Showing papers on "Breaking wave published in 2004"

Near Field Characteristics of Landslide Generated Impulse Waves

Abstract: Landslide generated impulse waves were investigated in a two-dimensional physical laboratory model based on the generalized Froude similarity. The recorded wave profiles were extremely unsteady and nonlinear. Four wave types were determined: weakly nonlinear oscillatory wave, non-linear transition wave, solitary-like wave and dissipative transient bore. Most of the generated impulse waves were located in the intermediate water depth wave regime. Nevertheless the propagation velocity of the leading wave crest closely followed the theoretical approximations for a solitary wave. Between 4 and 50% of the kinetic slide impact energy propagated outward in the impulse wave train. The applicability ranges of the classical nonlinear wave theories to landslide generated impulse waves were determined. The main wave characteristics were related to the landslide parameters driving the entire wave generation process. The slide Froude number was identified as the dominant parameter. The physical model results were compared to the giant rockslide generated impulse wave which struck the shores of the Lituya Bay, Alaska, in 1958.

Is the North Atlantic Oscillation a Breaking Wave

Abstract: Given the recent observational evidence that the positive (negative) phase of the North Atlantic Oscillation (NAO) is the remnant of anticyclonic (cyclonic) wave breaking, this study uses a multilevel primitive equation model to investigate important dynamical attributes of the above wave breaking behavior. For this purpose, a hierarchy of different basic states (two- and three-dimensional) and initial perturbations are used. With the three-dimensional climatological flow as the basic state, it is found that initial perturbations located equatorward (poleward) and upstream of the climatological Atlantic jet lead to wave breaking similar to that of the positive (negative) NAO phase. Consistently, analysis of observational data indeed shows that the Pacific storm track is displaced equatorward (poleward) prior the onset of the positive (negative) NAO phase. This result suggests that the latitudinal position of the Pacific storm track plays an important role for determining the phase of the NAO. Sen...

Wave Breaking and Ocean Surface Layer Thermal Response

Abstract: The effect of breaking waves on ocean surface temperatures and surface boundary layer deepening is investigated. The modification of the Mellor‐Yamada turbulence closure model by Craig and Banner and others to include surface wave breaking energetics reduces summertime surface temperatures when the surface layer is relatively shallow. The effect of the Charnock constant in the relevant drag coefficient relation is also studied.

Near-Surface Turbulence in the Presence of Breaking Waves

Abstract: Observations with a three-axis pulse-to-pulse coherent acoustic Doppler profiler and acoustic resonators reveal the turbulence and bubble field beneath breaking waves in the open ocean at wind speeds up to 14 m s−1. About 55%–80% of velocity wavenumber spectra, calculated with Hilbert spectral analysis based on empirical mode decomposition, are consistent with an inertial subrange. Time series of turbulent kinetic energy dissipation at approximately 1 m beneath the free surface and 1-Hz sampling rate are obtained. High turbulence levels with dissipation rates more than four orders larger than the background dissipation are linked to wave breaking. Initial dissipation levels beneath breaking waves yield the Hinze scale of the maximum bubble size aH ≅ 2 × 10−3 m. Turbulence induced by discrete breaking events was observed to decay as e ∝ tn, where n = −4.3 is close to the theoretical value for isotropic turbulence (−17/4). In the crest region above the mean waterline, dissipation increases as e(z) ...

Waves in the ocean and atmosphere : introduction to wave dynamics

Abstract: 1 Introduction.- 2 Kinematic Generalization.- 3 Equations of Motion Surface Gravity Waves.- 4 Fields of Motion in Gravity Waves and Energy.- 5 The Initial Value Problem.- 6 Discussion of Initial Value Problem [Continued).- 7 Internal Gravity Waves.- 8 Internal Waves, Group Velocity and Reflection.- 9 WKB Theory for Internal Gravity Waves.- 10 Vertical Propagation of Waves: Steady Flow and the Radiation Condition.- 11 Rotation and Potential Vorticity.- 12 Large-Scale Hydrostatic Motions.- 13 Shallow Water Waves in a Rotating Fluid Poincare and Kelvin Waves.- 14 Rossby Waves.- 15 Rossby Waves (Continued), Quasi-Geostrophy.- 16 Energy and Energy Flux in Rossby Waves.- 17 Laplace Tidal Equations and the Vertical Structure Equation.- 18 Equatorial Beta-Plane and Equatorial Waves.- 19 Stratified Quasi-Geostrophic Motion and Instability Waves.- 20 Energy Equation and Necessary Conditions for Instability.- 21 Wave-Mean Flow Interaction.- Problems.- References.

