Waves Due to a Moving Oscillatory Surface Pressure in a Stratified Fluid

1974 ◽  
Vol 41 (3) ◽  
pp. 571-574 ◽  
Author(s):  
A. K. Pramanik
Keyword(s):  
Free Surface ◽  
Steady State Solution ◽  
Integral Representations ◽  
Initial Value ◽  
Homogeneous Fluid ◽  
Asymptotic Evaluation ◽  
Progressive Waves ◽  
The Waves ◽  
Oscillatory Pressure ◽  
Passage To The Limit

The initial value problem of waves generated by an oscillatory pressure distribution moving uniformly on the free surface of a two-layer fluid is solved. The integral representations of the waves both on the free surface and on the surface of separation are obtained. By a passage to the limit t → ∞, the steady-state solution of the problem is derived through an asymptotic evaluation of these integrals at large distances. It is noticed that stratification sharply changes the number and the character of the progressive waves and also introduces two critical speeds instead of one as found in homogeneous fluid. At these speeds the solution becomes singular.

Waves on a shear flow

1974 ◽  
Vol 11 (2) ◽  
pp. 263-277 ◽  
Author(s):  
K.K. Puri
Keyword(s):  
Free Surface ◽  
Steady State ◽  
Shear Flow ◽  
Initial Value Problem ◽  
Finite Depth ◽  
Steady State Solution ◽  
State Solution ◽  
Wave System ◽  
Initial Value ◽  
Oscillatory Pressure

The propogation of disturbance when a shear flow with a free surface, in a channel of infinite horizontal extent and finite depth, is disturbed by the application of time-oscillatory pressure, is studied. The initial value problem is solved by using transform techniques and the steady state solution is obtained therefrom in the limit t → ∞. The effect of the initial shear on the development of the wave system is investigated.

Forced Oscillations in a Two-Layer Fluid of Finite Depth

1983 ◽  
Vol 50 (3) ◽  
pp. 506-510
Author(s):  
R. K. Manna
Keyword(s):  
Free Surface ◽  
Internal Wave ◽  
Pressure Distribution ◽  
Fourier Transformation ◽  
Finite Depth ◽  
Forced Oscillations ◽  
Wave System ◽  
Initial Value ◽  
Oscillatory Pressure ◽  
Generalized Fourier Transformation

An initial value investigation is made of the development of surface and internal wave motions generated by an oscillatory pressure distribution on the surface of a fluid that is composed of two layers of limited depths and of different densities. The displacement functions both on the free surface and on the interface are obtained with the help of generalized Fourier transformation. The method for the asymptotic evolution of the wave integrals is based on Bleistein’s method. The behavior of the solutions is examined for large values of time and distance. It is found that there are two classes of waves—the first corresponds to the usual surface waves with a changed amplitude and the second arises entirely due to stratification. Some interesting features of the wave system have also been studied.

Experimental Investigation of Boundary Layer Instabilities on the Free Surface of Non-Turbulent Jet

2012 ◽  
Author(s):  
Matthieu A. Andre ◽  
Philippe M. Bardet
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
High Speed ◽  
Particle Tracking Velocimetry ◽  
Capillary Waves ◽  
Wave Growth ◽  
Image Velocimetry ◽  
Planar Laser ◽  
Surface Visualization ◽  
The Waves

Shear instabilities induced by the relaxation of laminar boundary layer at the free surface of a high speed liquid jet are investigated experimentally. Physical insights into these instabilities and the resulting capillary wave growth are gained by performing non-intrusive measurements of flow structure in the direct vicinity of the surface. The experimental results are a combination of surface visualization, planar laser induced fluorescence (PLIF), particle image velocimetry (PIV), and particle tracking velocimetry (PTV). They suggest that 2D spanwise vortices in the shear layer play a major role in these instabilities by triggering 2D waves on the free surface as predicted by linear stability analysis. These vortices, however, are found to travel at a different speed than the capillary waves they initially created resulting in interference with the waves and wave growth. A new experimental facility was built; it consists of a 20.3 × 146.mm rectangular water wall jet with Reynolds number based on channel depth between 3.13 × 104 to 1.65 × 105 and 115. to 264. based on boundary layer momentum thickness.

Linear and non-linear potential-flow calculations of free-surface waves with lift and induced drag

2000 ◽  
Vol 214 (6) ◽  
pp. 801-812
Author(s):  
C-E Janson
Keyword(s):  
Free Surface ◽  
Potential Flow ◽  
Lift Force ◽  
Radiation Condition ◽  
Linear Potential ◽  
Surface Boundary ◽  
Model Approximation ◽  
Non Linear ◽  
Lifting Surfaces ◽  
The Waves

