scholarly journals Stratified Large-Amplitude Steady Periodic Water Waves with Critical Layers

2020 ◽  
Author(s):  
Susanna V. Haziot
Keyword(s):  
Conformal Mapping ◽  
Density Function ◽  
Water Waves ◽  
Large Amplitude ◽  
Bifurcation Theory ◽  
Critical Layers

Abstract By means of a conformal mapping and bifurcation theory, we prove the existence of large-amplitude steady stratified periodic water waves, with a density function depending linearly on the streamfunction, which may have critical layers and overhanging profiles. We also provide certain conditions for which these waves cannot overturn.

Large-amplitude unsteady flow in liquid-filled elastic tubes

1967 ◽  
Vol 29 (3) ◽  
pp. 513-538 ◽  
Author(s):  
John H. Olsen ◽  
Ascher H. Shapiro
Keyword(s):  
Water Waves ◽  
Large Amplitude ◽  
Linear Equations ◽  
Perturbation Expansion ◽  
Elastic Tube ◽  
Fluid Viscosity ◽  
Elastic Tubes ◽  
Non Linear ◽  
Laminar And Turbulent Flow ◽  
Large Amplitude Motion

Unsteady, large-amplitude motion of a viscous liquid in a long elastic tube is investigated theoretically and experimentally, in the context of physiological problems of blood flow in the larger arteries. Based on the assumptions of long wavelength and longitudinal tethering, a quasi-one-dimensional model is adopted, in which the tube wall moves only radially, and in which only longitudinal pressure gradients and fluid accelerations are important. The effects of fluid viscosity are treated for both laminar and turbulent flow. The governing non-linear equations are solved analytically in closed form by a perturbation expansion in the amplitude parameter, and, for comparison, by numerical integration of the characteristic curves. The two types of solution are compared with each other and with experimental data. Non-linear effects due to large amplitude motion are found to be not as large as those found in similar problems in gasdynamics and water waves.

Accurate calculations of Stokes water waves of large amplitude

1992 ◽  
Vol 43 (2) ◽  
pp. 367-384 ◽  
Author(s):  
W. M. Drennan ◽  
W. H. Hui ◽  
G. Tenti
Keyword(s):  
Water Waves ◽  
Large Amplitude

On analyticity of travelling water waves

2005 ◽  
Vol 461 (2057) ◽  
pp. 1283-1309 ◽  
Author(s):  
David P Nicholls ◽  
Fernando Reitich
Keyword(s):  
Water Waves ◽  
Bifurcation Theory ◽  
Amplitude Ratio ◽  
Travelling Waves ◽  
Three Dimensional ◽  
Perturbation Parameter ◽  
Boundary Perturbation ◽  
Classical Boundary ◽  
Boundary Model ◽  
Special Case

In this paper we establish the existence and analyticity of periodic solutions of a classical free-boundary model of the evolution of three-dimensional, capillary–gravity waves on the surface of an ideal fluid. The result is achieved through the application of bifurcation theory to a boundary perturbation formulation of the problem, and it yields analyticity jointly with respect to the perturbation parameter and the spatial variables. The travelling waves we find can be interpreted as resulting from the (nonlinear) interaction of two two-dimensional wavetrains, giving rise to a periodic travelling pattern. Our analyticity theorem extends the most sophisticated results known to date in the absence of resonance; ‘short crested waves’, which result from the interaction of two wavetrains with unit amplitude ratio are realized as a special case. Our method of proof also sheds light on the convergence and conditioning properties of classical boundary perturbation methods for the numerical approximation of travelling surface waves. Indeed, we demonstrate that the rather unstable numerical behaviour of these approaches can be attributed to the strong but subtle cancellations in the formulas underlying their classical implementations. These observations motivate the derivation and use of an alternative, stable, formulation which, in addition to providing our method of proof, suggests new stabilized implementations of boundary perturbation algorithms.

