scholarly journals Enhanced Energy Dissipation by Parasitic Capillaries on Short Gravity–Capillary Waves

2010 ◽  
Vol 40 (11) ◽  
pp. 2435-2450 ◽  
Author(s):  
Wu-ting Tsai ◽  
Li-ping Hung
Keyword(s):  
Energy Dissipation ◽  
Dissipation Rate ◽  
Capillary Wave ◽  
Wave Train ◽  
Three Dimensional ◽  
Local Maximum ◽  
Finite Amplitude ◽  
Capillary Waves ◽  
Carrier Wave ◽  
Order Of Magnitude

Abstract The increased energy dissipation caused by the formation of parasitic capillary wavelets on moderately short, steep gravity–capillary waves is studied numerically. This study focuses on understanding the mechanism leading to dissipation enhancement and on exploring the possible correlation between the enhanced dissipation rate and the characteristic parameters of the parasitic capillaries. The interaction between the parasitic capillary wave train and the underlying dominant flow of the carrier wave induces strong vortex shedding and imposes large straining immediately underneath the troughs of the capillary ripples. These localized strains are very effective in dissipating energy of the carrier gravity–capillary wave. The attenuation rate of the carrier wave can increase by more than one order of magnitude in the presence of capillary wavelets. Systematic simulations for various carrier wavelengths and steepnesses reveal that the enhanced dissipation rate can be quantified well by a simple parameter: the average of all the difference between the local maximum and minimum slopes along the entire carrier wave surface, which is equivalent to the mean slope of the parasitic capillary wave train. The enhanced dissipation rate increases approximately linearly with the carrier gravity–capillary wavenumber for a given mean slope of the capillary wave train. The increased energy dissipation caused by the formation of parasitic capillaries is also found to significantly impact on the characteristics of three-dimensional instabilities of finite-amplitude, uniform gravity–capillary waves.

scholarly journals The Formation of Parasitic Capillary Ripples on Gravity–Capillary Waves and the Underlying Vortical Structures

2009 ◽  
Vol 39 (2) ◽  
pp. 263-289 ◽  
Author(s):  
Li-Ping Hung ◽  
Wu-Ting Tsai
Keyword(s):  
Capillary Wave ◽  
Wave Train ◽  
Strong Dependence ◽  
Capillary Waves ◽  
Wave Crest ◽  
Carrier Wave ◽  
Vortical Structures ◽  
Steady Stage ◽  
Dimensional Gravity ◽  
Vortical Layer

Abstract The evolution of moderately short, steep two-dimensional gravity–capillary waves, from the onset of the parasitic capillary ripples to a fully developed quasi-steady stage, is studied numerically using a spectrally accurate model. The study focuses on understanding the precise mechanism of capillary generation, and on characterizing surface roughness and the underlying vortical structure associated with parasitic capillary waves. It is found that initiation of the first capillary ripple is triggered by the fore–aft asymmetry of the otherwise symmetric carrier wave, which then forms a localized pressure disturbance on the forward face near the crest, and subsequently develops an oscillatory train of capillary waves. Systematic numerical experiments reveal that there exists a minimum crest curvature of the carrier gravity–capillary wave for the formation of parasitic capillary ripples, and such a threshold curvature (≈0.25 cm−1) is almost independent of the carrier wavelength. The characteristics of the parasitic capillary wave train and the induced underlying vortical structures exhibit a strong dependence on the carrier wavelength. For a steep gravity–capillary wave with a shorter wavelength (e.g., 5 cm), the parasitic capillary wave train is distributed over the entire carrier wave surface at the stage when capillary ripples are fully developed. Immediately underneath the capillary wave train, weak vortices are observed to confine within a thin layer beneath the ripple crests whereas strong vortical layers with opposite orientation of vorticity are shed from the ripple troughs. These strong vortical layers are then convected upstream and accumulate within the carrier wave crest, forming a strong “capillary roller” as postulated by Longuet-Higgins. In contrast, as the wavelength of the gravity–capillary wave increases (e.g., 10 cm), parasitic capillary ripples appear as being trapped in the forward slope of the carrier wave. The strength of the vortical layer shed underneath the parasitic capillaries weakens, and its thickness and extent reduces. The vortices accumulating within the crest of the carrier wave, therefore, are not as pronounced as those observed in the shorter gravity–capillary waves.

