Internal Wave Propagation from Pulsating Sources in a Two-Layer Fluid of Finite Depth

2012 ◽  
Vol 201-202 ◽  
pp. 503-507
Author(s):  
David O. Manyanga ◽  
Wen Yang Duan
Keyword(s):  
Free Surface ◽  
Internal Wave ◽  
Internal Waves ◽  
Wave Length ◽  
Three Dimensional ◽  
Vertical Direction ◽  
Finite Depth ◽  
Green Functions ◽  
Design And Optimization ◽  
Underwater Structures

The influence of internal waves is very important in the Engineering Analysis, Design and Optimization. To study the internal wave properties, we model a two-layer fluid and generalize to multiple layers. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating due to the free surface and the interface. This is due to the density difference in the vertical direction of the water, due to the variation in salinity and temperature where waves from underwater structures are of importance. In this case the fluid is assumed to be non viscous, incompressible and the flow is non rotational. On the other hand, there is need for appropriate Green functions to analyze these properties. In this paper, we use the three dimensional Green functions for a stationary oscillating source to study the internal wave characteristics. Some of the behavior studied in this work includes effects of internal waves on the surface and internal wave amplitudes. Further, an investigation of the influence of internal waves on the wave length, frequency and period is made.

Calculation of Horizontal Sectional Loads and Torsional Moment

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Vladimir Shigunov ◽  
Alexander von Graefe ◽  
Ould el Moctar
Keyword(s):  
Free Surface ◽  
Shear Force ◽  
Three Dimensional ◽  
Bending Moment ◽  
Green Functions ◽  
Container Ship ◽  
Horizontal Shear ◽  
Torsional Moment ◽  
Oblique Waves ◽  
Rankine Source

Horizontal sectional loads (horizontal shear force and horizontal bending moment) and torsional moment are more difficult to predict with potential flow methods than vertical loads, especially in stern-quartering waves. Accurate computation of torsional moment is especially important for large modern container ships. The three-dimensional (3D) seakeeping code GL Rankine has been applied previously to the computation of vertical loads in head, following and oblique waves; this paper addresses horizontal loads and torsional moment in oblique waves at various forward speeds for a modern container ship. The results obtained with the Rankine source-patch method are compared with the computations using zero-speed free-surface Green functions and with model experiments.

Internal waves in a circular channel

1976 ◽  
Vol 74 (1) ◽  
pp. 183-192 ◽  
Author(s):  
W. H. Yang ◽  
Chia-Shun Yih
Keyword(s):  
Free Surface ◽  
Internal Wave ◽  
Internal Waves ◽  
Flow Patterns ◽  
Circular Channel ◽  
Fluid Layers ◽  
Wave Modes

The frequencies of the first four sloshing internal wave modes in two superposed fluid layers contained in a circular channel are calculated for two positions of the free surface and for various ratios of the depths of the two layers. Flow patterns are given for the first four sloshing modes for the case in which the fluids occupy a semicircular space and the depth of the upper layer is one-quarter of the radius.It is hoped that the results obtained will provide a guide for estimating the frequencies of sloshing internal wave modes in long lakes.

The translation of two bodies under the free surface of a heavy fluid

1950 ◽  
Vol 46 (3) ◽  
pp. 453-468 ◽  
Author(s):  
A. Coombs
Keyword(s):  
Free Surface ◽  
Large Range ◽  
Three Dimensional ◽  
Finite Depth ◽  
Arbitrary Cross Section ◽  
Wave Resistance ◽  
Vertical Force ◽  
First Approximation ◽  
Special Case ◽  
Two Bodies

1. Many investigations have been made to determine the wave resistance acting on a body moving horizontally and uniformly in a heavy, perfect fluid. Lamb obtained a first approximation for the wave resistance on a long circular cylinder, and this was later confirmed to be quite sufficient over a large range. In 1926 and 1928, Havelock (4, 5) obtained a second approximation for the wave resistance and a first approximation for the vertical force or lift. Later, in 1936(6), he gave a complete analytical solution to this problem, in which the forces were expressed in the form of infinite series in powers of the ratio of the radius of the cylinder to the depth of the centre below the free surface of the fluid. General expressions for the wave resistance and lift of a cylinder of arbitrary cross-section were found by Kotchin (7) using integral equations, and the special case of a flat plate was evaluated. He continued with a discussion of the motion of a three-dimensional body. More recently, Haskind (3) has examined the same problem when the stream has a finite depth.

