scholarly journals SPILLING BREAKERS, BORES, AND HYDRAULIC JUMPS

1978 ◽  
Vol 1 (16) ◽  
pp. 30 ◽  
Author(s):  
D.H. Peregrine ◽  
I.A. Svendsen
Keyword(s):  
Water Waves ◽  
Mean Flow ◽  
The Mean ◽  
White Water ◽  
Pass Through ◽  
Definition Of ◽  
Spilling Breakers ◽  
Almost All ◽  
Plunging Breaker ◽  
Spilling Breaker

On gently sloping beaches, almost all water waves break. After the initial breaking the water motion usually appears quite chaotic. However, for a moderate time, for example two or three times the descent time of the "plunge" in a plunging breaker, the flow can be relatively well organised despite the superficial view which is largely of spray and bubbles. If waves continue to break the breaking motion, or "white water" soon becomes fully turbulent and the mean motions become quasisteady. A reasonable definition of a quasi-steady wave is one which changes little during the time a water particle takes to pass through it. We exclude water particles which may become trapped in a surface roller and surf along with the wave. At this stage in its development a wave on a beach may be described as a spilling breaker or as a bore. In fact, there is a range of these waves from those with a little white water at the crest to examples where the whole front of the wave is fully turbulent. In investigating the properties of such waves it is desirable to start by looking at the whole range of related motions. The most obvious extension is to the hydraulic jump; since, in the simplest view, it is equivalent to a bore but in a frame of reference moving with the wave. It is also an example where the mean flow is steady rather than quasisteady.

Phase Averaging by Wavelet Transformation and the Application to Periodically Fluctuated Separation Flow

2002 ◽  
Author(s):  
Masaki Yamagishi ◽  
Tomoko Togano ◽  
Shinichi Tashiro
Keyword(s):  
Shear Layer ◽  
Wavelet Transformation ◽  
Dominant Frequency ◽  
Separation Flow ◽  
Mean Flow ◽  
Field Phase ◽  
Phase Averaging ◽  
Separated Shear Layer ◽  
The Mean ◽  
Almost All

The vortex structures in a separated region are generated by the motion of the separated shear layer caused by the introduction of periodic fluctuation. The main cause of the motion of the separated shear layer is the external fluctuation with the characteristic frequency. In order to investigate the principal motion of the velocity field, phase averaging was conducted to the velocity signals obtained by single hot-wire measurement. In phase averaging, wavelet analysis was applied to obtain the dominant frequency and the characteristic phase in the fluctuation. The profiles and the contours of the phase-averaged velocity could be found and discussed. The profiles vary dynamically at each phase and show the periodic motion of the shear layer. The separated shear layer flutters with the external fluctuation in the mean flow. If the suitable frequency is selected in the external fluctuation, the separated region disappears in almost all each phases owing to the depression of the shear layer near the wall.

Flow in a deep turbulent boundary layer over a surface distorted by water waves

1972 ◽  
Vol 55 (4) ◽  
pp. 719-735 ◽  
Author(s):  
A. A. Townsend
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Phase Velocity ◽  
Surface Stress ◽  
Water Waves ◽  
Turbulent Energy ◽  
Mean Flow ◽  
Boundary Layer Development ◽  
The Mean ◽  
Layer Development

Linearized equations for the mean flow and for the turbulent stresses over sinusoidal, travelling surface waves are derived using assumptions similar to those used by Bradshaw, Ferriss & Atwell (1967) to compute boundary-layer development. With the assumptions, the effects on the local turbulent stresses of advectal, vertical transport, generation and dissipation of turbulent energy can be assessed, and solutions of the equations are expected to resemble closely real flows with the same conditions. The calculated distributions of surface pressure indicate rates of wave growth (expressed as fractional energy gain during a radian advance of phase) of about 15(ρa/ρw) (τo/c2), where τo is the surface stress, co the phase velocity and ρa and ρw the densities of air and water, unless the wind velocity at height λ/2π is less than the phase velocity. The rates are considerably less than those measured by Snyder & Cox (1966), by Barnett & Wilkerson (1967) and by Dobson (1971), and arguments are presented to show that the linear approximation fails for wave slopes of order 0.1.

scholarly journals Structure and Motion of Severe-Wind-Producing Mesoscale Convective Systems and Derechos in Relation to the Mean Wind

2017 ◽  
Vol 32 (2) ◽  
pp. 423-439 ◽  
Author(s):  
Matthew A. Campbell ◽  
Ariel E. Cohen ◽  
Michael C. Coniglio ◽  
Andrew R. Dean ◽  
Stephen F. Corfidi ◽  
...  
Keyword(s):  
Large Scale ◽  
Mean Flow ◽  
Convective Systems ◽  
Structure And Motion ◽  
Mesoscale Convective ◽  
The Mean ◽  
Wind Events ◽  
Motion Characteristics ◽  
Definition Of ◽  
Convective Vortices

