scholarly journals Water Waves Provide Insight Into Landslides and Avalanche Models

Eos ◽  
2015 ◽  
Vol 96 ◽  
Author(s):  
David Shultz
Keyword(s):  
Gravity Waves ◽  
Water Waves ◽  
Granular Flows ◽  
Vertical Motion ◽  
Insight Into ◽  
Avalanche Models

Boussinesq-type gravity waves appear to accurately describe vertical motion in granular flows found in geophysics.

scholarly journals Influence of the Upstream Terrain on the Formation of a Cold Frontal Snowband in Northeast China

2021 ◽  
Author(s):  
Na Li ◽  
Baofeng Jiao ◽  
Lingkun Ran ◽  
Zongting Gao ◽  
Shouting Gao
Keyword(s):  
Gravity Waves ◽  
Northeast China ◽  
Large Scale ◽  
Control Experiment ◽  
Vertical Motion ◽  
Near Surface ◽  
Inertial Instability ◽  
Two Factors ◽  
Negative Effect ◽  
Conditional Instability

AbstractWe investigated the influence of upstream terrain on the formation of a cold frontal snowband in Northeast China. We conducted numerical sensitivity experiments that gradually removed the upstream terrain and compared the results with a control experiment. Our results indicate a clear negative effect of upstream terrain on the formation of snowbands, especially over large-scale terrain. By thoroughly examining the ingredients necessary for snowfall (instability, lifting and moisture), we found that the release of mid-level conditional instability, followed by the release of low-level or near surface instabilities (inertial instability, conditional instability or conditional symmetrical instability), contributed to formation of the snowband in both experiments. The lifting required for the release of these instabilities was mainly a result of frontogenetic forcing and upper gravity waves. However, the snowband in the control experiment developed later and was weaker than that in the experiment without upstream terrain. Two factors contributed to this negative topographic effect: (1) the mountain gravity waves over the upstream terrain, which perturbed the frontogenetic circulation by rapidly changing the vertical motion and therefore did not favor the release of instabilities in the absence of persistent ascending motion; and (2) the decrease in the supply of moisture as a result of blocking of the upstream terrain, which changed both the moisture and instability structures leeward of the mountains. A conceptual model is presented that shows the effects of the instabilities and lifting on the development of cold frontal snowbands in downstream mountains.

scholarly journals New exact relations for steady irrotational two-dimensional gravity and capillary surface waves

2017 ◽  
Vol 376 (2111) ◽  
pp. 20170220 ◽  
Author(s):  
Didier Clamond
Keyword(s):  
Free Surface ◽  
Gravity Waves ◽  
Water Waves ◽  
Two Dimensional ◽  
Physical Plane ◽  
Theme Issue ◽  
Nonlinear Water Waves ◽  
Dimensional Gravity ◽  
Irrotational Motion ◽  
Exact Relations

Steady two-dimensional surface capillary–gravity waves in irrotational motion are considered on constant depth. By exploiting the holomorphic properties in the physical plane and introducing some transformations of the boundary conditions at the free surface, new exact relations and equations for the free surface only are derived. In particular, a physical plane counterpart of the Babenko equation is obtained. This article is part of the theme issue ‘Nonlinear water waves’.

Steep gravity waves in water of arbitrary uniform depth

1977 ◽  
Vol 286 (1335) ◽  
pp. 183-230 ◽  
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Water Waves ◽  
Perturbation Parameter ◽  
Intermediate Energy ◽  
Finite Amplitude ◽  
Wave Profile ◽  
Accurate Calculation ◽  
Theoretical Developments ◽  
Deep Water Waves

Modern applications of water-wave studies, as well as some recent theoretical developments, have shown the need for a systematic and accurate calculation of the characteristics of steady, progressive gravity waves of finite amplitude in water of arbitrary uniform depth. In this paper the speed, momentum, energy and other integral properties are calculated accurately by means of series expansions in terms of a perturbation parameter whose range is known precisely and encompasses waves from the lowest to the highest possible. The series are extended to high order and summed with Padé approximants. For any given wavelength and depth it is found that the highest wave is not the fastest. Moreover the energy, momentum and their fluxes are found to be greatest for waves lower than the highest. This confirms and extends the results found previously for solitary and deep-water waves. By calculating the profile of deep-water waves we show that the profile of the almost-steepest wave, which has a sharp curvature at the crest, intersects that of a slightly less-steep wave near the crest and hence is lower over most of the wavelength. An integration along the wave profile cross-checks the Padé-approximant results and confirms the intermediate energy maximum. Values of the speed, energy and other integral properties are tabulated in the appendix for the complete range of wave steepnesses and for various ratios of depth to wavelength, from deep to very shallow water.