Inversion effects on mountain lee waves

Abstract: The effect of a sharp low-level temperature inversion on flow over a mountain is investigated via a series of two-dimensional idealized numerical model simulations. The main focus of the study is the effect of the inversion on the formation of lee waves, lee-wave rotors, low-level hydraulic jumps and the occurrence of wave breaking aloft. The idealized problem considered consists of an upwind velocity profile that is independent of height (above the boundary layer) and directed normal to an isolated two-dimensional ridge. The upstream stratification consists of a neutral layer immediately above the ground capped by a sharp temperature inversion. Above this, the atmosphere is stably stratified and the Brunt–Vaisala frequency is independent of height. Simulations were conducted for a range of inversion strengths (measured by the difference in potential temperature across the inversion) and inversion heights. The effect of both a free-slip and a no-slip lower boundary condition is investigated. Results show that, when the upwind Froude number (defined in the usual way for two-layer shallow-water flow) falls below a critical value, a short-wavelength resonant lee wave forms downwind of the mountain on the inversion. It is shown that both the critical Froude-number value and the wavelength of the lee wave are accurately predicted by linear theory. The lee-wave amplitude, however, can be significantly underestimated by linear theory if the wavelength is less than the hill length scale. In the case of a no-slip boundary condition, if the wave amplitude is sufficiently large, boundary-layer separation occurs underneath the wave crests and closed rotor circulations occur. In general, flow separation (and rotors) do not occur in the free-slip case. In both the free-slip and no-slip flows, as the Froude number decreases the lee wave is eventually replaced by a stationary hydraulic jump above the lee slope of the mountain. Copyright © 2004 Royal Meteorological Society.

Dynamics of 2-Day Equatorial Waves

Abstract: The dynamics of the 2-day wave, a type of convectively coupled disturbance that frequents the equatorial western Pacific, is examined using observations and a linear primitive equation model. A statistical composite of the wave’s kinematic and thermodynamic structure is presented. It is shown that 1) the wave’s wind and temperature perturbations can be modeled as linear responses to convective heating and cooling, and 2) the bulk of the wave’s dynamical and convective structure can be represented with two vertical modes. The observations and model results suggest that the 2-day wave is an n 5 1 westward-propagating inertio‐gravity wave with a shallow equivalent depth (14 m) that results from the partial cancelation of adiabatic temperature changes due to vertical motion by convective heating and cooling.

Effects of wave shape on sheet flow sediment transport

Abstract: [1] A two-phase model is implemented to study the effects of wave shape on the transport of coarse-grained sediment in the sheet flow regime. The model is based on balance equations for the average mass, momentum, and fluctuation energy for both the fluid and sediment phases. Model simulations indicate that the responses of the sheet flow, such as the velocity profiles, the instantaneous bed shear stress, the sediment flux, and the total amount of the mobilized sediment, cannot be fully parameterized by quasi-steady free-stream velocity and may be correlated with the magnitude of local horizontal pressure gradient (or free-stream acceleration). A net sediment flux in the direction of wave advance is obtained for both skewed and saw-tooth wave shapes typical of shoaled and breaking waves. The model further suggests that at critical values of the horizontal pressure gradient, there is a failure event within the bed that mobilizes more sediment into the mobile sheet and enhances the sediment flux. Preliminary attempts to parameterize the total bed shear stress and the total sediment flux appear promising.

Large Eddy Simulation of the Ocean Mixed Layer: The Effects of Wave Breaking and Langmuir Circulation

Abstract: Large eddy simulation (LES) of the ocean mixed layer was performed in which both wave breaking and Langmuir circulation are realized. Wave breaking was represented by random forcing consistent with the observed near-surface turbulence, and Langmuir circulation was realized by the Craig–Leibovich vortex force. High- resolution simulations were carried out using parallel computing with or without each contribution, wave breaking and Langmuir circulation, with an aim to clarify their respective roles in the ocean mixed layer. The effects of wave breaking were found to be mainly limited to the near-surface zone of the upper few meters. Langmuir circulations below it are not significantly modified, although they become somewhat weakened and less coherent. Under the influence of wave breaking, however, the turbulence production in the upper-ocean mixed layer becomes dominated by the turbulent kinetic energy flux, contrary to the case of the atmospheric boundary layer where it is dominated by shear prod...

