6,076 research outputs found
Wave modelling - the state of the art
This paper is the product of the wave modelling community and it tries to make a picture of the present situation in this branch of science, exploring the previous and the most recent results and looking ahead towards the solution of the problems we presently face. Both theory and applications are considered.
The many faces of the subject imply separate discussions. This is reflected into the single sections, seven of them, each dealing with a specific topic, the whole providing a broad and solid overview of the present state of the art. After an introduction framing the problem and the approach we followed, we deal in sequence with the following subjects: (Section) 2, generation by wind; 3, nonlinear interactions in deep water; 4, white-capping dissipation; 5, nonlinear interactions in shallow water; 6, dissipation at the sea bottom; 7, wave propagation; 8, numerics. The two final sections, 9 and 10, summarize the present situation from a general point of view and try to look at the future developments
Thermo-Mechanical Wave Propagation In Shape Memory Alloy Rod With Phase Transformations
Many new applications of ferroelastic materials require a better
understanding of their dynamics that often involve phase transformations. In
such cases, an important prerequisite is the understanding of wave propagation
caused by pulse-like loadings. In the present study, a mathematical model is
developed to analyze the wave propagation process in shape memory alloy rods.
The first order martensite transformations and associated thermo-mechanical
coupling effects are accounted for by employing the modified
Ginzburg-Landau-Devonshire theory. The Landau-type free energy function is
employed to characterize different phases, while a Ginzburg term is introduced
to account for energy contributions from phase boundaries. The effect of
internal friction is represented by a Rayleigh dissipation term. The resulted
nonlinear system of PDEs is reduced to a differential-algebraic system, and
Chebyshev's collocation method is employed together with the backward
differentiation method. A series of numerical experiments are performed. Wave
propagations caused by impact loadings are analyzed for different initial
temperatures. It is demonstrated that coupled waves will be induced in the
material. Such waves will be dissipated and dispersed during the propagation
process, and phase transformations in the material will complicate their
propagation patterns. Finally, the influence of internal friction and capillary
effects on the process of wave propagation is analyzed numerically.Comment: Keywords: nonlinear waves, thermo-mechanical coupling, martensite
transformations, Ginzburg-Landau theory, Chebyshev collocation metho
Damping of quasi-2D internal wave attractors by rigid-wall friction
The reflection of internal gravity waves at sloping boundaries leads to
focusing or defocusing. In closed domains, focusing typically dominates and
projects the wave energy onto 'wave attractors'. For small-amplitude internal
waves, the projection of energy onto higher wave numbers by geometric focusing
can be balanced by viscous dissipation at high wave numbers. Contrary to what
was previously suggested, viscous dissipation in interior shear layers may not
be sufficient to explain the experiments on wave attractors in the classical
quasi-2D trapezoidal laboratory set-ups. Applying standard boundary layer
theory, we provide an elaborate description of the viscous dissipation in the
interior shear layer, as well as at the rigid boundaries. Our analysis shows
that even if the thin lateral Stokes boundary layers consist of no more than 1%
of the wall-to-wall distance, dissipation by lateral walls dominates at
intermediate wave numbers. Our extended model for the spectrum of 3D wave
attractors in equilibrium closes the gap between observations and theory by
Hazewinkel et al. (2008)
Tsunami generation by paddle motion and its interaction with a beach: Lagrangian modelling and experiment
A 2D Lagrangian numerical wave model is presented and validated against a set of physical wave-flume experiments on interaction of tsunami waves with a sloping beach. An iterative methodology is proposed and applied for experimental generation of tsunami-like waves using a piston-type wavemaker with spectral control. Three distinct types of wave interaction with the beach are observed with forming of plunging or collapsing breaking waves. The Lagrangian model demonstrates good agreement with experiments. It proves to be efficient in modelling both wave propagation along the flume and initial stages of strongly non-linear wave interaction with a beach involving plunging breaking. Predictions of wave runup are in agreement with both experimental results and the theoretical runup law
Nonlinear Hydromagnetic Wave Support of a Stratified Molecular Cloud
We perform numerical simulations of nonlinear MHD waves in a gravitationally
stratified molecular cloud that is bounded by a hot and tenuous external
medium. We study the relation between the strength of the turbulence and
various global properties of a molecular cloud, within a 1.5-dimensional
approximation. Under the influence of a driving source of Alfvenic
disturbances, the cloud is lifted up by the pressure of MHD waves and reaches a
steady-state characterized by oscillations about a new time-averaged
equilibrium state. The nonlinear effect results in the generation of
longitudinal motions and many shock waves; however, the wave kinetic energy
remains predominantly in transverse, rather than longitudinal, motions. There
is an approximate equipartition of energy between the transverse velocity and
fluctuating magnetic field (aspredicted by small-amplitude theory) in the
region of the stratified cloud which contains most of the mass; however, this
relation breaks down in the outer regions, particularly near the cloud surface,
where the motions have a standing-wave character. This means that the
Chandrasekhar-Fermi formula applied to molecular clouds must be significantly
modified in such regions. Models of an ensemble of clouds show that, for
various strengths of the input energy, the velocity dispersion in the cloud
, where is a characteristic size of the
cloud.Furthermore, is always comparable to the mean Alfven velocity of
the cloud, consistent with observational results.Comment: 16 pages, 15 figures, emulateapj, to appear in ApJ, 2003 Oct 1,
higher resolution figures at http://www.astro.uwo.ca/~basu/pub.html or
http://www.astro.uwo.ca/~kudoh/pub.htm
A phase-field model for quasi-dynamic nucleation, growth, and propagation of rate-and-state faults
Despite its critical role in the study of earthquake processes, numerical
simulation of the entire stages of fault rupture remains a formidable task. The
main challenges in simulating a fault rupture process include complex evolution
of fault geometry, frictional contact, and off-fault damage over a wide range
of spatial and temporal scales. Here, we develop a phase-field model for
quasi-dynamic fault nucleation, growth, and propagation, which features two
standout advantages: (i) it does not require any sophisticated algorithms to
represent fault geometry and its evolution; and (ii) it allows for modeling
fault nucleation, propagation, and off-fault damage processes with a single
formulation. Built on a recently developed phase-field framework for shear
fractures with frictional contact, the proposed formulation incorporates rate-
and state-dependent friction, radiation damping, and their impacts on fault
mechanics and off-fault damage. We show that the numerical results of the
phase-field model are consistent with those obtained from well-verified
approaches that model the fault as a surface of discontinuity, without
suffering from the mesh convergence issue in the existing continuous approaches
to fault rupture (e.g. the stress glut method). Further, through numerical
examples of fault propagation in various settings, we demonstrate that the
phase-field approach may open new opportunities for investigating complex
earthquake processes that have remained overly challenging for the existing
numerical methods
- …