Study on Hydraulic Characteristics and Optimization of Siphon Channel with Two Inlets in Drydock

2014 ◽  
Vol 638-640 ◽  
pp. 1285-1292
Author(s):  
Peng Zhao ◽  
Yu Chuan Bai
Keyword(s):  
Energy Dissipation ◽  
Numerical Model ◽  
Kinetic Energy ◽  
Dissipation Rate ◽  
Three Dimensional ◽  
Flow State ◽  
Hydraulic Characteristics ◽  
Channel System ◽  
Guide Wall ◽  
Low Efficiency

Compared with the siphon channel with one inlet, the siphon channel with two inlets has some problems such as low efficiency of flooding. Combining with the model test of siphon channel with two inlets in a drydock, three-dimensional numerical model was built to study the hydraulic characteristics of siphon channel system. The reliability of numerical model was confirmed by comparing the calculated value and measured value of hump pressure and flooding rate. Results of turbulent kinetic energy and dissipation rate indicate that flow kinetic energy is mainly dissipated by the friction and its impacting the wall behind partition and the effect of energy dissipation pillars are not obvious. By comparing flow state in front of energy dissipation section and flooding rate between design scheme and modified scheme, it is suggested that the guide wall should be dismantled to ameliorate flow state.

Local energy flux and subgrid-scale statistics in three-dimensional turbulence

1998 ◽  
Vol 366 ◽  
pp. 1-31 ◽  
Author(s):  
VADIM BORUE ◽  
STEVEN A. ORSZAG
Keyword(s):  
Energy Transfer ◽  
Energy Dissipation ◽  
Energy Flux ◽  
Dissipation Rate ◽  
Three Dimensional ◽  
Energy Dissipation Rate ◽  
Inertial Range ◽  
Local Energy ◽  
Subgrid Scale ◽  
Velocity Gradients

Statistical properties of the subgrid-scale stress tensor, the local energy flux and filtered velocity gradients are analysed in numerical simulations of forced three-dimensional homogeneous turbulence. High Reynolds numbers are achieved by using hyperviscous dissipation. It is found that in the inertial range the subgrid-scale stress tensor and the local energy flux allow simple parametrization based on a tensor eddy viscosity. This parametrization underlines the role that negative skewness of filtered velocity gradients plays in the local energy transfer. It is found that the local energy flux only weakly correlates with the locally averaged energy dissipation rate. This fact reflects basic difficulties of large-eddy simulations of turbulence, namely the possibility of predicting the locally averaged energy dissipation rate through inertial-range quantities such as the local energy flux is limited. Statistical properties of subgrid-scale velocity gradients are systematically studied in an attempt to reveal the mechanism of local energy transfer.

FIFTH-ORDER EVOLUTION EQUATION OF GRAVITY–CAPILLARY WAVES

2017 ◽  
Vol 59 (1) ◽  
pp. 103-114
Author(s):  
DIPANKAR CHOWDHURY ◽  
SUMA DEBSARMA
Keyword(s):  
Evolution Equation ◽  
Evolution Equations ◽  
Capillary Wave ◽  
Wave Train ◽  
Critical Value ◽  
Capillary Waves ◽  
Wave Number ◽  
Region Of Stability ◽  
Fifth Order ◽  
Nonlinear Gravity

We extend the evolution equation for weak nonlinear gravity–capillary waves by including fifth-order nonlinear terms. Stability properties of a uniform Stokes gravity–capillary wave train is studied using the evolution equation obtained here. The region of stability in the perturbed wave-number plane determined by the fifth-order evolution equation is compared with that determined by third- and fourth-order evolution equations. We find that if the wave number of longitudinal perturbations exceeds a certain critical value, a uniform gravity–capillary wave train becomes unstable. This critical value increases as the wave steepness increases.