The oceanic boundary layer driven by wave breaking with stochastic variability. Part 1. Direct numerical simulations

Abstract: We devise a stochastic model for the effects of breaking waves and fit its distribution functions to laboratory and field data This is used to represent the space-time structure of momentum and energy forcing of the oceanic boundary layer in turbulence-resolving simulations The aptness of this breaker model is evaluated in a direct numerical simulation (DNS) of an otherwise quiescent fluid driven by an isolated breaking wave, and the results are in good agreement with laboratory measurements The breaker model faithfully reproduces the bulk features of a breaking event: the mean kinetic energy decays at a rate approaching t -1 , and a long-lived vortex (eddy) is generated close to the water surface The long lifetime of this vortex (more than 50 wave periods) makes it effective in energizing the surface region of oceanic boundary layers Next, a comparison of several different DNS of idealized oceanic boundary layers driven by different surface forcing (ie constant current (as in Couette flow), constant stress, or a mixture of constant stress plus stochastic breakers) elucidates the importance of intermittent stress transmission to the underlying currents A small amount of active breaking, about 16% of the total water surface area at any instant in time, significantly alters the instantaneous flow patterns as well as the ensemble statistics Near the water surface a vigorous downwelling-upwelling pattern develops at the head and tail of each three-dimensional breaker This enhances the vertical velocity variance and generates both negative- and positive-signed vertical momentum flux Analysis of the mean velocity and scalar profiles shows that breaking effectively increases the surface roughness z o by more than a factor of 30; for our simulations z o /λ004 to 006, where λ is the wavelength of the breaking wave Compared to a flow driven by a constant current, the extra mixing from breakers increases the mean eddy viscosity by more than a factor of 10 near the water surface Breaking waves alter the usual balance of production and dissipation in the turbulent kinetic energy (TKE) budget; turbulent and pressure transports and breaker work are important sources and sinks in the budget We also show that turbulent boundary layers driven by constant current and constant stress (ie with no breaking) differ in fundamental ways The additional freedom provided by a constant-stress boundary condition permits finite velocity variances at the water surface, so that flows driven by constant stress mimic flows with weakly and statistically homogeneous breaking waves

MHD wave propagation in the neighbourhood of a two-dimensional null point

Abstract: The nature of fast magnetoacoustic and Alfven waves is investigated in a zero β plasma. This gives an indication of wave propagation in the low β solar corona. It is found that for a two-dimensional null point, the fast wave is attracted to that point and the front of the wave slows down as it approaches the null point, causing the current density to accumulate there and rise rapidly. Ohmic dissipation will extract the energy in the wave at this point. This illustrates that null points play an important role in the rapid dissipation of fast magnetoacoustic waves and suggests the location where wave heating will occur in the corona. The Alfven wave behaves in a different manner in that the wave energy is dissipated along the separatrices. For Alfven waves that are decoupled from fast waves, the value of the plasma β is unimportant. However, the phenomenon of dissipating the majority of the wave energy at a specific place is a feature of both wave types.

Idealized Solutions for the Energy Balance of the Finescale Internal Wave Field

Abstract: Recent fine- and microstructure observations indicate enhanced finescale shear and strain in conjunction with bottom-intensified turbulent dissipation above rough bathymetry in the Brazil Basin. Such observations implicate the bottom boundary as an energy source for the finescale internal wave field. Simple analytical and numerical solutions to an equation governing the spatial and temporal evolution of the finescale wave field are described here. The governing equation implicitly treats the effects of wave breaking on the vertical propagation of internal waves through a flux representation of nonlinear transports associated with internal wave–wave interactions. These solutions identify the rate of dissipation of turbulent kinetic energy with downscale energy transports at high vertical wavenumber, resulting in an estimate of dissipation versus depth. The sensitivity of the turbulent dissipation depth profile to various environmental parameters is examined. Observed dissipation profiles and shear...

