Large-scale modulations of edge waves

1983 ◽  
Vol 132 ◽  
pp. 197-208 ◽  
Author(s):  
T. R. Akylas
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Physical Significance ◽  
Spatial Evolution ◽  
Edge Waves ◽  
Weakly Nonlinear ◽  
Resonant Interactions ◽  
Envelope Solitons ◽  
Temporal And Spatial ◽  
Sloping Beach

The temporal and spatial evolution of large-scale modulations of weakly nonlinear edge waves on a uniformly sloping beach is studied using the full water-wave formulation for beach angles α = π/2N. Equations governing the evolution of envelopes of edge waves, excited by resonant interactions with incident wavetrains, are derived. It is deduced that a uniform train of free periodic edge waves is always unstable to large-scale variations, so that envelope solitons will develop; the resulting three-dimensional solitons are described in detail. In addition, it is shown that steady-state standing subharmonic edge waves, excited by incident wavetrains on a long, mildly sloping beach, can be unstable to large-scale modulations. The possible physical significance of these findings is discussed.

Nonlinear spatial evolution of helical disturbances to an axial jet

1994 ◽  
Vol 281 ◽  
pp. 371-402 ◽  
Author(s):  
S. M. Churilov ◽  
I. G. Shukhman
Keyword(s):  
Three Dimensional ◽  
Spatial Evolution ◽  
Streamwise Direction ◽  
Perturbation Amplitude ◽  
Weakly Nonlinear ◽  
Parallel Flows ◽  
Non Local ◽  
Axisymmetrical Jet ◽  
Different Levels ◽  
Proper Account

We investigate the weakly nonlinear spatial evolution of helical disturbances of an axisymmetrical jet which are the analogue of three-dimensional disturbances, such as a single oblique wave (the wave vector is directed at an angle to the main flow velocity) in plane-parallel flows. It is shown that when a supercriticality is large enough, the perturbation amplitude A grows in the streamwise direction (along z) explosively: A ∼ (z0 — z)−5/2, though more slowly than in the case of essentially three-dimensional disturbances in the form of a pair of oblique waves (A ∼ (z0 — z)−3; Goldstein & Choi 1989). The nonlinearity needed for such a growth, is due equally to the cylindricity of shear layer and to the spatial character of the evolution (in the temporal problem the ‘evolution’ contribution is absent). At a smaller supercriticality, the evolution equation has a non-local (integral in z) nonlinearity, unusual for the regime of a viscous critical layer. Scenarios of disturbance development for different levels of supercriticality are studied, with proper account taken of viscous broadening of the flow.

The nonlinear excitation of synchronous edge waves by a monochromatic wave normally approaching a plane beach

1995 ◽  
Vol 301 ◽  
pp. 251-268 ◽  
Author(s):  
P. Blondeaux ◽  
G. Vittori
Keyword(s):  
Energy Transfer ◽  
Water Wave ◽  
Three Dimensional ◽  
Wave Theory ◽  
Monochromatic Wave ◽  
Edge Waves ◽  
Nonlinear Stability Analysis ◽  
Nonlinear Excitation ◽  
Incoming Wave ◽  
Weakly Nonlinear

The possible excitation of synchronous edge waves by a monocromatic wave normally approaching a plane beach is studied. Use is made of the full three-dimensional water wave theory but only beach angles β = π/(2N), where N is an integer, are considered. A weakly nonlinear stability analysis is used to investigate the interaction of subharmonic, synchronous and 3/2-frequency edge waves with the incoming wave field. It is shown that values of β exist for which an energy transfer from the incoming wave to the synchronous edge waves takes place through the intermediary of the subharmonic components.

scholarly journals Asymptotics of sloshing eigenvalues for a triangular prism

2021 ◽  
pp. 1-33
Author(s):  
JULIEN MAYRAND ◽  
CHARLES SENÉCAL ◽  
SIMON ST–AMANT
Keyword(s):  
Asymptotic Expansion ◽  
Surface Waves ◽  
Counting Function ◽  
Three Dimensional ◽  
Triangular Prism ◽  
Edge Waves ◽  
Counting Problem ◽  
Sloping Beach

