scholarly journals Dynamics of Three-Dimensional Gravity-Capillary Solitary Waves in Deep Water

2010 ◽  
Vol 70 (7) ◽  
pp. 2390-2408 ◽  
Author(s):  
Benjamin Akers ◽  
Paul A. Milewski
Keyword(s):  
Solitary Waves ◽  
Deep Water ◽  
Three Dimensional ◽  
Dimensional Gravity

Two-dimensional gravity–capillary solitary waves on deep water: generation and transverse instability

2017 ◽  
Vol 834 ◽  
pp. 92-124 ◽  
Author(s):  
Beomchan Park ◽  
Yeunwoo Cho
Keyword(s):  
Solitary Waves ◽  
Deep Water ◽  
Three Dimensional ◽  
Phase Speed ◽  
Narrow Slit ◽  
Two Dimensional ◽  
Transverse Instability ◽  
High Speeds ◽  
Linear Waves ◽  
Dimensional Gravity

Two-dimensional (2-D) gravity–capillary solitary waves are generated using a moving pressure jet from a 2-D narrow slit as a forcing onto the surface of deep water. The forcing moves horizontally over the surface of the deep water at speeds close to the minimum phase speed $c_{min}=23~\text{cm}~\text{s}^{-1}$. Four different states are observed according to the forcing speed. At relatively low speeds below $c_{min}$, small-amplitude depressions are observed and they move steadily just below the moving forcing. As the forcing speed increases towards $c_{min}$, nonlinear 2-D gravity–capillary solitary waves are observed, and they move steadily behind the moving forcing. When the forcing speed is very close to $c_{min}$, periodic shedding of a 2-D local depression is observed behind the moving forcing. Finally, at relatively high speeds above $c_{min}$, a pair of short and long linear waves is observed, respectively ahead of and behind the moving forcing. In addition, we observe the transverse instability of free 2-D gravity–capillary solitary waves and, further, the resultant formation of three-dimensional gravity–capillary solitary waves. These experimental observations are compared with numerical results based on a model equation that admits gravity–capillary solitary wave solutions near $c_{min}$. They agree with each other very well. In particular, based on a linear stability analysis, we give a theoretical proof for the transverse instability of the 2-D gravity–capillary solitary waves on deep water.

scholarly journals Transverse instability of gravity–capillary solitary waves on deep water in the presence of constant vorticity

2019 ◽  
Vol 871 ◽  
pp. 1028-1043
Author(s):  
M. Abid ◽  
C. Kharif ◽  
H.-C. Hsu ◽  
Y.-Y. Chen
Keyword(s):  
Growth Rate ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Deep Water ◽  
Capillary Waves ◽  
Two Dimensional ◽  
Transverse Instability ◽  
Constant Vorticity ◽  
Dimensional Gravity ◽  
Wave Properties

The bifurcation of two-dimensional gravity–capillary waves into solitary waves when the phase velocity and group velocity are nearly equal is investigated in the presence of constant vorticity. We found that gravity–capillary solitary waves with decaying oscillatory tails exist in deep water in the presence of vorticity. Furthermore we found that the presence of vorticity influences strongly (i) the solitary wave properties and (ii) the growth rate of unstable transverse perturbations. The growth rate and bandwidth instability are given numerically and analytically as a function of the vorticity.

scholarly journals Stability and dynamics of two-dimensional fully nonlinear gravity–capillary solitary waves in deep water

2016 ◽  
Vol 809 ◽  
pp. 530-552 ◽  
Author(s):  
Z. Wang
Keyword(s):  
Solitary Waves ◽  
Deep Water ◽  
Wave Equations ◽  
Turning Point ◽  
Phase Speed ◽  
Amplitude Curve ◽  
Two Dimensional ◽  
Fully Nonlinear ◽  
Dimensional Gravity ◽  
The Stability

The stability and dynamics of two-dimensional gravity–capillary solitary waves in deep water within the fully nonlinear water-wave equations are numerically studied. It is well known that there are two families of symmetric gravity–capillary solitary waves – depression waves and elevation waves – bifurcating from infinitesimal periodic waves at the minimum of the phase speed. The stability of both branches was previously examined by Calvo & Akylas (J. Fluid Mech., vol. 452, 2002, pp. 123–143) by means of a numerical spectral analysis. Their results show that the depression solitary waves with single-valued profiles are stable, while the elevation branch experiences a stability exchange at a turning point on the speed–amplitude curve. In the present paper, we provide numerical evidence that the depression solitary waves with an overhanging structure are also stable. On the other hand, Dias et al. (Eur. J. Mech. B, vol. 15, 1996, pp. 17–36) numerically traced the elevation branch and discovered that its speed–amplitude bifurcation curve features a ‘snake-like’ behaviour with many turning points, whereas Calvo & Akylas (J. Fluid Mech., vol. 452, 2002, pp. 123–143) only considered the stability exchange near the first turning point. Our results reveal that the stability exchange occurs again near the second turning point. A branch of asymmetric solitary waves is also considered and found to be unstable, even when the wave profile consists of a depression wave and a stable elevation one. The excitation of stable gravity–capillary solitary waves is carried out via direct numerical simulations. In particular, the stable elevation waves, which feature two troughs connected by a small dimple, can be excited by moving two fully localised, well-separated pressures on the free surface with the speed slightly below the phase speed minimum and removing the pressures simultaneously after a period of time.

