Computations of fully nonlinear three-dimensional wave–wave and wave–body interactions. Part 1. Dynamics of steep three-dimensional waves

2001 ◽  
Vol 438 ◽  
pp. 11-39 ◽  
Author(s):  
MING XUE ◽  
HONGBO XÜ ◽  
YUMING LIU ◽  
DICK K. P. YUE
Keyword(s):  
Three Dimensional ◽  
Breaking Waves ◽  
Stokes Wave ◽  
Two Dimensional ◽  
Wave Instability ◽  
Fully Nonlinear ◽  
Stokes Waves ◽  
Distinct Features ◽  
Wave Problems ◽  
Dimensional Wave

We develop an efficient high-order boundary-element method with the mixed-Eulerian–Lagrangian approach for the simulation of fully nonlinear three-dimensional wave–wave and wave–body interactions. For illustration, we apply this method to the study of two three-dimensional steep wave problems. (The application to wave–body interactions is addressed in an accompanying paper: Liu, Xue & Yue 2001.) In the first problem, we investigate the dynamics of three-dimensional overturning breaking waves. We obtain detailed kinematics and full quantification of three-dimensional effects upon wave plunging. Systematic simulations show that, compared to two-dimensional waves, three-dimensional waves generally break at higher surface elevations and greater maximum longitudinal accelerations, but with smaller tip velocities and less arched front faces. For the second problem, we study the generation mechanism of steep crescent waves. We show that the development of such waves is a result of three-dimensional (class II) Stokes wave instability. Starting with two-dimensional Stokes waves with small three-dimensional perturbations, we obtain direct simulations of the evolution of both L2 and L3 crescent waves. Our results compare quantitatively well with experimental measurements for all the distinct features and geometric properties of such waves.

Three-Dimensional Periodic Fully Nonlinear Potential Waves

2013 ◽  
Author(s):  
Dmitry Chalikov ◽  
Alexander V. Babanin
Keyword(s):  
Wave Field ◽  
Degrees Of Freedom ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Transform Method ◽  
Fully Nonlinear ◽  
Stokes Waves ◽  
Nonlinear Potential ◽  
The Fourier Transform

An exact numerical scheme for a long-term simulation of three-dimensional potential fully-nonlinear periodic gravity waves is suggested. The scheme is based on a surface-following non-orthogonal curvilinear coordinate system and does not use the technique based on expansion of the velocity potential. The Poisson equation for the velocity potential is solved iteratively. The Fourier transform method, the second-order accuracy approximation of the vertical derivatives on a stretched vertical grid and the fourth-order Runge-Kutta time stepping are used. The scheme is validated by simulation of steep Stokes waves. The model requires considerable computer resources, but the one-processor version of the model for PC allows us to simulate an evolution of a wave field with thousands degrees of freedom for hundreds of wave periods. The scheme is designed for investigation of the nonlinear two-dimensional surface waves, for generation of extreme waves as well as for the direct calculations of a nonlinear interaction rate. After implementation of the wave breaking parameterization and wind input, the model can be used for the direct simulation of a two-dimensional wave field evolution under the action of wind, nonlinear wave-wave interactions and dissipation. The model can be used for verification of different types of simplified models.

Three-dimensional wave instability near a critical level

1994 ◽  
Vol 272 ◽  
pp. 255-284 ◽  
Author(s):  
K. B. Winters ◽  
E. A. D’Asaro
Keyword(s):  
Wave Energy ◽  
Critical Level ◽  
Wave Packets ◽  
Three Dimensional ◽  
Internal Gravity Wave ◽  
Two Dimensional ◽  
Mean Flow ◽  
Wave Instability ◽  
Flow Acceleration ◽  
Dimensional Wave

The behaviour of internal gravity wave packets approaching a critical level is investigated through numerical simulation. Initial-value problems are formulated for both small- and large-amplitude wave packets. Wave propagation and the early stages of interaction with the mean shear are two-dimensional and result in the trapping of wave energy near a critical level. The subsequent dynamics of wave instability, however, are fundamentally different for two- and three-dimensional calculations. Three-dimensionality develops by transverse convective instability of the two-dimensional wave. The initialy two-dimensional flow eventually collapses into quasi-horizontal vortical structures. A detailed energy balance is presented. Of the initial wave energy, roughly one third reflects, one third results in mean flow acceleration and the remainder cascades to small scales where it is dissipated. The detailed budget depends on the wave amplitude, the amount of wave reflection being particularly sensitive.