Propagation through nonlinear time-dependent bubble clouds and the estimation of bubble populations from measured acoustic characteristics

Abstract: For several decades the propagation characteristics of acoustic pulses (attenuation and sound speed) have been inverted in attempts to measure the size distributions of gas bubbles in liquids. While this has biomedical and industrial applications, most notably it has been attempted in the ocean for defence and environmental purposes, where the bubbles are predominantly generated by breaking waves. Such inversions have required assumptions, and the state–of–the–art technique still assumes that the bubbles undergo linear, steady–state monochromatic pulsations in the free field, without interacting. The measurements always violate, to a greater or lesser extent, these assumptions. The errors incurred by the use of such assumptions have been difficult to quantify, but are expected to be most severe underneath breakers in the surf zone, where the void fraction is greatest. Very few measurements have been made in this important region of the ocean. This paper provides a method by which attenuation can be predicted through clouds of bubbles which need not be homogeneous, nor restricted to linear steady–state monochromatic pulsations. To allow inversion of measured surf zone attenuations to estimate bubble populations with current computational facilities, this model is simplified such that the bubble cloud is assumed to be homogeneous and the bubbles oscillating in steady state (although still nonlinearly). The uses of the new methods for assessing the errors introduced in using state–of–the–art inversions are discussed, as are their implications for oceanographic and industrial nonlinear bubble counters, for biomedical contrast agents, and for sonar target detection in the surf zone.

Microbreaking and the enhancement of air-water transfer velocity

Abstract: [1] The role of microscale wave breaking in controlling the air-water transfer of heat and gas is investigated in a laboratory wind-wave tank. The local heat transfer velocity, kH, is measured using an active infrared technique and the tank-averaged gas transfer velocity, kG, is measured using conservative mass balances. Simultaneous, colocated infrared and wave slope imagery show that wave-related areas of thermal boundary layer disruption and renewal are the turbulent wakes of microscale breaking waves, or microbreakers. The fractional area coverage of microbreakers, AB, is found to be 0.1–0.4 in the wind speed range 4.2–9.3 m s � 1 for cleaned and surfactant-influenced surfaces, and kH and kG are correlated with AB. The correlation of kH with AB is independent of fetch and the presence of surfactants, while that for kG with AB depends on surfactants. Additionally, AB is correlated with the mean square wave slope, hS 2 i, which has shown promise as a correlate for kG in previous studies. The ratio of kH measured inside and outside the microbreaker wakes is 3.4, demonstrating that at these wind speeds, up to 75% of the transfer is the direct result of microbreaking. These results provide quantitative evidence that microbreaking is the dominant mechanism contributing to air-water heat and gas transfer at low to moderate wind speeds. INDEX TERMS: 4504 Oceanography: Physical: Air/sea interactions (0312); 0312 Atmospheric Composition and Structure: Air/sea constituent fluxes (3339, 4504); 3339 Meteorology and Atmospheric Dynamics: Ocean/atmosphere interactions (0312, 4504); 4506 Oceanography: Physical: Capillary waves; 4568 Oceanography: Physical: Turbulence, diffusion, and mixing processes; KEYWORDS: microbreaking, gas transfer, waves

Observations of swash zone velocities: A note on friction coefficients

Abstract: [1] Vertical flow structure and turbulent dissipation in the swash zone are estimated using cross-shore fluid velocities observed on a low-sloped, fine-grained sandy beach [Raubenheimer, 2002] with two stacks of three current meters located about 2, 5, and 8 cm above the bed. The observations are consistent with an approximately logarithmic vertical decay of wave orbital velocities within 5 cm of the bed. The associated friction coefficients are similar in both the uprush and downrush, as in previous laboratory results. Turbulent dissipation rates estimated from velocity spectra increase with decreasing water depth from O(400 cm2/s3) in the inner surf zone to O(1000 cm2/s3) in the swash zone. Friction coefficients in the swash interior estimated with the logarithmic model and independently estimated by assuming that turbulent dissipation is balanced by production from vertical shear of the local mean flow and from wave breaking are between 0.02 and 0.06. These values are similar to the range of friction coefficients (0.02–0.05) recently estimated on impermeable, rough, nonerodible laboratory beaches and to the range of friction coefficients (0.01–0.03) previously estimated from field observations of the motion of the shoreward edge of the swash (run-up).