A potential-flow panel method is used to compute the waves and the lift force from surface-piercing and submerged bodies. In particular the interaction between the waves and the lift produced close to the free surface is studied. Both linear and non-linear free-surface boundary conditions are considered. The potential-flow method is of Rankine-source type using raised source panels on the free surface and a four-point upwind operator to compute the velocity derivatives and to enforce the radiation condition. The lift force is introduced as a dipole distribution on the lifting surfaces and on the trailing wake, together with a flow tangency condition at the trailing edge of the lifting surface. Different approximations for the spanwise circulation distribution at the free surface were tested for a surface-piercing wing and it was concluded that a double-model approximation should be used for low speeds while a single-model, which allows for a vortex at the free surface, was preferred at higher speeds. The lift force and waves from three surface-piercing wings, a hydrofoil and a sailing yacht were computed and compared with measurements and good agreement was obtained.

scholarly journals Diagnostic and prognostic simulations with a full Stokes model accounting for superimposed ice of Midtre Lovénbreen, Svalbard

2009 ◽  
Vol 3 (2) ◽  
pp. 217-229 ◽  
Author(s):  
T. Zwinger ◽  
J. C. Moore
Keyword(s):  
Free Surface ◽  
Steady State ◽  
Thermal State ◽  
Steady State Solution ◽  
Radar Data ◽  
Data Set ◽  
Surface Evolution ◽  
Steady State Model ◽  
Elevation Changes ◽  
Ground Penetrating

Abstract. We present steady state (diagnostic) and transient (prognostic) simulations of Midtre Lovénbreen, Svalbard performed with the thermo-mechanically coupled full-Stokes code Elmer. This glacier has an extensive data set of geophysical measurements available spanning several decades, that allow for constraints on model descriptions. Consistent with this data set, we included a simple model accounting for the formation of superimposed ice. Diagnostic results indicated that a dynamic adaptation of the free surface is necessary, to prevent non-physically high velocities in a region of under determined bedrock depths. Observations from ground penetrating radar of the basal thermal state agree very well with model predictions, while the dip angles of isochrones in radar data also match reasonably well with modelled isochrones, despite the numerical deficiencies of estimating ages with a steady state model. Prognostic runs for 53 years, using a constant accumulation/ablation pattern starting from the steady state solution obtained from the configuration of the 1977 DEM show that: 1 the unrealistic velocities in the under determined parts of the DEM quickly damp out; 2 the free surface evolution matches well measured elevation changes; 3 the retreat of the glacier under this scenario continues with the glacier tongue in a projection to 2030 being situated ≈500 m behind the position in 1977.

Nonlinear Aspects of Subcritical Shallow-Water Flow Past Two-Dimensional Obstructions

1978 ◽  
Vol 22 (04) ◽  
pp. 203-211
Author(s):  
Nils Salvesen ◽  
C. von Kerczek
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Flow Problem ◽  
Free Stream ◽  
The Body ◽  
Two Dimensional ◽  
Third Order ◽  
Submerged Body ◽  
The Mean ◽  
The Waves

Some nonlinear aspects of the two-dimensional problem of a submerged body moving with constant speed in otherwise undisturbed water of uniform depth are considered. It is shown that a theory of Benjamin which predicts a uniform rise of the free surface ahead of the body and the lowering of the mean level of the waves behind it agrees well with experimental data. The local steady-flow problem is solved by a numerical method which satisfies the exact free-surface conditions. Third-order perturbation formulas for the downstream free waves are also presented. It is found that in sufficiently shallow water, the wavelength increases with increasing disturbance strength for fixed values of the free-stream-Froude number. This is opposite to the deepwater case where the wavelength decreases with increasing disturbance strength.

scholarly journals Graphene-Based One-Dimensional Terahertz Phononic Crystal: Band Structures and Surface Modes

Nanomaterials ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. 2205
Author(s):  
Ilyasse Quotane ◽  
El Houssaine El Boudouti ◽  
Bahram Djafari-Rouhani
Keyword(s):  
Free Surface ◽  
Sagittal Plane ◽  
Numerical Study ◽  
Phononic Crystal ◽  
Acoustic Properties ◽  
Band Structures ◽  
Surface Modes ◽  
Acoustic Modes ◽  
And Behavior ◽  
The Waves

In this paper, we provide a theoretical and numerical study of the acoustic properties of infinite and semi-infinite superlattices made out of graphene-semiconductor bilayers. In addition to the band structure, we emphasize the existence and behavior of localized and resonant acoustic modes associated with the free surface of such structures. These modes are polarized in the sagittal plane, defined by the incident wavevector and the normal to the layers. The surface modes are obtained from the peaks of the density of states, either inside the bulk bands or inside the minigaps of the superlattice. In these structures, the two directions of vibrations (longitudinal and transverse) are coupled giving rise to two bulk bands associated with the two polarizations of the waves. The creation of the free surface of the superlattice induces true surface localized modes inside the terahertz acoustic forbidden gaps, but also pseudo-surface modes which appear as well-defined resonances inside the allowed bands of the superlattice. Despite the low thickness of the graphene layer, and though graphene is a gapless material, when it is inserted periodically in a semiconductor, it allows the opening of wide gaps for all values of the wave vector k// (parallel to the interfaces). Numerical illustrations of the band structures and surface modes are given for graphene-Si superlattices, and the surface layer can be either Si or graphene. These surface acoustic modes can be used to realize liquid or bio-sensors graphene-based phononic crystal operating in the THz frequency domain.