The limiting form of internal waves

1984 ◽  
Vol 394 (1807) ◽  
pp. 329-344 ◽  
Keyword(s):  
Free Surface ◽  
Internal Wave ◽  
Internal Waves ◽  
Solitary Waves ◽  
The Other ◽  
Stokes Wave ◽  
Internal Solitary Waves ◽  
Two Dimensional ◽  
Extreme Form ◽  
Eddy Formation

The bifurcation of two-dimensional internal solitary waves in a perfect density stratified fluid between horizontal walls under gravity is studied near to a point of incipient eddy formation. It is shown that eddies do not attach to the walls. Moreover, along the bifurcating branch there is always a flow with a singular cusped streamline before the formation of eddies. This flow with the cusped streamline is an example of what we call an internal wave of limiting form, by analogy with the Stokes wave of extreme form in the free surface problem. Two examples are given where the primary density stratification ensures the existence of a limiting wave of depression in one case, and of elevation in the other.

scholarly journals Oblique internal-wave chain resonance over seabed corrugations

2017 ◽  
Vol 833 ◽  
pp. 538-562
Author(s):  
Louis-Alexandre Couston ◽  
Yong Liang ◽  
Mohammad-Reza Alam
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Resonance Condition ◽  
Incidence Angle ◽  
Three Dimensional ◽  
Resonant Interactions ◽  
Near Resonance ◽  
Chain Resonance ◽  
Small Scales ◽  
A Chain

Here we show that monochromatic long-crested corrugations on an otherwise flat seafloor can coherently scatter the energy of an oblique incident internal wave to multiple multi-directional higher-mode internal waves via a series of resonant interactions. We demonstrate that a resonance between seabed corrugations and a normally or slightly oblique incident internal wave results in a series of follow-up resonant interactions, which take place between the same corrugations and successively resonated shorter waves. A chain resonance of internal waves that carries energy to small scales is thus obtained, and we find that the Richardson number decreases by several orders of magnitude over the corrugated patch. If the incidence angle is large, and the incident wave perfectly satisfies a resonance condition with the topography, it turns out that not many higher-mode resonance or near-resonance conditions can be satisfied, such that energy stays confined within the first few modes. Nevertheless, if the incident waves are sufficiently detuned from satisfying a perfect resonance condition with the seabed corrugations, then we show that this frequency detuning may balance off the large detuning due to oblique incidence, leading to a chain resonance that again carries energy to small scales. The evolution of the incident and resonated wave amplitudes is predicted from the envelope equation for internal waves over resonant seabed topography in a three-dimensional rotating fluid, which we derive considering the Boussinesq and $f$-plane approximations with $f$ the Coriolis frequency, linear density stratification and small-amplitude corrugations. Our results suggest that topographic features on the ocean floor with a well-defined dominant wavenumber vector, through the chain resonance mechanism elucidated here, may play a more important role than previously thought in the enhancement of diapycnal mixing and energy dissipation.

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.

scholarly journals Some explicit solutions of the three-dimensional Euler equations with a free surface

2021 ◽  
Author(s):  
Calin I. Martin
Keyword(s):  
Functional Equation ◽  
Free Surface ◽  
Euler Equations ◽  
Vertical Structure ◽  
Three Dimensional ◽  
Finite Depth ◽  
Radial Solutions ◽  
Pressure Function ◽  
Constant Vorticity ◽  
Vorticity Vector

AbstractWe present a family of radial solutions (given in Eulerian coordinates) to the three-dimensional Euler equations in a fluid domain with a free surface and having finite depth. The solutions that we find exhibit vertical structure and a non-constant vorticity vector. Moreover, the flows described by these solutions display a density that depends on the depth. While the velocity field and the pressure function corresponding to these solutions are given explicitly through (relatively) simple formulas, the free surface defining function is specified (in general) implicitly by a functional equation which is analysed by functional analytic methods. The elaborate nature of the latter functional equation becomes simpler when the density function has a particular form leading to an explicit formula of the free surface. We subject these solutions to a stability analysis by means of a Wentzel–Kramers–Brillouin (WKB) ansatz.

