Spatial vs. Temporal Evolution of Nonlinear Wave Groups: Experiments and Modeling Based on the Dysthe Equation

2008 ◽  
Author(s):  
Lev Shemer ◽  
Boris Dorfman
Keyword(s):  
Nonlinear Wave ◽  
Temporal Evolution ◽  
Side Wall ◽  
Digital Processing ◽  
Quantitative Agreement ◽  
Wave Number ◽  
Spatial Form ◽  
Frequency Spectra ◽  
Wave Groups ◽  
Dysthe Equation

The evolution along the tank of unidirectional nonlinear wave groups with narrow spectrum is studied both experimentally and numerically. Measurements of the instantaneous surface elevation within the tank are carried out using digital processing of video-recorded sequences of images of the contact line movement at the tank side wall. The accuracy of the video-derived results is verified by measurements performed by conventional resistance-type wave gauges. An experimental procedure is developed that enables processing of large volumes of video images and capturing the spatial structure of the instantaneous wave field in the whole tank. The experimentally obtained data are compared quantitatively with the solutions of the modified nonlinear Schro¨dinger (MNLS, or Dysthe) equation written in either temporal or spatial form. Results on the evolution along the tank of wave frequency spectra and on the temporal evolution of the wave number spectra are presented. It is demonstrated that accounting for the 2nd order bound (locked) waves is essential for getting a qualitative and quantitative agreement between the measured and the computed spectra.

scholarly journals Experimental and numerical study of spatial and temporal evolution of nonlinear wave groups

2008 ◽  
Vol 15 (6) ◽  
pp. 931-942 ◽  
Author(s):  
L. Shemer ◽  
B. Dorfman
Keyword(s):  
Nonlinear Wave ◽  
Numerical Study ◽  
Side Wall ◽  
Digital Processing ◽  
Quantitative Agreement ◽  
Wave Number ◽  
Spatial Form ◽  
Frequency Spectra ◽  
Wave Groups ◽  
Dysthe Equation

Abstract. The evolution along the tank of unidirectional nonlinear wave groups with narrow spectrum is studied both experimentally and numerically. Measurements of the instantaneous surface elevation within the tank are carried out using digital processing of video-recorded sequences of images of the contact line movement at the tank side wall. The accuracy of the video-derived results is verified by measurements performed by conventional resistance-type wave gauges. An experimental procedure is developed that enables processing of large volumes of video images and thus allows capturing the spatial structure of the instantaneous wave field along the whole tank. The experimentally obtained data are compared quantitatively with the solutions of the Modified Nonlinear Schrödinger (MNLS, or Dysthe) equation written in either temporal or spatial form. The adopted approach allows studying evolution along the tank of wave frequency spectra, as well as the temporal variation of the wave number spectra. It is demonstrated that accounting for the 2nd order bound (locked) waves is essential for getting a qualitative and quantitative agreement between the measured and the computed spectra. The relation between the frequency and the wave number spectra is discussed.

‘Inactive’ motion and pressure fluctuations in turbulent boundary layers

1967 ◽  
Vol 30 (2) ◽  
pp. 241-258 ◽  
Author(s):  
P. Bradshaw
Keyword(s):  
Boundary Layer ◽  
Outer Layer ◽  
Pressure Fluctuations ◽  
Turbulent Energy ◽  
Viscous Sublayer ◽  
Wave Number ◽  
Noticeable Effect ◽  
Frequency Spectra ◽  
Active Motion ◽  
Order Of Magnitude

Townsend's (1961) hypothesis that the turbulent motion in the inner region of a boundary layer consists of (i) an ‘active’ part which produces the shear stress τ and whose statistical properties are universal functions of τ and y, and (ii) an ‘inactive’ and effectively irrotational part determined by the turbulence in the outer layer, is supported in the present paper by measurements of frequency spectra in a strongly retarded boundary layer, in which the ‘inactive’ motion is particularly intense. The only noticeable effect of the inactive motion is an increased dissipation of kinetic energy into heat in the viscous sublayer, supplied by turbulent energy diffusion from the outer layer towards the surface. The required diffusion is of the right order of magnitude to explain the non-universal values of the triple products measured near the surface, which can therefore be reconciled with universality of the ‘active’ motion.Dimensional analysis shows that the contribution of the ‘active’ inner layer motion to the one-dimensional wave-number spectrum of the surface pressure fluctuations varies as τ2w/k1 up to a wave-number inversely proportional to the thickness of the viscous sublayer. This result is strongly supported by the recent measurements of Hodgson (1967), made with a much smaller ratio of microphone diameter to boundary-layer thickness than has been achieved previously. The disagreement of the result with most other measurements is attributed to inadequate transducer resolution in the other experiments.