Laboratory measurements of limiting freak waves on currents

Abstract: [1] The results of laboratory measurements on limiting freak waves in the presence of currents are reported. Both dispersive spatial-temporal focusing and wave-current interaction are used to generate freak waves in a partial random wave field in the presence of currents. Wave group structure, for example, spectral slope and frequency bandwidth, is found to be critical to the formation and the geometric properties of freak waves. A nondimensional spectral bandwidth is shown to well represent wave group structure and proves to be a good indicator in determining limiting freak wave characteristics. The role of a co-existing current in the freak wave formation is recognized. Experimental results confirm that a random wave field does not prevent freak wave formation due to dispersive focusing. Strong opposing currents inducing partial wave blocking significantly elevate the limiting steepness and asymmetry of freak waves. At the location where a freak wave occurs, the Fourier spectrum exhibits local energy transfer to high-frequency waves. The Hilbert-Huang spectrum, a time-frequency-amplitude spectrum, depicts both the temporal and spectral evolution of freak waves. A strong correlation between the magnitude of interwave instantaneous frequency modulation and the freak wave nonlinearity (steepness) is observed. The experimental results provide an explanation to address the occurrence and characteristic of freak waves in consideration of the onset of wave breaking.

Wave breaking for a shallow water equation

Abstract: In this paper, we establish sufficient conditions on the initial data to guarantee ware breakings for a shallow water equation.

Damping and pumping of a vortex Rossby wave in a monotonic cyclone: Critical layer stirring versus inertia-buoyancy wave emission

Abstract: This paper further examines the rate at which potential vorticity in the core of a monotonic cyclone becomes vertically aligned and horizontally axisymmetric. We consider the case in which symmetrization occurs by the damping of a discrete vortex Rossby (VR) wave. The damping of the VR wave is caused by its stirring of potential vorticity at a critical radius r*, outside the core of the cyclone. The decay rate generally increases with the radial gradient of potential vorticity at r*. Previous theories for the decay rate were based on “balance models” of the vortex dynamics. Such models filter out inertia–buoyancy (IB) oscillations, i.e., gravity waves. However, if the Rossby number is greater than unity, the core VR wave can excite a frequency-matched outward propagating IB wave, which has positive feedback. To accurately account for this radiation, we here develop a theory for the decay rate that is based on the hydrostatic primitive equations. Starting from conservation of wave activity (angular pseudom...

Animation and control of breaking waves

Abstract: Controlling fluids is still an open and challenging problem in fluid animation. In this paper we develop a novel fluid animation control approach and we present its application to controlling breaking waves. In our Slice Method framework an animator defines the shape of a breaking wave at a desired moment in its evolution based on a library of breaking waves. Our system computes then the subsequent dynamics with the aid of a 3D Navier-Stokes solver. The wave dynamics previous to the moment the animator exerts control can also be generated based on the wave library. The animator is thus enabled to obtain a full animation of a breaking wave while controlling the shape and the timing of the breaking. An additional advantage of the method is that it provides a significantly faster method for obtaining the full 3D breaking wave evolution compared to starting the simulation at an early stage and using solely the 3D Navier-Stokes equations. We present a series of 2D and 3D breaking wave animations to demonstrate the power of the method.

Frontal geostrophic adjustment and nonlinear wave phenomena in one-dimensional rotating shallow water. Part 2. High-resolution numerical simulations

Abstract: High-resolution shock-capturing finite-volume numerical methods are applied to investigate nonlinear geostrophic adjustment of rectilinear fronts and jets in the rotating shallow-water model. Numerical experiments for various jet/front configurations show that for localized initial conditions in the open domain an adjusted state is always attained. This is the case even when the initial potential vorticity (PV) is not positive-definite, the situation where no proof of existence of the adjusted state is available. Adjustment of the vortex, PV-bearing, part of the flow is rapid and is achieved within a couple of inertial periods. However, the PV-less low-energy quasi-inertial oscillations remain for a long time in the vicinity of the jet core. It is demonstrated that they represent a long-wave part of the initial perturbation and decay according to the standard dispersion law ${\sim}t^{-1/2}$ . For geostrophic adjustment in a periodic domain, an exact periodic nonlinear wave solution is found to emerge spontaneously during the evolution of wave perturbations allowing us to conjecture that this solution is an attractor. In both cases of adjustment in open and periodic domains, it is shown that shock-formation is ubiquitous. It takes place immediately in the jet core and, thus, plays an important role in fully nonlinear adjustment. Although shocks dissipate energy effectively, the PV distribution is not changed owing to the passage of shocks in the case of strictly rectilinear flows.