scholarly journals Impact of Gravity Waves on Marine Stratocumulus Variability

2012 ◽  
Vol 69 (12) ◽  
pp. 3633-3651 ◽  
Author(s):  
Qingfang Jiang ◽  
Shouping Wang
Keyword(s):  
Gravity Waves ◽  
Vertical Motion ◽  
Liquid Water Path ◽  
Marine Stratocumulus ◽  
Large Eddy Simulation Model ◽  
Cloud Albedo ◽  
Eddy Simulation ◽  
Aerosol Number Concentration ◽  
Wave Induced ◽  
The Impact

Abstract The impact of gravity waves on marine stratocumulus is investigated using a large-eddy simulation model initialized with sounding profiles composited from the Variability of American Monsoon Systems (VAMOS) Ocean–Cloud–Atmosphere–Land Study Regional Experiment (VOCALS-Rex) aircraft measurements and forced by convergence or divergence that mimics mesoscale diurnal, semidiurnal, and quarter-diurnal waves. These simulations suggest that wave-induced vertical motion can dramatically modify the cloud albedo and morphology through nonlinear cloud–aerosol–precipitation–circulation–turbulence feedback. In general, wave-induced ascent tends to increase the liquid water path (LWP) and the cloud albedo. With a proper aerosol number concentration, the increase in the LWP leads to enhanced precipitation, which triggers or strengthens mesoscale circulations in the boundary layer and accelerates cloud cellularization. Precipitation also tends to create a decoupling structure by weakening the turbulence in the subcloud layer. Wave-induced descent decreases the cloud albedo by dissipating clouds and forcing a transition from overcast to scattered clouds or from closed to open cells. The overall effect of gravity waves on the cloud variability and morphology depends on the cloud property, aerosol concentration, and wave characteristics. In several simulations, a transition from closed to open cells occurs under the influence of gravity waves, implying that some of the pockets of clouds (POCs) observed over open oceans may be related to gravity wave activities.

Uniformly travelling water waves from a dynamical systems viewpoint: some insights into bifurcations from Stokes’ family

1992 ◽  
Vol 241 ◽  
pp. 333-347 ◽  
Author(s):  
C. Baesens ◽  
R. S. Mackay
Keyword(s):  
Gravity Waves ◽  
Water Waves ◽  
Travelling Waves ◽  
Hamiltonian Formulation ◽  
Inviscid Fluid ◽  
Centre Manifold ◽  
Numerical Work ◽  
Bifurcation Tree ◽  
Area Preserving

Numerical work of many people on the bifurcations of uniformly travelling water waves (two-dimensional irrotational gravity waves on inviscid fluid of infinite depth) suggests that uniformly travelling water waves have a reversible Hamiltonian formulation, where the role of time is played by horizontal position in the wave frame. In this paper such a formulation is presented. Based on this viewpoint, some insights are given into bifurcations from Stokes’ family of periodic waves. It is demonstrated numerically that there is a ‘fold point’ at amplitude A0 ≈ 0.40222. Assuming non-degeneracy of the fold and existence of an associated centre manifold, this explains why a sequence of p/q-bifurcations occurs on one side of A0, with 0 < p/q [les ] ½, in the order of the rationals. Secondly, it explains why no symmetry-breaking bifurcation is observed at A0, contrary to the expectations of some. Thirdly, it explains why the bifurcation tree for periodic uniformly travelling waves looks so much like that for the area-preserving Hénon map. Fourthly, it leads to predictions of a rich variety of spatially quasi-periodic, heteroclinic and chaotic waves.

Theory of water waves derived from a Lagrangian. Part 1. Standing waves

2000 ◽  
Vol 423 ◽  
pp. 275-291 ◽  
Author(s):  
MICHAEL S. LONGUET-HIGGINS
Keyword(s):  
Gravity Waves ◽  
Water Waves ◽  
Fourier Coefficients ◽  
Equations Of Motion ◽  
Standing Waves ◽  
System Of Equations ◽  
Practical Applications ◽  
Low Degree ◽  
Sharp Corners ◽  
New System

A new system of equations for calculating time-dependent motions of deep-water gravity waves (Balk 1996) is here developed analytically and set in a form suitable for practical applications. The method is fully nonlinear, and has the advantage of essential simplicity. Both the potential and the kinetic energy involve polynomial expressions of low degree in the Fourier coefficients Yn(t). This leads to equations of motion of correspondingly low degree. Moreover the constants in the equations are very simple. In this paper the equations of motion are specialized to standing waves, where the coefficients Yn are all real. Truncation of the series at low values of [mid ]n[mid ], say n < N, leads to ‘partial waves’ with solutions apparently periodic in the time t. For physical applications N must however be large. The method will be applied to the breaking of standing waves by the forming of sharp corners at the crests, and the generation of vertical jets rising from the wave troughs.

