scholarly journals Initial surface disturbance on a shear current: The Cauchy-Poisson problem with a twist

2014 ◽  
Vol 26 (8) ◽  
pp. 082104 ◽  
Author(s):  
Simen Å. Ellingsen
Keyword(s):  
Initial Surface ◽  
Poisson Problem ◽  
Shear Current ◽  
Surface Disturbance

scholarly journals Generation of Surface Waves Due to Initial Axisymmetric Surface Disturbance in Water with a Porous Bottom

2019 ◽  
Vol 24 (3) ◽  
pp. 625-644 ◽  
Author(s):  
P. Kundu ◽  
B.N. Mandal
Keyword(s):  
Free Surface ◽  
Asymptotic Form ◽  
Velocity Potential ◽  
Hankel Transform ◽  
Initial Surface ◽  
Initial Value ◽  
Poisson Problem ◽  
Different Types ◽  
Surface Disturbance ◽  
Infinite Integral

Abstract A two-dimensional Cauchy Poisson problem for water with a porous bottom generated by an axisymmetric initial surface disturbance is investigated here. The problem is formulated as an initial value problem for the velocity potential describing the motion in the fluid. The Laplace and Hankel transform techniques have been used in the mathematical analysis to obtain the form of the free surface in terms of a multiple infinite integral. This integral is then evaluated asymptotically by the method of stationary phase. The asymptotic form of the free surface is depicted graphically in a number of figures for different values of the porosity parameter and for different types of initial disturbances.

Nonlinear instability of liquid jets with thermocapillarity

1995 ◽  
Vol 283 ◽  
pp. 97-123 ◽  
Author(s):  
F. Mashayek ◽  
N. Ashgriz
Keyword(s):  
Ambient Temperature ◽  
Liquid Jets ◽  
Stable Configuration ◽  
Initial Surface ◽  
Breakup Mechanism ◽  
Capillary Flows ◽  
First Case ◽  
Satellite Drops ◽  
Thermal Disturbance ◽  
Surface Disturbance

The breakup mechanism of a capillary jet with thermocapillarity is investigated. Effects of the heat transfer from the liquid to the surrounding ambient, the liquid thermal conductivity, and the temperature-dependent surface tension coefficient on the jet instability and the formation of satellite drops are considered. Two different disturbances are imposed on the jet. In the first case, the jet is exposed to a spatially periodic ambient temperature. In addition to the thermal boundary condition, an initial surface disturbance with the same wavenumber as the thermal disturbance is also imposed on the jet. Both in-phase and out-of-phase thermal disturbances with respect to surface disturbances are considered. For the in-phase thermal disturbances, a parameter set is obtained at which capillary and thermocapillary effects can cancel each other and the jet attains a stable configuration. No such parameter set can be obtained when the thermocapillary flows are in the same direction as the capillary flows, as in the out-of-phase thermal disturbances. In the second case, only an initial thermal disturbance is imposed on the surface of the liquid while the ambient temperature is kept spatially and temporally uniform.

scholarly journals Weakly nonlinear transient waves on a shear current: ring waves and skewed Langmuir rolls

2019 ◽  
Vol 863 ◽  
pp. 114-149 ◽  
Author(s):  
Andreas H. Akselsen ◽  
Simen Å. Ellingsen
Keyword(s):  
Mode Coupling ◽  
Continuous Wave ◽  
Wave Spectrum ◽  
Vortex Structures ◽  
Second Order ◽  
Ocean Current ◽  
Initial Surface ◽  
Weakly Nonlinear ◽  
Special Cases ◽  
Shear Current