scholarly journals SURFACE TENSION OF SERUM

1922 ◽  
Vol 35 (5) ◽  
pp. 707-735 ◽  
Author(s):  
P. Lecomte du Noüy
Keyword(s):  
Surface Tension ◽  
Surface Layer ◽  
Free Surface ◽  
Organic Compounds ◽  
Sodium Oleate ◽  
Mean Value ◽  
Physiological Solution ◽  
Optimum Concentration ◽  
Initial Value ◽  
Ring Method

The application of the ring method to the measurement of solutions of serum and of certain organic compounds has brought forth new facts, mainly the decrease of the surface tension of such solutions in function of time. 1. In serum diluted at such a low concentration as 1:1,000,000 in NaCl, physiological solution, the surface tension of the liquid is lowered by 3 or 4 dynes in 2 hours; at 1:100,000, by about 11 dynes (mean value) in 2 hours, and by 20 dynes in 24 hours; at 1:10,000 by about 13 to 16 dynes in 2 hours. 2. The drop in surface tension is much more rapid in the first 30 minutes and follows generally the law of adsorption in the surface layer in function of the time. 3. Stirring or shaking after the drop causes the surface tension to rise, but generally below its initial value. 4. The same phenomena occur when using sodium oleate, glycocholate, or saponin instead of serum. 5. For every serum, as well as for the substances mentioned above a maximum drop occurs in certain conditions at a given optimum concentration. 6. Not only are the substances which lower the surface tension adsorbed in the surface layer, in the case in which they are present with crystalloids, but also the crystalloids themselves, in contradiction to Gibbs' statement. This is plainly shown by the evaporation of such solutions in watch-glasses which, instead of a small group of sharp, large, well defined crystals at the bottom, leaves a white disc almost as large as the initial free surface itself, due to the liberation of the salt by the surface layer as it crawls down the concave surface of the glass. 7. In these conditions, solutions of serum are characterized by a very peculiar periodic and concentric distribution of the crystals, at a concentration of 1:100 only. The same ring-like aspect is observed with sodium oleate, glycocholate, and saponin, but not at the same concentration, as was to be expected, since serum is a solution in itself.

Free surface over a horizontal shear layer: vorticity generation and air entrainment mechanisms

2017 ◽  
Vol 813 ◽  
pp. 1007-1044 ◽  
Author(s):  
Matthieu A. André ◽  
Philippe M. Bardet
Keyword(s):  
Free Surface ◽  
Shear Layer ◽  
Air Entrainment ◽  
Horizontal Shear ◽  
Vortex Instability ◽  
Image Velocimetry ◽  
Planar Laser ◽  
Spatio Temporal ◽  
The Waves

Two air entrainment mechanisms driven by vortex instability are reported in the unstable relaxation of a horizontal shear layer below a free surface. This flow is experimentally investigated by means of planar laser-induced fluorescence (PLIF) and particle image velocimetry (PIV) coupled with surface profilometry. PLIF identifies counter-rotating vortex pairs (CRVP) emanating from the surface following the growth of high steepness two-dimensional millimetre-size waves for Reynolds and Weber numbers based on the momentum thickness of 177 to 222 and 7.59 to 13.9, respectively. High spatio-temporal resolution PIV reveals the role of surface-generated vorticity and flow separation in the highly curved trough of the waves on the injection of a CRVP. Air bubbles are entrapped in the wake of these CRVPs at Reynolds number above 190. PIV data and spanwise PLIF images show two initiation mechanisms: primary vortex instability modulating the spanwise location where the flow separates, resulting in the pinch off of an air ligament, and secondary vortex instability turning a CRVP into$\unicode[STIX]{x1D6FA}$-shaped loops pulling the surface down. Instability wavelengths agree with linear stability analysis, and models for these new air entrainment mechanisms are proposed.

The effect of a semi-contaminated free surface on mass transport

1974 ◽  
Vol 75 (2) ◽  
pp. 283-294 ◽  
Author(s):  
D. Porter ◽  
B. D. Dore
Keyword(s):  
Free Surface ◽  
Velocity Field ◽  
Mass Transport ◽  
Mixed Boundary ◽  
Surface Film ◽  
Vertical Displacement ◽  
Mass Transport Velocity ◽  
Harmonic Equation ◽  
The Waves

AbstractThe mass transport velocity field is determined for surface waves which propagate from a region with a clean free surface into a region beneath an inextensible surface film. The waves are assumed to be incident normally on the edge of the film. Determination of this velocity field requires the investigation of a mixed boundary value problem for the bi-harmonic equation, the solution of which is obtained using the Wiener–Hopf technique. Streamlines for the mean motion of the fluid particles are thus obtained. It is found that considerable vertical displacement of fluid is possible due to the presence of the surface film.

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