propagating beyond 7 lock radii the intrusion runs out of fluid. Thereafter, the wave continues to spread radially at a constant speed, however, the amplitude decreases sufficiently so that linear dispersion dominates and the amplitude decays with distance as r-1.

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.

Hydroelastic solitary wave during the head-on collision process in a stratified fluid

2019 ◽  
Vol 233 (17) ◽  
pp. 6135-6148 ◽  
Author(s):  
MM Bhatti ◽  
DQ Lu
Keyword(s):  
Elastic Plate ◽  
Wave Speed ◽  
Lower Layer ◽  
Order Approximation ◽  
Asymptotic Series ◽  
Density Ratio ◽  
Thin Elastic Plate ◽  
Series Solutions ◽  
Interfacial Wave ◽  
Highly Nonlinear

In this study, head-on collision between hydroelastic solitary waves propagating in a two-layer fluid beneath a thin elastic plate is analytically investigated. The plate structure is modeled using the Euler–Bernoulli beam theory with the effect of compressive stress. We consider that the lower- and upper-layer fluids having different constant densities are incompressible, and the motion is irrotational. The asymptotic series solutions of the resulting highly nonlinear coupled differential equations are deduced with the combination of a method of strained coordinates and the Poincaré–Lighthill–Kuo method. The series solutions obtained are presented up to the third-order approximation. The inclusion of all the emerging parameters is discussed graphically and mathematically against interfacial waves, plate deflection, wave speed, phase shift, maximum run-up amplitude, and the velocity functions. The presence of the elastic plate reveals a decreasing impact on the wave profiles in the upper- and lower-layer fluid. However, the distortion profile shows converse behavior in the upper-layer fluid as compared with the lower-layer fluid. Interfacial wave speed also tends to diminish due to the elastic plate parameter and the density ratio as the wave amplitude is high.

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.

Turbulence, waves and mixing at shear-free density interfaces. Part 1. A theoretical model

1997 ◽  
Vol 347 ◽  
pp. 197-234 ◽  
Author(s):  
H. J. S. FERNANDO ◽  
J. C. R. HUNT
Keyword(s):  
Theoretical Model ◽  
Critical Frequency ◽  
Lower Layer ◽  
Breaking Waves ◽  
Turbulent Motion ◽  
Interfacial Wave ◽  
Full Spectrum ◽  
Turbulent Layer ◽  
Entrainment Velocity ◽  
Linear Waves

This paper presents a theoretical model of turbulence and mixing at a shear-free stable density interface. In one case (single-sided stirring) the interface separates a layer of fluid of density ρ in turbulent motion, with r.m.s. velocity uH and lengthscale LH, from a non-turbulent layer with density ρ+Δρ, while in the second case (double-sided stirring) the lower layer is also in turbulent motion. In both cases, the external Richardson number Ri=ΔbLH/ u2H (where Δb is the buoyancy jump across the interface) is assumed to be large. Based on the hypotheses that the effect of the interface on the turbulence is as if it were suddenly imposed (which is equivalent to generating irrotational motions) and that linear waves are generated in the interface, the techniques of rapid distortion theory are used to analyse the linear aspects of the distortion of turbulence and of the interfacial motions. New physical concepts are introduced to account for the nonlinear aspects.To describe the spectra and variations of the r.m.s. fluctuations of velocity and displacements, a statistically steady linear model is used for frequencies above a critical frequency ωr/μc, where ωr(=Δb/2uH) is the maximum resonant frequency and μc<1. As in other nonlinear systems, observations below this critical frequency show the existence of long waves on the interface that can grow, break and cause mixing between the two fluid layers. A nonlinear model is constructed based on the fact that these breaking waves have steep slopes (which determines the form of the displacement spectrum) and on the physical argument that the energy of the vertical motions of these dissipative nonlinear waves should be comparable to that of the forced linear waves, which leads to an approximately constant value for the parameter μc. The model predictions of the vertical r.m.s. interfacial velocity, the interfacial wave amplitude and the velocity spectra agree closely with new and published experimental results.An exact unsteady inviscid linear analysis is used to derive the growth rate of the full spectrum, which asymptotically leads to the growth of resonant waves and to the energy transfer from the turbulent region to the wave motion of the stratified layer. Mean energy flux into the stratified layer, averaged over a typical wave cycle, is used to estimate the boundary entrainment velocity for the single-sided stirring case and the flux entrainment velocity for the double-sided stirring case, by making the assumption that the ratio of buoyancy flux to dissipation rate in forced stratified layers is constant with Ri and has the same value as in other stratified turbulent flows. The calculations are in good agreement with laboratory measurements conducted in mixing boxes and in wind tunnels. The contribution of Kelvin–Helmholtz instabilities induced by the velocity of turbulent eddies parallel to the interface is estimated to be insignificant compared to that of internal waves excited by turbulence.