Abstract The goal of this study is to document differences in the convective structure and motion of long-track, severe-wind-producing MCSs from short-track severe-wind-producing MCSs in relation to the mean wind. An ancillary goal is to determine if these differences are large enough that some criterion for MCS motion relative to the mean wind could be used in future definitions of “derechos.” Results confirm past investigations that well-organized MCSs, including those that produce derechos, tend to move faster than the mean wind, exhibiting a significantly larger degree of propagation (component of MCS motion in addition to the component contributed by the mean flow). Furthermore, well-organized systems that produce shorter-track swaths of damaging winds likewise tend to move faster than the mean wind with a significant propagation component along the mean wind. Therefore, propagation in the direction of the mean wind is not necessarily a characteristic that can be used to distinguish derechos from nonderechos. However, there is some indication that long-track damaging wind events that occur without large-scale or persistent bow echoes and mesoscale convective vortices (MCVs) require a strong propagation component along the mean wind direction to become long lived. Overall, however, there does not appear to be enough separation in the motion characteristics among the MCS types to warrant the inclusion of a mean-wind criterion into the definition of a derecho at this time.

Hydraulic control of homogeneous shear flows

2003 ◽  
Vol 475 ◽  
pp. 163-172 ◽  
Author(s):  
CHRIS GARRETT ◽  
FRANK GERDES
Keyword(s):  
Shear Flow ◽  
Velocity Profile ◽  
Water Waves ◽  
Flow Speed ◽  
Hydraulic Control ◽  
Mean Flow ◽  
Shallow Water Waves ◽  
Homogeneous Fluid ◽  
Apparent Paradox ◽  
The Mean

If a shear flow of a homogeneous fluid preserves the shape of its velocity profile, a standard formula for the condition for hydraulic control suggests that this is achieved when the depth-averaged flow speed is less than (gh)1/2. On the other hand, shallow-water waves have a speed relative to the mean flow of more than (gh)1/2, suggesting that information could propagate upstream. This apparent paradox is resolved by showing that the internal stress required to maintain a constant velocity profile depends on flow derivatives along the channel, thus altering the wave speed without introducing damping. By contrast, an inviscid shear flow does not maintain the same profile shape, but it can be shown that long waves are stationary at a position of hydraulic control.

scholarly journals Southern Hemisphere Winter Extratropical Cyclone Characteristics and Vertical Organization Observed with the ERA-40 Data in 1979–2001

2007 ◽  
Vol 20 (11) ◽  
pp. 2675-2690 ◽  
Author(s):  
Eun-Pa Lim ◽  
Ian Simmonds
Keyword(s):  
Southern Hemisphere ◽  
Extratropical Cyclones ◽  
The Novel ◽  
Sea Level Pressure ◽  
Surface Development ◽  
Vertical Organization ◽  
The Mean ◽  
Definition Of ◽  
Hemisphere Winter ◽  
Almost All

Abstract The mean characteristics and trends of Southern Hemisphere (SH) winter extratropical cyclones occurring at six levels of the troposphere over the period 1979–2001 have been investigated using the 40-yr ECMWF Re-Analysis (ERA-40) data. Cyclonic systems were identified with the Melbourne University cyclone finding and tracking scheme. This study shows that mean sea level pressure (MSLP) cyclones are more numerous, more intense, smaller, deeper, and slower moving than higher-level cyclones. The novel vertical tracing scheme devised for this research revealed that about 52% of SH winter MSLP cyclones have a vertically well organized structure, extending through to the 500-hPa level. About 80% of these vertically coherent SH cyclones keep their westward tilt until the surface cyclones reach their maximum depths, and the mean distance is 300 km between the surface and the 500-hPa level cyclone centers when the surface cyclones obtain their maturity. According to the authors’ definition of vertical organization, explosively developing cyclones are vertically very well organized systems, whose surface development is antecedent to their 500-hPa level counterpart. Over 1979–2001 cyclones have increased in their system density, intensity, and translational velocity but decreased in their scale at almost all levels. However, some of the trends are not statistically significant. The proportion of vertically well organized systems in the entire population of SH winter extratropical cyclones has considerably increased over the last 23 yr, and the mean distance between the surface and the 500-hPa- level cyclone centers has decreased. Such changes in vertical organization of extratropical cyclones are statistically significant at the 95% confidence level.

