scholarly journals Steep unidirectional wave groups – fully nonlinear simulations vs. experiments

2015 ◽  
Vol 22 (6) ◽  
pp. 737-747 ◽  
Author(s):  
L. Shemer ◽  
B. K. Ee

Abstract. A detailed quantitative comparison of fully nonlinear computations with the measurements of unidirectional wave groups is presented. Computational results on evolving wave groups were compared with previous available experiments. The local surface elevation variation, the evolution of envelope shapes, the velocity of propagation of the steepest crests in the group and their relation to the height of the crests were obtained numerically and experimentally. Conditions corresponding to incipient wave breaking were investigated in greater detail. The results shed additional light on mechanisms leading to the breaking of steep waves, as well as on the crucial importance of exact matching between initial conditions in computations and experiments.

2015 ◽  
Vol 2 (4) ◽  
pp. 1159-1195 ◽  
Author(s):  
L. Shemer ◽  
B. K. Ee

Abstract. A method was developed to carry out detailed qualitative comparison of fully nonlinear computations with the measurements of unidirectional wave groups. Computational results on evolving wave groups were compared with the available experiments. The local surface elevation variation, evolution of envelope shapes, the velocity of propagation of the steepest crests in the group and their relation to the height of the crests were obtained numerically and experimentally. Conditions corresponding to incipient wave breaking were investigated in greater detail. The results shed additional light on the limits of applicability of the computational results, as well as on mechanisms leading to the breaking of steep waves.


Author(s):  
Lev Shemer ◽  
Bernard K. Ee

A method was developed to carry out detailed qualitative comparison of fully nonlinear computations with the measurements of unidirectional wave groups. Computational results on evolving wave groups were compared with the available experiments. The local surface elevation variation, evolution of envelope shapes, the velocity of propagation of the steepest crests in the group and their relation to the height of the crests were obtained numerically and experimentally. The results shed additional light on the mechanisms leading to the breaking of steep waves.


2009 ◽  
Vol 66 (11) ◽  
pp. 3401-3418 ◽  
Author(s):  
Patrick A. Reinecke ◽  
Dale R. Durran

Abstract The sensitivity of downslope wind forecasts to small changes in initial conditions is explored by using 70-member ensemble simulations of two prototypical windstorms observed during the Terrain-Induced Rotor Experiment (T-REX). The 10 weakest and 10 strongest ensemble members are composited and compared for each event. In the first case, the 6-h ensemble-mean forecast shows a large-amplitude breaking mountain wave and severe downslope winds. Nevertheless, the forecasts are very sensitive to the initial conditions because the difference in the downslope wind speeds predicted by the strong- and weak-member composites grows to larger than 28 m s−1 over the 6-h forecast. The structure of the synoptic-scale flow one hour prior to the windstorm and during the windstorm is very similar in both the weak- and strong-member composites. Wave breaking is not a significant factor in the second case, in which the strong winds are generated by a layer of high static stability flowing beneath a layer of weaker mid- and upper-tropospheric stability. In this case, the sensitivity to initial conditions is weaker but still significant. The difference in downslope wind speeds between the weak- and strong-member composites grows to 22 m s−1 over 12 h. During and one hour before the windstorm, the synoptic-scale flow exhibits appreciable differences between the strong- and weak-member composites. Although this case appears to be more predictable than the wave-breaking event, neither case suggests that much confidence should be placed in the intensity of downslope winds forecast 12 or more hours in advance.


2018 ◽  
Vol 48 (12) ◽  
pp. 2937-2948 ◽  
Author(s):  
David W. Wang ◽  
Hemantha W. Wijesekera

AbstractIt has been recognized that modulated wave groups trigger wave breaking and generate energy dissipation events on the ocean surface. Quantitative examination of wave-breaking events and associated turbulent kinetic energy (TKE) dissipation rates within a modulated wave group in the open ocean is not a trivial task. To address this challenging topic, a set of laboratory experiments was carried out in an outdoor facility, the Oil and Hazardous Material Simulated Environment Test Tank (203 m long, 20 m wide, 3.5 m deep). TKE dissipation rates at multiple depths were estimated directly while moving the sensor platform at a speed of about 0.53 m s−1 toward incoming wave groups generated by the wave maker. The largest TKE dissipation rates and significant whitecaps were found at or near the center of wave groups where steepening waves approached the geometric limit of waves. The TKE dissipation rate was O(10−2) W kg−1 during wave breaking, which is two to three orders of magnitude larger than before and after wave breaking. The enhanced TKE dissipation rate was limited to a layer of half the wave height in depth. Observations indicate that the impact of wave breaking was not significant at depths deeper than one wave height from the surface. The TKE dissipation rate of breaking waves within wave groups can be parameterized by local wave phase speed with a proportionality breaking strength coefficient dependent on local steepness. The characterization of energy dissipation in wave groups from local wave properties will enable a better determination of near-surface TKE dissipation of breaking waves.