Essence of Electric Charge of elementary particles according of New axioms and Laws

2020 ◽  
Vol 3 (4) ◽  
Keyword(s):  
Electromagnetic Field ◽  
Electron Pair ◽  
Constant Speed ◽  
Longitudinal Vortex ◽  
Uniform Motion ◽  
Variable Velocity ◽  
Variable Speed ◽  
External Observer ◽  
Closed Circle ◽  
The Waves

Two new Axioms and eight new Laws have been proposed and developed in previous reports. This report uses both axioms and only four laws. According to the first axiom (Axiom1), we can replace uniform motion in a closed circle with non-uniform motion in an open vortex. According to the second axiom (Axiom2), there are pairs of vortices that are mutually orthogonal or they tend to work in a system by a special type of resonance. Of all the variants of vortex pairs, the most probable is the pair: accelerating vortex from the center outwards connected with a delayed vortex from the periphery inwards. This pair is a model of the connected proton-electron pair. The behavior of a free electron and a proton in an Electromagnetic Field is studied. Actually like a cross vortex from outside to inside the electron will be directed to the positive pole. Therefore, an external observer who does not know what the internal structure of the electron is will think and will be deceived that the electron carries a negative charge. The exact opposite is observed for the proton. The properties of a system of linked electrons and protons are also studied. It is known that the Electromagnetic Field propagates at a constant speed and when pulsating the waves are only transverse. According to the new Axioms and Laws in the electron-proton system, the internal connections are of variable speed and when pulsating, the waves are not only transverse and longitudinal. Because the Electromagnetic field is only transverse at a constant speed , it appears that the interaction between the proton and the electron is not Electromagnetic but some other interaction. The interaction between the protons includes cross vortex with variable velocity and longitudinal vortex with variable velocity

scholarly journals The evolution of second mode internal solitary waves over variable topography

2017 ◽  
Vol 836 ◽  
pp. 238-259 ◽  
Author(s):  
C. Yuan ◽  
R. Grimshaw ◽  
E. Johnson
Keyword(s):  
Solitary Wave ◽  
General Circulation ◽  
Transition Point ◽  
Lower Layer ◽  
Nonlinear Coefficient ◽  
Circulation Model ◽  
Internal Solitary Wave ◽  
Layer System ◽  
Mode 2 ◽  
Polarity Change

A study of the propagation of a mode-2 internal solitary wave over a slope-shelf topography is presented. The methodology is based on a variable-coefficient Korteweg–de Vries (vKdV) equation, using both analysis and numerical simulations, and simulations using the MIT general circulation model (MITgcm). Two configurations are considered. One is a mode-2 internal solitary wave propagating up the slope, from one three-layer system to another three-layer system. Depending on the height of the shelf, which determines the variation of the nonlinear coefficient of the vKdV equation, this can be classified into two cases. First, the case of a polarity change, in which the coefficient of the quadratic nonlinear term changes sign at a certain critical point on the slope, and second, the case with no such polarity change. In both these cases there is a small transfer of energy from the mode-2 wave to mode-1 waves. The other configuration is when the lower layer in the three-layer system goes to zero at a transition point on the slope, and beyond that point, there is a two-layer fluid system. A mode-2 internal solitary wave propagating up the slope cannot exist past this transition point. Instead it is extinguished and replaced by a mode-1 bore and trailing wave packet which moves onto the shelf.