scholarly journals An exact theory of nonlinear waves on a Lagrangian-mean flow

1978 ◽  
Vol 89 (4) ◽  
pp. 609-646 ◽  
Author(s):  
D. G. Andrews ◽  
M. E. Mcintyre
Keyword(s):  
Water Waves ◽  
Finite Amplitude ◽  
Mean Flow ◽  
Radiation Stress ◽  
Initial State ◽  
Mean Velocity ◽  
Generalized Lagrangian ◽  
Flow Evolution ◽  
The Mean ◽  
The Waves

An exact and very general Lagrangian-mean description of the back effect of oscillatory disturbances upon the mean state is given. The basic formalism applies to any problem whose governing equations are given in the usual Eulerian form, and irrespective of whether spatial, temporal, ensemble, or ‘two-timing’ averages are appropriate. The generalized Lagrangian-mean velocity cannot be defined exactly as the ‘mean following a single fluid particle’, but in cases where spatial averages are taken can easily be visualized, for instance, as the motion of the centre of mass of a tube of fluid particles which lay along the direction of averaging in a hypothetical initial state of no disturbance.The equations for the Lagrangian-mean flow are more useful than their Eulerian-mean counterparts in significant respects, for instance in explicitly representing the effect upon mean-flow evolution of wave dissipation or forcing. Applications to irrotational acoustic or water waves, and to astrogeophysical problems of waves on axisymmetric mean flows are discussed. In the latter context the equations embody generalizations of the Eliassen-Palm and Charney-Drazin theorems showing the effects on the mean flow of departures from steady, conservative waves, for arbitrary, finite-amplitude disturbances to a stratified, rotating fluid, with allowance for self-gravitation as well as for an external gravitational field.The equations show generally how the pseudomomentum (or wave ‘momentum’) enters problems of mean-flow evolution. They also indicate the extent to which the net effect of the waves on the mean flow can be described by a ‘radiation stress’, and provide a general framework for explaining the asymmetry of radiation-stress tensors along the lines proposed by Jones (1973).

A Coupled-Mode Technique for the Prediction of Wave-Induced Set-Up and Mean Flow in Variable Bathymetry Domains

2007 ◽  
Author(s):  
K. A. Belibassakis ◽  
Th. P. Gerostathis ◽  
G. A. Athanassoulis
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Water Environment ◽  
Wave Model ◽  
Mean Flow ◽  
Flow Equations ◽  
Coupled Mode ◽  
The Mean ◽  
Set Up ◽  
Wave Induced

In the present work, a complete, phase-resolving wave model is coupled with an iterative solver of the mean-flow equations in intermediate and shallow water depth, permitting an accurate calculation of wave set-up and wave-induced current in intermediate and shallow water environment with possibly steep bathymetric variations. The wave model is based on the consistent coupled-mode system of equations, developed by Athanassoulis & Belibassakis (1999) for the propagation of water waves in variable bathymetry regions. This model improves the predictions of the mild-slope equation, permitting the treatment of wave propagation in regions with steep bottom slope and/or large curvature. In addition, it supports the consistent calculation of wave velocity up to and including the bottom boundary. The above wave model has been further extended to include the effects of bottom friction and wave breaking, which are important factors for the calculation of radiation stresses on decreasing depth. The latter have been used as forcing terms to the mean flow equations in order to predict wave-induced set up and mean flow in open and closed domains. Numerical results obtained by the present model are presented and compared with predictions obtained by the mild-slope approximation (Massel & Gourlay 2000), and experimental data (Gourlay 1996).

scholarly journals Turbulence structure and interaction with steep breaking waves

2011 ◽  
Vol 674 ◽  
pp. 522-577 ◽  
Author(s):  
DJAMEL LAKEHAL ◽  
PETAR LIOVIC
Keyword(s):  
Fluid Flow ◽  
Water Waves ◽  
Three Dimensional ◽  
Breaking Waves ◽  
Small Scale ◽  
Breaking Wave ◽  
Turbulence Structure ◽  
Mean Flow ◽  
Scale Breaking ◽  
The Mean

Large-eddy and interface simulation using an interface tracking-based multi-fluid flow solver is conducted to investigate the breaking of steep water waves on a beach of constant bed slope. The present investigation focuses mainly on the ‘weak plunger’ breaking wave type and provides a detailed analysis of the two-way interaction between the mean fluid flow and the sub-modal motions, encompassing wave dynamics and turbulence. The flow is analysed from two points of views: mean to sub-modal exchange, and wave to turbulence interaction within the sub-modal range. Wave growth and propagation are due to energy transfer from the mean flow to the waves, and transport of mean momentum by these waves. The vigorous downwelling–upwelling patterns developing at the head and tail of each breaker are shown to generate both negative- and positive-signed energy exchange contributions in the thin sublayer underneath the water surface. The details of these exchange mechanisms are thoroughly discussed in this paper, together with the interplay between three-dimensional small-scale breaking associated with turbulence and the dominant two-dimensional wave motion. A conditional zonal analysis is proposed for the first time to understand the transient mechanisms of turbulent kinetic energy production, decay, diffusion and transport and their dependence and/or impact on surface wrinkling over the entire breaking process. The simulations provide a thorough picture of air–liquid coherent structures that develop over the breaking process, and link them to the transient mechanisms responsible for their local incidence.