Abstract We consider the three-dimensional sloshing problem on a triangular prism whose angles with the sloshing surface are of the form ${\pi}/{2q}$ , where q is an integer. We are interested in finding a two-term asymptotic expansion of the eigenvalue counting function. When both angles are ${\pi}/{4}$ , we compute the exact value of the second term. As for the general case, we conjecture an asymptotic expansion by constructing quasimodes for the problem and computing the counting function of the related quasi-eigenvalues. These quasimodes come from solutions of the sloping beach problem and correspond to two kinds of waves, edge waves and surface waves. We show that the quasi-eigenvalues are exponentially close to real eigenvalues of the sloshing problem. The asymptotic expansion of their counting function is closely related to a lattice counting problem inside a perturbed ellipse where the perturbation is in a sense random. The contribution of the angles can then be detected through that perturbation.

Space and Time Distribution of Hard X-Ray Emission in a Loop at the Beginning of a Flare

1994 ◽  
Vol 144 ◽  
pp. 275-277
Author(s):  
M. Karlický ◽  
J. C. Hénoux
Keyword(s):  
Time Distribution ◽  
Electron Bombardment ◽  
Spatial Evolution ◽  
Superthermal Electrons ◽  
Flare Loop ◽  
X Ray ◽  
Superthermal Electron ◽  
Flare Loops ◽  
Chromospheric Evaporation ◽  
Temporal And Spatial

AbstractUsing a new ID hybrid model of the electron bombardment in flare loops, we study not only the evolution of densities, plasma velocities and temperatures in the loop, but also the temporal and spatial evolution of hard X-ray emission. In the present paper a continuous bombardment by electrons isotropically accelerated at the top of flare loop with a power-law injection distribution function is considered. The computations include the effects of the return-current that reduces significantly the depth of the chromospheric layer which is evaporated. The present modelling is made with superthermal electron parameters corresponding to the classical resistivity regime for an input energy flux of superthermal electrons of 109erg cm−2s−1. It was found that due to the electron bombardment the two chromospheric evaporation waves are generated at both feet of the loop and they propagate up to the top, where they collide and cause temporary density and hard X-ray enhancements.

scholarly journals Large-Scale Analysis of the Spatiotemporal Changes of Net Ecosystem Production in Hindu Kush Himalayan Region

2021 ◽  
Vol 13 (6) ◽  
pp. 1180
Author(s):  
Da Guo ◽  
Xiaoning Song ◽  
Ronghai Hu ◽  
Xinming Zhu ◽  
Yazhen Jiang ◽  
...  
Keyword(s):  
Large Scale ◽  
Net Primary Production ◽  
Carbon Sink ◽  
Carbon Sources ◽  
Spatial Dynamics ◽  
Tibet Plateau ◽  
Geostatistical Model ◽  
Hindu Kush ◽  
Temporal And Spatial ◽  
The Difference

The Hindu Kush Himalayan (HKH) region is one of the most ecologically vulnerable regions in the world. Several studies have been conducted on the dynamic changes of grassland in the HKH region, but few have considered grassland net ecosystem productivity (NEP). In this study, we quantitatively analyzed the temporal and spatial changes of NEP magnitude and the influence of climate factors on the HKH region from 2001 to 2018. The NEP magnitude was obtained by calculating the difference between the net primary production (NPP) estimated by the Carnegie–Ames Stanford Approach (CASA) model and the heterotrophic respiration (Rh) estimated by the geostatistical model. The results showed that the grassland ecosystem in the HKH region exhibited weak net carbon uptake with NEP values of 42.03 gC∙m−2∙yr−1, and the total net carbon sequestration was 0.077 Pg C. The distribution of NEP gradually increased from west to east, and in the Qinghai–Tibet Plateau, it gradually increased from northwest to southeast. The grassland carbon sources and sinks differed at different altitudes. The grassland was a carbon sink at 3000–5000 m, while grasslands below 3000 m and above 5000 m were carbon sources. Grassland NEP exhibited the strongest correlation with precipitation, and it had a lagging effect on precipitation. The correlation between NEP and the precipitation of the previous year was stronger than that of the current year. NEP was negatively correlated with temperature but not with solar radiation. The study of the temporal and spatial dynamics of NEP in the HKH region can provide a theoretical basis to help herders balance grazing and forage.