We investigate the weakly nonlinear dynamics of transient gravity waves at infinite depth under the influence of a shear current varying linearly with depth. The shear field makes this problem three-dimensional and rotational in nature, but an analytical solution is permitted via integration of the Euler equations. Although similar problems were investigated in the 1960s and 70s for special cases of resonance, this is to our knowledge the first general wave interaction (mode coupling) solution derived to second order with a shear current present. Wave interactions are integrable in a spectral convolution to yield the second-order dynamics of initial value problems. To second order, irrotational wave dynamics interacts with the background vorticity field in a way that creates new vortex structures. A notable example is the large parallel vortices which drive Langmuir circulation as oblique plane waves interact with an ocean current. We also investigate the effect on wave pairs which are misaligned with the shear current to find that similar, but skewed, vortex structures are generated in every case except when the mean wave direction is precisely perpendicular to the direction of the current. This is in contrast to a conjecture by Leibovich (Annu. Rev. Fluid Mech., vol. 15, 1983, pp. 391–427). Similar nonlinear wave–shear interactions are found to also generate near-field vortex structures in the Cauchy–Poisson problem with an initial surface elevation. These interactions create further groups of dispersive ring waves in addition to those present in linear theory. The second-order solution is derived in a general manner which accommodates any initial condition through mode coupling over a continuous wave spectrum. It is therefore applicable to a range of problems including special cases of resonance. As a by-product of the general theory, a simple expression for the Stokes drift due to a monochromatic wave propagating at oblique angle with a current of uniform vorticity is derived, for the first time to our knowledge.

Effect of Anisotropic Shape on Ship Wakes in Presence of Shear Current of Uniform Vorticity

2016 ◽  
Author(s):  
Yan Li ◽  
Simen Å. Ellingsen
Keyword(s):  
Aspect Ratio ◽  
Three Dimensional ◽  
Ship Waves ◽  
Aspect Ratios ◽  
Asymptotic Expressions ◽  
Shear Current ◽  
Ship Wakes ◽  
Surface Disturbance ◽  
Dimensional Shape ◽  
Three Dimensional Shape

We analyze the interactions between a subsurface shear current of uniform vorticity and a moving surface disturbance of anisotropic shape which generates surface gravity waves. The problem extends previous analysis of ship waves in the presence of a shear current varying linearly with depth, now also accounting for the three dimensional shape of real ships, in order to study the interplay of aspect ratio and the shear current. Based on general solutions derived previously, we apply an elliptical Gaussian pressure disturbance at the surface moving at constant velocity as a model for a real “ship”. Wave contributions in the far field and expressions for the Mach angle (of maximum wave amplitude) based on asymptotic expressions for high Froude numbers, are derived thereafter. Through numerical calculations we present wave patterns, as well as Kelvin and Mach angles, at moderate Froude numbers under different shear strenghts and aspect ratios. Results show that the aspect ratio has negligible effect on the value of the critical shear vorticity and Kelvin angle, whereas a subtle interplay of aspect ratio and shear strenght is found to affect the Mach angle at moderate Froude numbers.

scholarly journals Multiple resonances of a moving oscillating surface disturbance on a shear current

2016 ◽  
Vol 808 ◽  
pp. 668-689 ◽  
Author(s):  
Yan Li ◽  
Simen Å. Ellingsen
Keyword(s):  
Free Surface ◽  
Dispersion Relation ◽  
Constant Velocity ◽  
Critical Value ◽  
Far Field ◽  
Gravitational Acceleration ◽  
Ship Waves ◽  
Infinite Depth ◽  
Shear Current ◽  
Surface Disturbance