Wave-driven currents and vortex dynamics on barred beaches

2001 ◽  
Vol 449 ◽  
pp. 313-339 ◽  
Author(s):  
OLIVER BÜHLER ◽  
TIVON E. JACOBSON
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Waves ◽  
Wave Breaking ◽  
Bottom Topography ◽  
Breaking Waves ◽  
Vortex Structures ◽  
Water Model ◽  
Mean Flow ◽  
The Mean

We present a theoretical and numerical investigation of longshore currents driven by breaking waves on beaches, especially barred beaches. The novel feature considered here is that the wave envelope is allowed to vary in the alongshore direction, which leads to the generation of strong dipolar vortex structures where the waves are breaking. The nonlinear evolution of these vortex structures is studied in detail using a simple analytical theory to model the effect of a sloping beach. One of our findings is that the vortex evolution provides a robust mechanism through which the preferred location of the longshore current can move shorewards from the location of wave breaking. Such current dislocation is an often-observed (but ill-understood) phenomenon on real barred beaches.To underpin our results, we present a comprehensive theoretical description of the relevant wave–mean interaction theory in the context of a shallow-water model for the beach. Therein we link the radiation-stress theory of Longuet-Higgins & Stewart to recently established results concerning the mean vorticity generation due to breaking waves. This leads to detailed results for the entire life-cycle of the mean-flow vortex evolution, from its initial generation by wave breaking until its eventual dissipative decay due to bottom friction.In order to test and illustrate our theory we also present idealized nonlinear numerical simulations of both waves and vortices using the full shallow-water equations with bottom topography. In these simulations wave breaking occurs through shock formation of the shallow-water waves. We note that because the shallow-water equations also describe the two-dimensional flow of a homentropic perfect gas, our theoretical and numerical results can also be applied to nonlinear acoustics and sound–vortex interactions.

Momentum transport by gravity waves in a perfectly conducting shear flow

1972 ◽  
Vol 54 (2) ◽  
pp. 217-240 ◽  
Author(s):  
N. Rudraiah ◽  
M. Venkatachalappa
Keyword(s):  
Magnetic Field ◽  
Gravity Waves ◽  
Critical Level ◽  
Critical Levels ◽  
Mean Flow ◽  
Critical Layers ◽  
The Mean ◽  
Pass Through ◽  
The Waves ◽  
Aligned Magnetic Field

Alfvén-gravitational waves propagating in a Boussinesq, inviscid, adiabatic, perfectly conducting fluid in the presence of a uniform aligned magnetic field in which the mean horizontal velocityU(z)depends on heightzonly are considered. The governing wave equation has three singularities, at the Doppler-shifted frequencies Ωd= 0, ± ΩA, where ΩAis the Alfvén frequency. Hence the effect of the Lorentz force is to introduce two more critical levels, called hydromagnetic critical levels, in addition to the hydrodynamic critical level. To study the influence of magnetic field on the attenuation of waves two situations, one concerning waves far away from the critical levels (i.e. Ωd[Gt ] ΩA) and the other waves at moderate distances from the critical levels (i.e. Ωd> ΩA), are investigated. In the former case, if the hydrodynamic Richardson numberJHexceeds one quarter the waves are attenuated by a factor exp{−2π(JH−¼)½} as they pass through the hydromagnetic critical levels, at which Ωd= ± ΩA, and momentum is transferred to the mean flow there. Whereas in the case of waves at moderate distances from the critical levels the ratio of momentum fluxes on either side of the hydromagnetic critical levels differ by a factor exp {−2π(J−¼)½}, whereJ(> ¼) is the algebraic sum of hydrodynamic and hydromagnetic Richardson numbers. Thus the solutions to the hydromagnetic system approach asymptotically those of the hydrodynamic system sufficiently far on either side of the magnetic critical layers, though their behaviour in the vicinity of such levels is quite dissimilar. There is no attenuation and momentum transfer to the mean flow across the hydrodynamic critical level, at which Ωd= 0. The general theory is applied to a particular problem of flow over a sinusoidal corrugation. This is significant in considering the propagation of Alfvén-gravity waves, in the presence of a geomagnetic field, from troposphere to ionosphere.

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