The signature of the tropospheric gravity wave background in observed mesoscale motion

2021 ◽  
Author(s):  
Claudia Stephan ◽  
Alexis Mariaccia
Keyword(s):  
Gravity Waves ◽  
Functional Dependence ◽  
Vertical Motion ◽  
Numerical Data ◽  
Reanalysis Data ◽  
Horizontal Resolution ◽  
Energy Spectra ◽  
Equivalent Radius ◽  
Individual Wave ◽  
Inertia Gravity Waves

&lt;p&gt;How convection couples to mesoscale vertical motion and what determines these motions is poorly understood. We diagnose profiles of area-averaged mesoscale divergence from measurements of horizontal winds collected by an extensive upper-air sounding network of a recent campaign over the western tropical North Atlantic, the Elucidating the Role of Clouds-Circulation Coupling in Climate (EUREC&lt;sup&gt;4&lt;/sup&gt;A) campaign. Observed area-averaged divergence amplitudes scale approximately inversely with area equivalent radius. This functional dependence is also confirmed in reanalysis data and a global freely-evolving simulation run at 2.5 km horizontal resolution. Based on the numerical data it is demonstrated that the energy spectra of inertia gravity waves can explain the scaling of divergence amplitudes with area. At individual times, however, few waves can dominate the region. Nearly monochromatic tropospheric waves are diagnosed in the soundings by means of an optimized hodograph analysis. For one day, results suggest that an individual wave directly modulated the satellite observed cloud pattern. However, because such immediate wave impacts are rare, the systematic modulation of vertical motion due to inertia-gravity waves may be more relevant as a convection-modulating factor. We propose an analytic relationship between energy spectra and divergence amplitudes, which, if confirmed by future studies, could be used to design better external forcing methods for regional models.&lt;/p&gt;

Surface Gravity Waves

2017 ◽  
Author(s):  
John A. Adam
Keyword(s):  
Gravity Waves ◽  
Water Waves ◽  
Water Surface ◽  
Wave Pattern ◽  
The Body ◽  
Surface Gravity ◽  
Shallow Water Waves ◽  
Ship Waves ◽  
Surface Gravity Waves ◽  
Basic Fluid

This chapter deals with the underlying mathematics of surface gravity waves, defined as gravity waves observed on an air–sea interface of the ocean. Surface gravity waves, or surface waves, differ from internal waves, gravity waves that occur within the body of the water (such as between parts of different densities). Examples of gravity waves are wind-generated waves on the water surface, as well tsunamis and ocean tides. Wind-generated gravity waves on the free surface of the Earth's seas, oceans, ponds, and lakes have a period of between 0.3 and 30 seconds. The chapter first describes the basic fluid equations before discussing the dispersion relations, with a particular focus on deep water waves, shallow water waves, and wavepackets. It also considers ship waves and how dispersion affects the wave pattern produced by a moving object, along with long and short waves.

scholarly journals Quantum Mechanical and Optical Analogies in Surface Gravity Water Waves

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 96 ◽  
Author(s):  
Georgi Gary Rozenman ◽  
Shenhe Fu ◽  
Ady Arie ◽  
Lev Shemer
Keyword(s):  
Quantum Mechanics ◽  
Gravity Waves ◽  
Water Waves ◽  
Water Wave ◽  
Wave Packets ◽  
Theoretical Models ◽  
Surface Gravity ◽  
Finite Width ◽  
Self Healing ◽  
Surface Gravity Waves

We present the theoretical models and review the most recent results of a class of experiments in the field of surface gravity waves. These experiments serve as demonstration of an analogy to a broad variety of phenomena in optics and quantum mechanics. In particular, experiments involving Airy water-wave packets were carried out. The Airy wave packets have attracted tremendous attention in optics and quantum mechanics owing to their unique properties, spanning from an ability to propagate along parabolic trajectories without spreading, and to accumulating a phase that scales with the cubic power of time. Non-dispersive Cosine-Gauss wave packets and self-similar Hermite-Gauss wave packets, also well known in the field of optics and quantum mechanics, were recently studied using surface gravity waves as well. These wave packets demonstrated self-healing properties in water wave pulses as well, preserving their width despite being dispersive. Finally, this new approach also allows to observe diffractive focusing from a temporal slit with finite width.

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