Suppressing van der Waals driven rupture through shear

2010 ◽  
Vol 661 ◽  
pp. 522-539 ◽  
Author(s):  
M. J. DAVIS ◽  
M. B. GRATTON ◽  
S. H. DAVIS
Keyword(s):  
Free Surface ◽  
Wind Shear ◽  
Capillary Wave ◽  
Van Der Waals ◽  
Three Dimensional ◽  
Angular Speed ◽  
Critical Value ◽  
Finite Amplitude ◽  
Two Dimensions ◽  
Sivashinsky Equation

An ultra-thin viscous film on a substrate is susceptible to rupture instabilities driven by van der Waals attractions. When a unidirectional ‘wind’ shear τ is applied to the free surface, the rupture instability in two dimensions is suppressed when τ exceeds a critical value τc and is replaced by a permanent finite-amplitude structure, an intermolecular-capillary wave, that travels at approximately the speed of the surface. For small amplitudes, the wave is governed by the Kuramoto–Sivashinsky equation. If three-dimensional disturbances are allowed, the shear is decoupled from disturbances perpendicular to the flow, and line rupture would occur. In this case, replacing the unidirectional shear with a shear whose direction rotates with angular speed, , suppresses the rupture if τ ≳ 2τc. For the most dangerous wavenumber, τc ≈ 10−2 dyn cm−2 at ≈ 1 rad s−1 for a film with physical properties similar to water at a thickness of 100 nm.

Experiments on nonlinear gravity–capillary waves

1999 ◽  
Vol 380 ◽  
pp. 205-232 ◽  
Author(s):  
LEV SHEMER ◽  
MELAD CHAMESSE
Keyword(s):  
Narrow Band ◽  
Numerical Study ◽  
Three Dimensional ◽  
Capillary Waves ◽  
Carrier Wave ◽  
Nls Equation ◽  
Zakharov Equation ◽  
The Stability ◽  
Nonlinear Gravity

Benjamin–Feir instability of nonlinear gravity–capillary waves is studied experimentally. The experimental results are compared with computations performed for values of wavelength and steepness identical to those employed in the experiments. The theoretical approach is based on the Zakharov nonlinear equation which is modified here to incorporate weak viscous dissipation. Experiments are performed in a wave ume which has an accurately controlled wavemaker for generation of the carrier wave, as well as an additional independent conical wavemaker for generation of controlled three-dimensional disturbances. The approach adopted in the present experimental investigation allows therefore the determination of the actual boundaries of the instability domain, and not just the most unstable disturbances. Instantaneous surface elevation measurements are performed with capacitance-type wave gauges. Multipoint measurements make it possible to determine the angular dependence of the amplitude of the forced and unforced disturbances, as well as their variation along the tank. The limits of the instability domains obtained experimentally for each set of carrier wave parameters agree favourably with those computed numerically using the model equation. The numerical study shows that application of the Zakharov equation, which is free of the narrow-band approximation adopted in the derivation of the nonlinear Schrödinger (NLS) equation, may lead to qualitatively different results regarding the stability of nonlinear gravity–capillary waves. The present experiments support the results of the numerical investigation.