Computations of fully nonlinear three-dimensional wave–wave and wave–body interactions. Part 2. Nonlinear waves and forces on a body

2001 ◽  
Vol 438 ◽  
pp. 41-66 ◽  
Author(s):  
YUMING LIU ◽  
MING XUE ◽  
DICK K. P. YUE
Keyword(s):  
Steady State ◽  
Wave Diffraction ◽  
High Harmonic ◽  
Three Dimensional ◽  
Vertical Cylinder ◽  
Fully Nonlinear ◽  
Bow Wave ◽  
Stokes Waves ◽  
State Force ◽  
Dimensional Wave

The mixed-Eulerian–Lagrangian method using high-order boundary elements, described in Xue et al. (2001) for the simulation of fully nonlinear three-dimensional wave–wave and wave–body interactions, is here extended and applied to the study of two nonlinear three-dimensional wave–body problems: (a) the development of bow waves on an advancing ship; and (b) the steep wave diffraction and nonlinear high-harmonic loads on a surface-piercing vertical cylinder. For (a), we obtain convergent steady-state bow wave profiles for a flared wedge, and the Wigley and Series 60 hulls. We compare our predictions with experimental measurements and find good agreement. It is shown that upstream influence, typically not accounted for in quasi-two-dimensional theory, plays an important role in bow wave prediction even for fine bows. For (b), the primary interest is in the higher-harmonic ‘ringing’ excitations observed and quantified in experiments. From simulations, we obtain fully nonlinear steady-state force histories on the cylinder in incident Stokes waves. Fourier analysis of such histories provides accurate predictions of harmonic loads for which excellent comparisons to experiments are obtained even at third order. This confirms that ‘ringing’ excitations are directly a result of nonlinear wave diffraction.

Two- and three-dimensional locomotion of the nematode Nippostrongylus brasiliensis

Parasitology ◽  
1990 ◽  
Vol 101 (2) ◽  
pp. 301-308 ◽  
Author(s):  
D. L. Lee ◽  
W. D. Biggs
Keyword(s):  
Sodium Alginate ◽  
Intestinal Mucosa ◽  
Three Dimensional ◽  
Viscous Medium ◽  
Nippostrongylus Brasiliensis ◽  
Two Dimensional ◽  
Immune Rejection ◽  
Forward Movement ◽  
Helical Wave ◽  
Dimensional Wave

Locomotion of adult Nippostrongylus brasiliensis has been studied in saline, in 0.6% agar, in sodium alginate of different viscosities and amongst sand grains in these media. In saline the nematode formed two-dimensional waves but there was little forward progression. Amongst sand grains in saline the nematode moved forwards by thrusting against sand grains, but thigmokinetic behaviour later resulted in quiescence. In 0.6% agar and in alginates of weak viscosity the nematode produced two-dimensional waves and sometimes a three-dimensional helical wave which resulted in forward movement. The formation of three-dimensional waves and the distance travelled increased with increasing viscosity up to 4% sodium alginate and also amongst sand gains in these media. In 8% sodium alginate the nematode became coiled like a spring but remained almost stationary. The three-dimensional wave is formed with torsion and obtains thrust from the viscous medium. In the intestine of the host thrust will be obtained from the mucus and villi of the intestinal mucosa. The ability of this nematode to move by two-and three-dimensional undulatory propulsion is probably related to its complex ridged cuticle. Attention is drawn to the role that increased viscosity of mucus may play in entrapping nematodes during their immune rejection.

A three-dimensional supramolecular framework built from two-dimensional wave-shaped layers

2006 ◽  
Vol 59 (8) ◽  
pp. 883-890 ◽  
Author(s):  
Linlin Fan ◽  
Chao Qin ◽  
Yangguang Li ◽  
Enbo Wang ◽  
Xinlong Wang ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Supramolecular Framework ◽  
Dimensional Wave

Stability of flow in a channel with longitudinal grooves

2014 ◽  
Vol 757 ◽  
pp. 613-648 ◽  
Author(s):  
H. V. Moradi ◽  
J. M. Floryan
Keyword(s):  
Reynolds Number ◽  
Small Amplitude ◽  
Arbitrary Shape ◽  
Critical Reynolds Number ◽  
Critical Role ◽  
Three Dimensional ◽  
Travelling Wave ◽  
Two Dimensional ◽  
Wave Instability ◽  
Long Wavelength