scholarly journals Three-dimensional gravity-capillary solitary waves in water of finite depth and related problems

2005 ◽  
Vol 17 (12) ◽  
pp. 122101 ◽  
Author(s):  
E. I. Părău ◽  
J.-M. Vanden-Broeck ◽  
M. J. Cooker
Keyword(s):  
Solitary Waves ◽  
Three Dimensional ◽  
Finite Depth ◽  
Dimensional Gravity

scholarly journals Nonlinear three-dimensional gravity–capillary solitary waves

2005 ◽  
Vol 536 ◽  
pp. 99-105 ◽  
Author(s):  
E. I. PĂRĂU ◽  
J.-M. VANDEN-BROECK ◽  
M. J. COOKER
Keyword(s):  
Solitary Waves ◽  
Three Dimensional ◽  
Dimensional Gravity

Experimental observation of gravity–capillary solitary waves generated by a moving air suction

2016 ◽  
Vol 808 ◽  
pp. 168-188 ◽  
Author(s):  
Beomchan Park ◽  
Yeunwoo Cho
Keyword(s):  
Experimental Observation ◽  
Solitary Waves ◽  
Deep Water ◽  
Small Amplitude ◽  
Three Dimensional ◽  
Phase Speed ◽  
Linear Phase ◽  
Wave Patterns ◽  
Air Blowing ◽  
Linear And Nonlinear

Gravity–capillary solitary waves are generated by a moving ‘air-suction’ forcing instead of a moving ‘air-blowing’ forcing. The air-suction forcing moves horizontally over the surface of deep water with speeds close to the minimum linear phase speed $c_{min}=23~\text{cm}~\text{s}^{-1}$. Three different states are observed according to forcing speeds below $c_{min}$. At relatively low speeds below $c_{min}$, small-amplitude linear circular depressions are observed, and they move steadily ahead of and along with the moving forcing. As the forcing speed increases close to $c_{min}$, however, nonlinear three-dimensional (3-D) gravity–capillary solitary waves are observed, and they move steadily ahead of and along with the moving forcing. Finally, when the forcing speed is very close to $c_{min}$, oblique shedding phenomena of 3-D gravity–capillary solitary waves are observed ahead of the moving forcing. We found that all the linear and nonlinear wave patterns generated by the air-suction forcing correspond to those generated by the air-blowing forcing. The main difference is that 3-D gravity–capillary solitary waves are observed ‘ahead of’ the air-suction forcing whereas the same waves are observed ‘behind’ the air-blowing forcing.

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

Study of dynamic pressure on the packer for deep-water perforation

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 215-223
Author(s):  
Hao Huang ◽  
Qiao Deng ◽  
Hui Zhang
Keyword(s):  
Deep Water ◽  
Peak Pressure ◽  
Orthogonal Design ◽  
Dynamic Pressure ◽  
Three Dimensional ◽  
Calculation Model ◽  
Well Testing ◽  
Technical Problems ◽  
Wellbore Pressure ◽  
Three Dimensional Finite Element

Abstract The packer is one of the most important tools in deep-water perforation combined well testing, and its safety directly determines the success of perforation test operations. The study of dynamic perforating pressure on the packer is one of the key technical problems in the production of deep-water wells. However, there are few studies on the safety of packers with shock loads. In this article, the three-dimensional finite element models of downhole perforation have been established, and a series of numerical simulations are carried out by using orthogonal design. The relationship between the perforating peak pressure on the packer with the factors such as perforating charge quantity, wellbore pressure, perforating explosion volume, formation pressure, and elastic modulus is established. Meanwhile, the database is established based on the results of numerical simulation, and the calculation model of peak pressure on the packer during perforating is obtained by considering the reflection and transmission of shock waves on the packer. The results of this study have been applied in the field case of deep-water well, and the safety optimization program for deep-water downhole perforation safety has been put forward. This study provides important theoretical guidance for the safety of the packer during deep-water perforating.

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