scholarly journals Evolution and Influencing Factors of Township Spatial Form: A Two-Dimensional Perspective

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Yanpeng Gao ◽  
Wenjun Chen
Keyword(s):  
Land Use ◽  
Influencing Factors ◽  
Temporal Evolution ◽  
Morphological Changes ◽  
Fractal Theory ◽  
Center Of Gravity ◽  
Expansion Rate ◽  
Rural Settlements ◽  
Spatial Form ◽  
Maximum Expansion

The countryside is the habitat of food, ecology, and culture, and the indispensable basis for human survival and development. Assessing the spatial and temporal evolution of rural settlements contributes to the promotion of rural scientific developments. This study used the fractal theory, center-of-gravity model, and spatial syntax to analyze the spatial and temporal evolution of Shenyang Ciyutuo Subdistrict and its influencing factors based on geospatial data from 2009‒2019, from the perspectives of internal characteristics and external morphological changes. In terms of the external characteristics, from 2009‒2019, the compactness index increased from 0.414 to 0.454, the expansion rate increased from 1.17% to 3.11%, and the expansion intensity increased from 0.05% to 0.15%. From 2014‒2019, the western part of the subdistrict experienced the maximum expansion rate and expansion intensity. The center-of-gravity of the construction land shifted to the west and southwest. The internal characteristics of land use depended on geographical conditions. Clusters of rural settlements were formed in a north-south direction due to the topography and along the riverside in a band-like manner. From 2009‒2019, the integration level of the subdistrict improved and the scale and number of integration axis increased, forming a multicore tree-shaped structure. Pearson’s correlation analysis showed that urbanization is the main factor affecting the spatial and temporal land-use evolution, with transportation convenience, industrial park, and proximity to the river having little effects. This study provides a theoretical basis for the development of Ciyutuo Subdistrict and provides a reference for the development of similar commercial towns.

The damping of surface gravity waves in a bounded liquid

1973 ◽  
Vol 59 (2) ◽  
pp. 239-256 ◽  
Author(s):  
C. C. Mei ◽  
L. F. Liu
Keyword(s):  
Boundary Layer ◽  
Gravity Waves ◽  
Side Wall ◽  
The Other ◽  
Wave Number ◽  
Viscous Damping ◽  
Alternative Derivation ◽  
Surface Gravity Waves ◽  
Damping Rate ◽  
Side Walls

In deducing the viscous damping rate in surface waves confined by side walls, Ursell found in an example that two different calculations, one by energy dissipation within and the other by pressure working on the edge of the side-wall boundary layers, gave different answers. This discrepancy occurs in other examples also and is resolved here by examining the energy transfer in the neighbourhood of the free-surface meniscus. With due care near the meniscus a boundary-layer–Poincaré method is employed to give an alternative derivation for the rate of attenuation and to obtain in addition the frequency (or wave-number) shift due to viscosity. Surface tension is not considered.

Theoretical and experimental studies of three-dimensional wavemaking in narrow tanks, including nonlinear phenomena near resonance

1994 ◽  
Vol 276 ◽  
pp. 211-232 ◽  
Author(s):  
Yitao Yao ◽  
Marshall P. Tulin ◽  
Ali R. Kolaini
Keyword(s):  
Nonlinear Wave ◽  
Near Field ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Analytical Techniques ◽  
Nonlinear Phenomena ◽  
Far Field ◽  
Wave Groups ◽  
Near Resonance ◽  
Matching Techniques