AbstractThe travelling wave instability in a channel with small-amplitude longitudinal grooves of arbitrary shape has been studied. The disturbance velocity field is always three-dimensional with disturbances which connect to the two-dimensional waves in the limit of zero groove amplitude playing the critical role. The presence of grooves destabilizes the flow if the groove wavenumber $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\beta $ is larger than $\beta _{tran}\approx 4.22$, but stabilizes the flow for smaller $\beta $. It has been found that $\beta _{tran}$ does not depend on the groove amplitude. The dependence of the critical Reynolds number on the groove amplitude and wavenumber has been determined. Special attention has been paid to the drag-reducing long-wavelength grooves, including the optimal grooves. It has been demonstrated that such grooves slightly increase the critical Reynolds number, i.e. such grooves do not cause an early breakdown into turbulence.

Instabilities of three-dimensional viscous falling films

1992 ◽  
Vol 242 ◽  
pp. 529-547 ◽  
Author(s):  
S. W. Joo ◽  
S. H. Davis
Keyword(s):  
Evolution Equation ◽  
Three Dimensional ◽  
Falling Film ◽  
Two Dimensional ◽  
Wave Evolution ◽  
Strongly Nonlinear ◽  
Long Wave ◽  
Threshold Amplitude ◽  
Permanent Wave ◽  
Dimensional Wave

A long-wave evolution equation is used to study a falling film on a vertical plate. For certain wavenumbers there exists a two-dimensional strongly nonlinear permanent wave. A new secondary instability is identified in which the three-dimensional disturbance is spatially synchronous with the two-dimensional wave. The instability grows for sufficiently small cross-stream wavenumbers and does not require a threshold amplitude; the two-dimensional wave is always unstable. In addition, the nonlinear evolution of three-dimensional layers is studied by posing various initial-value problems and numerically integrating the long-wave evolution equation.

The development of three-dimensional wave-packets in unbounded parallel flows

1968 ◽  
Vol 32 (4) ◽  
pp. 801-808 ◽  
Author(s):  
M. Gaster ◽  
A. Davey
Keyword(s):  
Wave Packet ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Mean Flow ◽  
Physical Plane ◽  
Parallel Flows ◽  
Flow Velocity Profile ◽  
The Stability ◽  
Special Case ◽  
Dimensional Wave

In this paper we examine the stability of a two-dimensional wake profile of the form u(y) = U∞(1 – r e-sy2) with respect to a pulsed disturbance at a point in the fluid. The disturbed flow forms an expanding wave packet which is convected downstream. Far downstream, where asymptotic expansions are valid, the motion at any point in the wave packet is described by a particular three-dimensional wave having complex wave-numbers. In the special case of very unstable flows, where viscosity does not have a significant influence, it is possible to evaluate the three-dimensional eigenvalues in terms of two-dimensional ones using the inviscid form of Squire's transformation. In this way each point in the physical plane can be linked to a particular two-dimensional wave growing in both space and time by simple algebraic expressions which are independent of the mean flow velocity profile. Computed eigenvalues for the wake profile are used in these relations to find the behaviour of the wave packet in the physical plane.

FREQUENCY DOMAIN RECONSTRUCTION FOR PHOTO- AND THERMOACOUSTIC TOMOGRAPHY WITH LINE DETECTORS

2009 ◽  
Vol 19 (02) ◽  
pp. 283-306 ◽  
Author(s):  
MARKUS HALTMEIER
Keyword(s):  
Wave Equation ◽  
Frequency Domain ◽  
Boundary Data ◽  
Three Dimensional ◽  
Photoacoustic Tomography ◽  
Two Dimensional ◽  
Reconstruction Problem ◽  
Acoustic Data ◽  
Dimensional Wave ◽  
Frequency Domain Reconstruction

This paper is concerned with a version of photoacoustic tomography, that uses line shaped detectors (instead of point-like ones) for the recording of acoustic data. The three-dimensional image reconstruction problem is reduced to a series of two-dimensional ones. First, the initial data of the two-dimensional wave equation is recovered from boundary data, and second, the classical two-dimensional Radon transform is inverted. We discuss uniqueness and stability of reconstruction, and compare frequency domain reconstruction formulas for various geometries.

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