Relationship between right ventricular wave speed and elastance in dogs

2006 ◽  
Vol 84 (8-9) ◽  
pp. 943-951 ◽  
Author(s):  
Yichun Sun ◽  
Jiun-Jr Wang ◽  
Israel Belenkie ◽  
John V. Tyberg
Keyword(s):  
Right Ventricular ◽  
Wave Speed ◽  
Pulse Generator ◽  
Right Atrial ◽  
Power Relationships ◽  
Intensity Analysis ◽  
Pressure Transducers ◽  
Pulmonary Arterial ◽  
The Waves ◽  
Combined Data

Wave speed (c) must be known to separate forward- and backward-going waves during wave-intensity analysis, which measures the energy transported by the waves in the circulation. c is related to elastance; the present study was performed to measure right ventricular (RV) c during the cardiac cycle and to compare c with RV elastance. In 7 dogs, we measured right atrial, pulmonary arterial, pericardial and 2 RV pressures, and pulmonary arterial flow. A pulse generator was connected to the RV apex, and c was measured by determining the transit time between the 2 high-fidelity RV pressure transducers; the distance was measured roentgenographically. Eight sonomicrometry crystals were implanted in the RV endocardium to calculate RV volume and, thereby, elastance. RV c ranged from ~1 m/s during diastole to ~4 m/s during systole. Log–log plots of c vs. elastance were linear. These slopes represent the power relationships between c and elastance and ranged from 0.30 to 0.56; for the combined data, it was 0.31. Given knowledge of c, forward- and backward-going waves can be identified and their energy quantitated. In the canine RV, c is approximately proportional to 1/3 the power of elastance: log c = 0.31·log E – 2.05.

scholarly journals The interaction of waves with horizontal cylinders in two-layer fluids

1995 ◽  
Vol 304 ◽  
pp. 213-229 ◽  
Author(s):  
C. M. Linton ◽  
M. McIver
Keyword(s):  
Lower Layer ◽  
Single Layer ◽  
Wave Theory ◽  
Finite Depth ◽  
Scattering Problems ◽  
Infinite Layer ◽  
Linear Water Wave Theory ◽  
Interaction Of Waves ◽  
Reciprocity Relations ◽  
Horizontal Cylinders

We consider two-dimensional problems based on linear water wave theory concerning the interaction of waves with horizontal cylinders in a fluid consisting of a layer of finite depth bounded above by a free surface and below by an infinite layer of fluid of greater density. For such a situation time-harmonic waves can propagate with two different wavenumbers K and k. In a single-layer fluid there are a number of reciprocity relations that exist connecting the various hydrodynamic quantities that arise. These relations are systematically extended to the two-fluid case. It is shown that for symmetric bodies the solutions to scattering problems where the incident wave has wavenumber K and those where it has wavenumber k are related so that the solution to both can be found by just solving one of them. The particular problems of wave scattering by a horizontal circular cylinder in either the upper or lower layer are then solved using multipole expansions.

Analysis of the swimming of long and narrow animals

1952 ◽  
Vol 214 (1117) ◽  
pp. 158-183 ◽  
Keyword(s):  
Reynolds Number ◽  
Wave Length ◽  
Constant Speed ◽  
Forward Speed ◽  
Constant Amplitude ◽  
Flexible Cylinder ◽  
Cylinder Diameter ◽  
Wide Range ◽  
The Waves ◽  
Marine Worms

The swimming of long animals like snakes, eels and marine worms is idealized by considering the equilibrium of a flexible cylinder immersed in water when waves of bending of constant amplitude travel down it at constant speed. The force of each element of the cylinder is assumed to be the same as that which would act on a corresponding element of a long straight cylinder moving at the same speed and inclination to the direction of motion. Relevant aerodynamic data for smooth cylinders are first generalized to make them applicable over a wide range of speed and cylinder diameter. The formulae so obtained are applied to the idealized animal and a connexion established between B / λ , V / U and R 1 . Here B and λ are the amplitude and wave-length, V the velocity attained when the wave is propagated with velocity U , R 1 is the Reynolds number Udρ / μ , where d is the diameter of the cylinder, ρ and μ are the density and viscosity of water. The results of calculation are compared with James Gray’s photographs of a swimming snake and a leech. The amplitude of the waves which produce the greatest forward speed for a given output of energy is calculated and found, in the case of the snake, to be very close to that revealed by photographs. Similar calculations using force formulae applicable to rough cylinders yield results which differ from those for smooth ones in that when the roughness is sufficiently great and has a certain directional character propulsion can be achieved by a wave of bending which is propagated forward instead of backward. Gray’s photographs of a marine worm show that this remarkable method of propulsion does in fact occur in the animal world.

Sign in / Sign up

Export Citation Format

Share Document