Large-Amplitude Solitary Water Waves with Vorticity

2013 ◽  
Vol 45 (5) ◽  
pp. 2937-2994 ◽  
Author(s):  
Miles H. Wheeler
Keyword(s):  
Water Waves ◽  
Large Amplitude

Numerical Study of the Motions in Shallow Water Waves of Floating Bodies Elastically Linked to Bottom

2009 ◽  
Author(s):  
Marcio Michiharu Tsukamoto ◽  
Liang-Yee Cheng ◽  
Kazuo Nishimoto
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Large Amplitude ◽  
Numerical Study ◽  
Numerical Approach ◽  
Floating Bodies ◽  
Restoring Force ◽  
Hydrodynamic Loads ◽  
Elastic Links ◽  
Analytical Approaches

The motion of floating bodies linked elastically to the bottom of seas and waterways is of great interest in the analysis of the wave suppressing devices, such as wave breakers, and the behaviors of the floating structures, such as buoys and tension leg platforms (TLP). For the modeling of the dynamics, the coupling between the hydrodynamic loads due to waves and the restoring forces due to the elastic link must be considered. In some simpler cases, the analytical approaches are available. However, in case of large amplitude waves and floating bodies with complex geometries, the analytical solutions do not give accurate results. In the present study, a numerical model based on MPS (moving particle semi-implicit method) for the hydrodynamic loads coupled with the Hook’s Law for the restoring force is adopted to analyze the motion of floating bodies with one or several elastic links to the bottom of shallow water under large amplitude waves. Initially, the results of 2D numerical simulation of simple oscillating buoys are compared with the analytical and experimental ones to validate the numerical approach. After that, the approach is applied to the study of the shallow water wave supressing devices. Heave, surge and pitching motions of the floaters are assessed as well as the hydrodynamic coefficients to show the effect of the elastic links in the nonlinear wave hydrodynamics.

Large-amplitude steady rotational water waves

2008 ◽  
Vol 27 (2) ◽  
pp. 96-109 ◽  
Author(s):  
Joy Ko ◽  
Walter Strauss
Keyword(s):  
Water Waves ◽  
Large Amplitude

Effect of vorticity on steady water waves

2008 ◽  
Vol 608 ◽  
pp. 197-215 ◽  
Author(s):  
JOY KO ◽  
WALTER STRAUSS
Keyword(s):  
Shear Layer ◽  
Stagnation Point ◽  
Mass Flux ◽  
Water Waves ◽  
Large Amplitude ◽  
Maximum Amplitude ◽  
Finite Depth ◽  
Hydraulic Head ◽  
Two Dimensional

Two-dimensional, finite-depth periodic steady water waves with variable vorticity ω=γ(ψ) and large amplitude a are computed for a large number of cases. In particular, the effect of a shear layer at the top, the middle or the bottom is considered. The maximum amplitude amax varies monotonically with the vorticity function γ(ċ). It is increasing if the stagnation point is at the crest, and is decreasing if the stagnation point is in the interior of the fluid or on the bottom. Relationships between the amplitude, hydraulic head, depth and mass flux are investigated.

scholarly journals Nonlinear low-frequency gravity waves in a water-filled cylindrical vessel subjected to high-frequency excitations

2013 ◽  
Vol 469 (2153) ◽  
pp. 20120536 ◽  
Author(s):  
Chunyan Zhou ◽  
Dajun Wang ◽  
Song Shen ◽  
Jing Tang Xing
Keyword(s):  
Gravity Waves ◽  
High Frequency ◽  
Water Waves ◽  
Large Amplitude ◽  
Low Frequency ◽  
Approximation Model ◽  
Fluid Structure Interactions ◽  
Governing Equations ◽  
Low Frequencies ◽  
Nonlinear Fluid

In the experiments of a water storage cylindrical shell, excited by a horizontal external force of sufficient large amplitude and high frequency, it has been observed that gravity water waves of low frequencies may be generated. This paper intends to investigate this phenomenon in order to reveal its mechanism. Considering nonlinear fluid–structure interactions, we derive the governing equations and the numerical equations describing the dynamics of the system, using a variational principle. Following the developed generalized equations, a four-mode approximation model is proposed with which an experimental case example is studied. Numerical calculation and spectrum analysis demonstrate that an external excitation with sufficient large amplitude and high frequency can produce gravity water waves with lower frequencies. The excitation magnitude and frequencies required for onset of the gravity waves are found based on the model. Transitions between different gravity waves are also revealed through the numerical analysis. The findings developed by this method are validated by available experimental observations.

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