We consider waves radiated by a disturbance of oscillating strength moving at constant velocity along the free surface of a shear flow, which, when undisturbed, has uniform horizontal vorticity of magnitude $S$. When no current is present the problem is a classical one and much studied, and in deep water a resonance is known to occur when $\unicode[STIX]{x1D70F}=|\boldsymbol{V}|\unicode[STIX]{x1D714}_{0}/g$ equals the critical value $1/4$ ($\boldsymbol{V}$: velocity of disturbance, $\unicode[STIX]{x1D714}_{0}$: oscillation frequency, $g$: gravitational acceleration). We show that the presence of a subsurface shear current can change this picture radically. Not only does the resonant value of $\unicode[STIX]{x1D70F}$ depend strongly on the angle between $\boldsymbol{V}$ and the current’s direction and the ‘shear-Froude number’ $\mathit{Fr}_{s}=|\boldsymbol{V}|S/g$; when $\mathit{Fr}_{s}>1/3$, multiple resonant values – as many as four – can occur for some directions of motion. At sufficiently large values of $\mathit{Fr}_{s}$, the smallest resonance frequency tends to zero, representing the phenomenon of critical velocity for ship waves. We provide a detailed analysis of the dispersion relation for the moving oscillating disturbance, in both finite and infinite water depth, including for the latter case an overview of the different far-field waves which exist in different sectors of wave-vector space under different conditions. Owing to the large number of parameters, a detailed discussion of the structure of resonances is provided for infinite depth only, where analytical results are available.

scholarly journals Surface Waves Generated by a Translating and Oscillating Source Atop Realistic Shear Flows

2018 ◽  
Author(s):  
Yan Li ◽  
Simen Å. Ellingsen
Keyword(s):  
Surface Waves ◽  
River Estuary ◽  
Dimensionless Frequency ◽  
Gravitational Acceleration ◽  
Columbia River Estuary ◽  
Depth Dependence ◽  
Shear Current ◽  
Surface Disturbance ◽  
Numerical Tools ◽  
A Current

We analyze surface waves generated by a translating, oscillating surface disturbance atop a horizontal background flow of arbitrary depth dependence, with a focus on determining the Doppler resonance. For a critical value of the dimensionless frequency τ = ωV/g (ω: oscillation frequency, V: source velocity, g: gravitational acceleration) at which generated waves cannot escape. In the absence of shear the resonant value is famously 1/4; the presence of a shear current modifies this. We derive the theoretical and numerical tools for studying this problem, and present the first calculation of the Doppler resonance for a source atop a real, measured shear current to our knowledge. Studying graphical solutions to the (numerically obtained) dispersion relation allows derivation of criteria determining the number of far-field waves that exist in different sectors of propagation directions, from which the criteria for Doppler resonance follow. As example flows we study a typical wind-driven current, and a current measured in the Columbia River estuary. We show that modeling these currents as uniform or with a linear depth dependence based on surface measures may lead to large discrepancies, in particular for long and moderate wavelengths.

The Influence of Barrier and Applied Voltage Parameters on the Impulse Surface Discharge Characteristics

2020 ◽  
Vol 11 (11) ◽  
pp. 17-27
Author(s):  
Vadim V. VOEVODIN ◽  
◽  
Marina V. SOKOLOVA ◽  
Viktor R. SOLOV’YEV ◽  
Nikolay Yu. LYSOV ◽  
...  
Keyword(s):  
Applied Voltage ◽  
Voltage Pulse ◽  
Discharge Zone ◽  
Surface Discharge ◽  
Initial Surface ◽  
Barrier Material ◽  
Dielectric Barrier ◽  
Discharge Ignition ◽  
Study Results ◽  
Wide Range

The results from an experimental study of impulse surface discharge occurring in an electrode system containing a dielectric plate are presented. On one of its sides, the plate had a corona-producing electrode made of 50 mm thick copper foil grounded through a current shunt for measuring the discharge current. On its other side, the plate had a high-voltage electrode, to which the voltage from a pulse generator was applied. The article presents the results from measurements of the initial voltage and the sizes of the surface discharge area in air when applying single voltage pulses with different pulse front steepness in the range 0,1–3,4 kV/ms and amplitude in the range 7–15 kV. The measurements were carried out for different dielectric barrier materials with the e values from 2 to 35. The dielectric barrier thickness was 0,9–1,8 mm. The study results have shown that the initial surface discharge ignition voltage depends essentially on the voltage pulse parameters, whereas the barrier characteristics have a weaker effect on this voltage. It has been determined that the discharge has different discharge zone length and different structure depending on the dielectric barrier properties and applied voltage parameters. The streamer zone sizes decrease with increasing the barrier material e value at the same voltage pulse steepness and increase with increasing the steepness for each barrier material. The data obtained for a wide range of external conditions can be used in numerical modeling of discharge.