2013 ◽  
Vol 1 (3) ◽  
pp. 2831-2857
Author(s):  
M. H. Dao ◽  
H. Xu ◽  
E. S. Chan ◽  
P. Tkalich

Abstract. Accurate predictions of wave run-up and run-down are important for coastal impact assessment of relatively long waves such as tsunami or storm waves. Wave run-up is, however, a complex process involving nonlinear build-up of the wave front, intensive wave breaking and strong turbulent flow, making the numerical approximation challenging. Recent advanced modeling methodologies could help to overcome these numerical challenges. For a demonstration, we study run-up of non-breaking and breaking solitary waves on vertical wall using two methods, the enhanced Smoothed Particle Hydrodynamics (SPH) method and the traditional non-breaking nonlinear model Tunami-N2. The Tunami-N2 model fails to capture the evolution of steep waves at the proximity of breaking that observed in the experiments. Whereas, the SPH method successfully simulate the wave propagation, breaking, impact on structure and the reform and breaking processes of wave run-down. The study also indicates that inadequate approximation of the wave breaking could lead to significant under-predictions of wave height and impact pressure on structures. The SPH model shows potential applications for accurate impact assessments of wave run-up onto coastal structures.


2013 ◽  
Vol 13 (8) ◽  
pp. 2101-2107 ◽  
Author(s):  
L. Shemer

Abstract. Experiments on extremely steep deterministic waves generated in a large wave tank by focusing of a broad-banded wave train serve as a motivation for the theoretical analysis of the conditions leading to wave breaking. Particular attention is given to the crest of the steepest wave where both the horizontal velocity and the vertical acceleration attain their maxima. Analysis is carried out up to the third order in wave steepness. The apparent, Eulerian and Lagrangian accelerations are computed for wave parameters observed in experiments. It is demonstrated that for a wave group with a wide spectrum, the crest propagation velocity differs significantly from both the phase and the group velocities of the peak wave. Conclusions are drawn regarding the applicability of various criteria for wave breaking.


2006 ◽  
Vol 16 (09) ◽  
pp. 2705-2711 ◽  
Author(s):  
RODICA BORCIA ◽  
DOMNIC MERKT ◽  
MICHAEL BESTEHORN

Recently, we have developed a phase field model to describe Marangoni convection with evaporation in a compressible fluid of van der Waals type away from criticality [Eur. Phys. J. B44 (2005)]. Using this model, we report now 2D fully nonlinear simulations where we emphasize the influence of evaporation on convective patterns.


2011 ◽  
Vol 41 (5) ◽  
pp. 837-856 ◽  
Author(s):  
Juan M. Restrepo ◽  
Jorge M. Ramírez ◽  
James C. McWilliams ◽  
Michael Banner

Abstract Whitecapping affects the Reynolds stresses near the ocean surface. A model for the conservative dynamics of waves and currents is modified to include the averaged effect of multiple, short-lived, and random wave-breaking events on large spatiotemporal scales. In this study’s treatment, whitecapping is parameterized stochastically as an additive uncertainty in the fluid velocity. It is coupled to the Stokes drift as well as to the current velocity in the form of nonlinear momentum terms in the vortex force and the Bernoulli head. The effects of whitecapping on tracer dynamics, mass balances, and boundary conditions are also derived here. Whitecapping also modifies the dynamics and the size of the sea surface boundary layer. This study does not resolve the boundary layer, however, the authors appeal to traditional viscosity parameterizations to include these diffusive effects, modified for the context of wave–current interactions. The parameterized breaking velocity field is endowed with empirical rules that link their generation in space and time to properties and dynamics of wave groups. The energy convergence rate of wave groups is used as an indicator for the onset of wave breaking. A methodology is proposed for evaluating this criterion over an evolving random Gaussian model for the ocean surface. The expected spatiotemporal statistics of the breaking events are not imposed, but rather computed, and are found to agree with the general expectation of its Poisson character. The authors also compute, rather than impose, the shear stress associated with the breaking events and find it to agree with theoretical expectations. When the relative role played by waves and breaking events on currents is compared, this study finds that waves, via the vortex force, purely advect the vorticity of currents that are essentially only dependent on transverse coordinates. The authors show that currents will tend to get rougher in the direction of steady wind, when whitecapping is present. Breaking events can alter and even suppress the rate of advection in the vortex force. When comparing the rates of transport, the waves will tend to dominate the short term and the whitecapping of the long-term rate.


Some simple general properties of wave breaking are deduced from the known behaviour of surface gravity waves in deep water, on the assumption that breaking occurs in association with wave groups. In particular we derive equations for the time interval, ז, between the onset of breaking of successive waves: ז ═ T / |1 – ( c ⋅ c g )/ c 2 |, and for the propagation vector c b (referred to as the ‘wave-breaking vector’) of the position at which breaking, once initiated, will proceed: c b ═ c (1 – c ⋅ c g / c 2 )+ c g . Here c is the phase velocity, and c g the group velocity, of waves of period T . Interfacial waves, internal gravity waves, inertial waves and planetary waves are considered as particular examples. The results apply not only to wave breaking, but to the movement of any property (e. g. fluid acceleration, gradient Richardson number) that is carried through a medium in association with waves. One application is to describe the distribution, in space and time, of regions of turbulent mixing, or transitional phenomena, in the oceans or atmosphere.


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