scholarly journals A Review on Additive Manufacturing Possibilities for Electrical Machines

Energies ◽  
2021 ◽  
Vol 14 (7) ◽  
pp. 1940
Author(s):  
Muhammad Usman Naseer ◽  
Ants Kallaste ◽  
Bilal Asad ◽  
Toomas Vaimann ◽  
Anton Rassõlkin
Keyword(s):  
Additive Manufacturing ◽  
Large Scale ◽  
Three Dimensional ◽  
Electrical Machines ◽  
Electromagnetic Properties ◽  
Scale Production ◽  
Performance Parameters ◽  
Large Scale Production ◽  
One Step ◽  
Manufacturing Techniques

This paper presents current research trends and prospects of utilizing additive manufacturing (AM) techniques to manufacture electrical machines. Modern-day machine applications require extraordinary performance parameters such as high power-density, integrated functionalities, improved thermal, mechanical & electromagnetic properties. AM offers a higher degree of design flexibility to achieve these performance parameters, which is impossible to realize through conventional manufacturing techniques. AM has a lot to offer in every aspect of machine fabrication, such that from size/weight reduction to the realization of complex geometric designs. However, some practical limitations of existing AM techniques restrict their utilization in large scale production industry. The introduction of three-dimensional asymmetry in machine design is an aspect that can be exploited most with the prevalent level of research in AM. In order to take one step further towards the enablement of large-scale production of AM-built electrical machines, this paper also discusses some machine types which can best utilize existing developments in the field of AM.

scholarly journals Vibration characteristics of triple-gear-rotor system in compressed air energy storage under variable torque load

2021 ◽  
Vol 104 (1) ◽  
pp. 003685042098705
Author(s):  
Xinran Wang ◽  
Yangli Zhu ◽  
Wen Li ◽  
Dongxu Hu ◽  
Xuehui Zhang ◽  
...  
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Element Model ◽  
Rotor System ◽  
Dynamic Responses ◽  
System Response ◽  
Rotating Speed ◽  
Torque Load ◽  
Set Up ◽  
Two Stages

This paper focuses on the effects of the off-design operation of CAES on the dynamic characteristics of the triple-gear-rotor system. A finite element model of the system is set up with unbalanced excitations, torque load excitations, and backlash which lead to variations of tooth contact status. An experiment is carried out to verify the accuracy of the mathematical model. The results show that when the system is subjected to large-scale torque load lifting at a high rotating speed, it has two stages of relatively strong periodicity when the torque load is light, and of chaotic when the torque load is heavy, with the transition between the two states being relatively quick and violent. The analysis of the three-dimensional acceleration spectrum and the meshing force shows that the variation in the meshing state and the fluctuation of the meshing force is the basic reasons for the variation in the system response with the torque load. In addition, the three rotors in the triple-gear-rotor system studied show a strong similarity in the meshing states and meshing force fluctuations, which result in the similarity in the dynamic responses of the three rotors.

scholarly journals Shell-crossing in a ΛCDM Universe

2020 ◽  
Vol 501 (1) ◽  
pp. L71-L75
Author(s):  
Cornelius Rampf ◽  
Oliver Hahn
Keyword(s):  
Dark Matter ◽  
Perturbation Theory ◽  
Large Scale ◽  
Cold Dark Matter ◽  
Three Dimensional ◽  
Random Initial Data ◽  
Recursion Relations ◽  
Indispensable Tool ◽  
First Time ◽  
Very High

ABSTRACT Perturbation theory is an indispensable tool for studying the cosmic large-scale structure, and establishing its limits is therefore of utmost importance. One crucial limitation of perturbation theory is shell-crossing, which is the instance when cold-dark-matter trajectories intersect for the first time. We investigate Lagrangian perturbation theory (LPT) at very high orders in the vicinity of the first shell-crossing for random initial data in a realistic three-dimensional Universe. For this, we have numerically implemented the all-order recursion relations for the matter trajectories, from which the convergence of the LPT series at shell-crossing is established. Convergence studies performed at large orders reveal the nature of the convergence-limiting singularities. These singularities are not the well-known density singularities at shell-crossing but occur at later times when LPT already ceased to provide physically meaningful results.

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