In view of several practical ramifications of this problem, computational-analytical techniques for calculating waves induced by heaving arbitrary bodies in narrow tanks have been developed, including nonlinear wave groups produced near tank resonance. These feature computational near-field solutions matched with appropriate far-field solutions. In the linear case, the far field is provided by linear mode superposition. In the nonlinear case, the far field is described by a suitable nonlinear evolution equation of the cubic Schrödinger type. Matching techniques were developed. Calculations were successfully carried out and the results confirm the important effect of tank walls on added mass and damping.Results of computations have been compared with some data obtained with a conical wavemaker in a narrow tank. Pronounced nonlinear wave groups were obtained near resonance, and these are well reproduced in some detail by the nonlinear theory and computations, without considering any effects of dissipation.The related problem of resonant wave groups produced by a segmented paddle wavemaker has also been treated by analysis and subject to computation, with good general agreement with past experiments. The technique features matching near- and far-field computations using energy considerations.

scholarly journals Array-Based Guided Wave Source Location Using Dispersion Compensation

2021 ◽  
Vol 4 (4) ◽  
Author(s):  
Andrew Downs ◽  
Ronald Roberts ◽  
Jiming Song
Keyword(s):  
Experimental Data ◽  
Guided Waves ◽  
Dispersion Compensation ◽  
Back Propagation ◽  
Source Location ◽  
Guided Wave ◽  
Wave Number ◽  
Frequency Spectra ◽  
Wave Source ◽  
Bulk Waves

Abstract An important advantage of guided waves is their ability to propagate large distances and yield more information about flaws than bulk waves. Unfortunately, the multi-modal, dispersive nature of guided waves makes them difficult to use for locating flaws. In this work, we present a method and experimental data for removing the deleterious effects of multi-mode dispersion allowing for source localization at frequencies comparable to those of bulk waves. Time domain signals are obtained using a novel 64-element phased array and processed to extract wave number and frequency spectra. By an application of Auld’s electro-mechanical reciprocity relation, mode contributions are extracted approximately using a variational method. Once mode contributions have been obtained, the dispersion for each mode is removed via back-propagation techniques. Excepting the presence of a small artifact at high frequency-thicknesses, experimental data successfully demonstrate the robustness and viability of this approach to guided wave source location.

scholarly journals NONLINEAR WAVE PRESSURES GIVEN BY EXTREME WAVES ON AN UPRIGHT BREAKWATER: THEORY AND EXPERIMENTAL VALIDATION

2012 ◽  
Vol 1 (33) ◽  
pp. 33
Author(s):  
Alessandra Romolo ◽  
Felice Arena
Keyword(s):  
Nonlinear Wave ◽  
Three Dimensional ◽  
Surface Displacement ◽  
Nonlinear Effects ◽  
Breaking Waves ◽  
Small Scale ◽  
Ocean Engineering ◽  
Wave Groups ◽  
Free Surface Displacement ◽  
Experimental Comparisons

An analytical nonlinear theory is presented for the interaction between three-dimensional sea wave groups and a seawall during the occurrence of an exceptionally high crest or deep trough of the water elevation. The solution to the second order of the free surface displacement and of the velocity potential is derived by considering an irrotational, inviscid, incompressible flow bounded by a horizontal seabed and a vertical impermeable seawall. The analytical expression of the nonlinear wave pressure is derived. The resulting theory is able to fully describe the mechanics at the seawall and in front of it, which represents a strongly nonhomogeneous wave field, then demonstrating that it is influenced by characteristic parameters and wave conditions. The theoretical results are in good agreement with measurements carried out during a small-scale field experiment at the Natural Ocean Engineering Laboratory in Reggio Calabria (Italy). The theoretical and experimental comparisons show that some distinctive phenomena regarding wave pressures of very high standing wave groups at a seawall, in the absence of either overturning or breaking waves, may be associated with nonlinear effects.

Wave number frequency spectra of a lifting wake for broadband noise prediction

AIAA Journal ◽  
1998 ◽  
Vol 36 ◽  
pp. 881-887
Author(s):  
William J. Devenport ◽  
Christian W. Wenger ◽  
Stewart A. Glegg ◽  
Joseph A. Miranda
Keyword(s):  
Broadband Noise ◽  
Wave Number ◽  
Noise Prediction ◽  
Frequency Spectra ◽  
Number Frequency
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