Factors Affecting the Wear Behavior of Monolithic Zirconia and the Antagonists: Literature Review

2020 ◽  
Vol 2 (1) ◽  
pp. 4-11
Author(s):  
Marcia Borba ◽  
Paula Benetti ◽  
Giordana P. Furini ◽  
Kátia R. Weber ◽  
Tábata M. da Silva
Keyword(s):  
Literature Review ◽  
Glass Ceramic ◽  
Wear Behavior ◽  
Glass Ceramics ◽  
Surface Treatments ◽  
Human Tooth ◽  
Initial Surface ◽  
Monolithic Zirconia ◽  
Feldspathic Porcelain

Background: The use of zirconia-based ceramics to produce monolithic restorations has increased due to improvements in the optical properties of the materials. Traditionally, zirconiabased ceramics were veneered with porcelain or glass-ceramic and were not directly exposed to the oral environment. Therefore, there are several doubts regarding the wear of the monolithic zirconia restoration and their antagonists. Additionally, different surface treatments are recommended to promote a smooth surface, including glaze and several polishing protocols. To support the correct clinical application, it is important to understand the advantages and limitations of each surface treatment. Objective: The aim of this short literature review is to investigate the factors that may affect the wear of monolithic zirconia restorations in service and their antagonists. Methods: Pubmed/Medline database was accessed to review the literature from a 10-year period using the keywords: zirconia, monolithic, prosthesis, wear. Both clinical and in vitro studies were included in the review. Results: Studies investigated the effect of several surface treatments, including grinding with diamond- burs, polishing and glazing, on the surface roughness, phase transformation and wear capacity of monolithic zirconia. The wear behavior of monolithic zirconia was frequently compared to the wear behavior of other ceramics, such as feldspathic porcelain, lithium disilicate-based glassceramic and leucite-reinforced glass-ceramic. Human tooth, ceramics and resin composites were used as antagonist in the investigations. Only short-term clinical studies are available (up to 2 years). Conclusion: Literature findings suggest that zirconia monolithic restorations are wear resistant and unlikely to cause excessive wear to the antagonist, especially when compared to feldspathic porcelain and glass-ceramics. Monolithic zirconia should be polished rather than glazed. Yet, none of the polishing systems studied was able to completely restore the initial surface conditions of zirconia after being adjusted with burs. More clinical evidence of the antagonist tooth wear potential of monolithic zirconia is needed.

scholarly journals Transverse Hilbert schemes and completely integrable systems

2017 ◽  
Vol 4 (1) ◽  
pp. 263-272 ◽  
Author(s):  
Niccolò Lora Lamia Donin
Keyword(s):  
Integrable Systems ◽  
Hilbert Scheme ◽  
Symplectic Form ◽  
Initial Surface ◽  
Hilbert Schemes ◽  
Completely Integrable Systems ◽  
Completely Integrable ◽  
Symplectic Surface ◽  
Complex Symplectic ◽  
Minimum Polynomial

Abstract In this paper we consider a special class of completely integrable systems that arise as transverse Hilbert schemes of d points of a complex symplectic surface S projecting onto ℂ via a surjective map p which is a submersion outside a discrete subset of S. We explicitly endow the transverse Hilbert scheme Sp[d] with a symplectic form and an endomorphism A of its tangent space with 2-dimensional eigenspaces and such that its characteristic polynomial is the square of its minimum polynomial and show it has the maximal number of commuting Hamiltonians.We then provide the inverse construction, starting from a 2ddimensional holomorphic integrable system W which has an endomorphism A: TW → TW satisfying the above properties and recover our initial surface S with W ≌ Sp[d].

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