Nonlinear evolution of waves on a vertically falling film

1993 ◽  
Vol 250 ◽  
pp. 433-480 ◽  
Author(s):  
H.-C. Chang ◽  
E. A. Demekhin ◽  
D. I. Kopelevich
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Travelling Wave ◽  
Finite Amplitude ◽  
Capillary Waves ◽  
Stationary Waves ◽  
Falling Film ◽  
Linear Mode

Wave formation on a falling film is an intriguing hydrodynamic phenomenon involving transitions among a rich variety of spatial and temporal structures. Immediately beyond an inception region, short, near-sinusoidal capillary waves are observed. Further downstream, long, near-solitary waves with large tear-drop humps preceded by short, front-running capillary waves appear. Both kinds of waves evolve slowly downstream such that over about ten wavelengths, they resemble stationary waves which propagate at constant speeds and shapes. We exploit this quasi-steady property here to study wave evolution and selection on a vertically falling film. All finite-amplitude stationary waves with the same average thickness as the Nusselt flat film are constructed numerically from a boundary-layer approximation of the equations of motion. As is consistent with earlier near-critical analyses, two travelling wave families are found, each parameterized by the wavelength or the speed. One family γ1travels slower than infinitesimally small waves of the same wavelength while the other family γ2and its hybrids travel faster. Stability analyses of these waves involving three-dimensional disturbances of arbitrary wavelength indicate that there exists a unique nearly sinusoidal wave on the slow family γ1with wavenumber αs(or α2) that has the lowest growth rate. This wave is slightly shorter than the fastest growing linear mode with wavenumber αmand approaches the wave on γ1with the highest flow rate at low Reynolds numbers. On the fast γ2family, however, multiple bands of near-solitary waves bounded below by αfare found to be stable to two-dimensional disturbances. This multiplicity of stable bands can be interpreted as a result of favourable interaction among solitary-wave-like coherent structures to form a periodic train. (All waves are unstable to three-dimensional disturbances with small growth rates.) The suggested selection mechanism is consistent with literature data and our numerical experiments that indicate waves slow down immediately beyond inception as they approach the short capillary wave with wavenumber α2of the slow γ1family. They then approach the long stable waves on the γ2family further downstream and hence accelerate and develop into the unique solitary wave shapes, before they succumb to the slowly evolving transverse disturbances.

scholarly journals Study of finite amplitude capillary waves stability

2018 ◽  
Vol 211 ◽  
pp. 04008
Author(s):  
Alexander Petrov ◽  
Mariana Lopushanski
Keyword(s):  
Lyapunov Function ◽  
Lyapunov Method ◽  
Capillary Wave ◽  
Momentum Conservation ◽  
Finite Amplitude ◽  
Positive Definite ◽  
Capillary Waves ◽  
Dynamic Equations ◽  
Direct Lyapunov Method ◽  
Energy And Momentum

The direct Lyapunov method is used to study capillary waves. The dynamic equations of the capillary wave are presented in the form of an infinite Euler-Lagrange chain of equations for the Stokes coefficients. The stationary solution found for these equations is the Crapper solution for capillary waves. With the help of energy and momentum conservation laws the Lyapunov function is constructed. It is shown that the Lyapunov function is positive definite with respect to any perturbations of waves surfaces with the period that is a multiple of the wave period.

scholarly journals Hydraulic Characteristics and Numerical Simulation of the Entrance Section of Ladder-Shaped Spillway

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
X. B. Gu ◽  
Q. H. Wu ◽  
Y. Wang ◽  
H. X. Zhao
Keyword(s):  
Numerical Simulation ◽  
Energy Dissipation ◽  
Dissipation Rate ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Energy Dissipation Rate ◽  
Numerical Results ◽  
Experimental Results ◽  
Flow State ◽  
Hydraulic Characteristics

The ladder-shaped spillway in a certain reservoir junction is set as the engineering background in the paper. The hydraulic similarly model experiment and three-dimensional numerical simulation of hydraulic characteristics of water flow are performed. The outflow capacity, flow state analysis, velocity distribution, water surface line, pressure, and the energy dissipation rate are analyzed, and experimental results are compared with the numerical results. The conclusions demonstrate that the numerical results of the flow characteristics are very proximate to actual experimental results, the changeable law is the same, and their energy dissipation rate is basically consistent; it shows the feasibility of three-dimensional numerical simulation; the conclusions can provide the basis for the optimization about the flow state of the ladder-shaped spillway in the future.

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