Mechanical Stress Analysis of Different Shapes Pillars with Cnoidal Internal Wave Action

2013 ◽  
Vol 732-733 ◽  
pp. 417-420
Author(s):  
Xiao Chao Fan ◽  
Rui Jing Shi ◽  
Feng Ting Li ◽  
Bo Wei ◽  
Yue Dang
Keyword(s):  
Internal Wave ◽  
Stress Analysis ◽  
Internal Waves ◽  
Three Dimensional ◽  
Wave Force ◽  
Viscous Force ◽  
Inertia Force ◽  
Converted Wave ◽  
Numerical Wave Flume ◽  
Wave Flume

The numerical simulations of the flow around different pillars acted by the cnoidal internal waves have been made by building numerical wave flume based on FLUENT software. The cnoidal internal wave was created by using the push-pedal method, and the free surface was tracked by using VOF (volume of fluid) method. The three-dimensional different amplitude and period cnoidal internal waves were simulated. The inertia force and viscous force trends were analyzed, and for different pillars the total wave force were compared. There were some significance for stress analysis of the offshore terminal pillars. The converted wave force could alternative and treatment problems about square columns.

Low-Frequency Acoustic Propagation Through Crossing Internal Waves in Shallow Water

2020 ◽  
Vol 28 (03) ◽  
pp. 1950013
Author(s):  
Alexey Shmelev ◽  
Ying-Tsong Lin ◽  
James Lynch
Keyword(s):  
Internal Wave ◽  
Shallow Water ◽  
Internal Waves ◽  
Three Dimensional ◽  
Low Frequency ◽  
Acoustic Energy ◽  
Full Field ◽  
Wave Trains ◽  
Acoustic Ducts ◽  
Numerical Approaches

Crossing internal wave trains are commonly observed in continental shelf shallow water. In this paper, we study the effects of crossing internal wave structures on three-dimensional acoustic ducts with both theoretical and numerical approaches. We show that, depending on the crossing angle, acoustic energy, which is trapped laterally between internal waves of one train, can be either scattered, cross-ducted or reflected by the internal waves in the crossing train. We describe the governing physics of these effects and illustrate them for selected internal wave scenarios using full-field numerical simulations.

scholarly journals Internal wave attractors in three-dimensional geometries: trapping by oblique reflection

2018 ◽  
Vol 845 ◽  
pp. 203-225 ◽  
Author(s):  
G. Pillet ◽  
E. V. Ermanyuk ◽  
L. R. M. Maas ◽  
I. N. Sibgatullin ◽  
T. Dauxois
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Wave Energy ◽  
Transverse Direction ◽  
Three Dimensional ◽  
Direction Parallel ◽  
3D Geometry ◽  
Experimental Parameters ◽  
Set Up

We study experimentally the propagation of internal waves in two different three-dimensional (3D) geometries, with a special emphasis on the refractive focusing due to the 3D reflection of obliquely incident internal waves on a slope. Both studies are initiated by ray tracing calculations to determine the appropriate experimental parameters. First, we consider a 3D geometry, the classical set-up to get simple, two-dimensional (2D) parallelogram-shaped attractors in which waves are forced in a direction perpendicular to a sloping bottom. Here, however, the forcing is of reduced extent in the along-slope, transverse direction. We show how the refractive focusing mechanism explains the formation of attractors over the whole width of the tank, even away from the forcing region. Direct numerical simulations confirm the dynamics, emphasize the role of boundary conditions and reveal the phase shifting in the transverse direction. Second, we consider a long and narrow tank having an inclined bottom, to simply reproduce a canal. In this case, the energy is injected in a direction parallel to the slope. Interestingly, the wave energy ends up forming 2D internal wave attractors in planes that are transverse to the initial propagation direction. This focusing mechanism prevents indefinite transmission of most of the internal wave energy along the canal.

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