Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session E3: Waves I |
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Chair: James Kirby, University of Delaware Room: 303 |
Sunday, November 20, 2011 4:40PM - 4:53PM |
E3.00001: A wave vortex force formalism for wave-current interaction in strongly sheared flows Zhifei Dong, James T. Kirby In the river plume, waves can be strongly affected by spatial and temporal variations in ambient current fields, which can induce shoaling, refractive and focussing/defocussing and breaking effects in analogy to variations in bathymetry. In turn, waves can modify the current distribution, determining the shape of river plume by affecting its centerline velocity, lateral spreading and plume thickness. As part of the ongoing study of highly concentrated sediment transport in plumes developed by small mountainous rivers, we formulate a general framework for describing the interaction of small amplitude surface gravity waves and relatively strongly sheared currents in finite depth water, where shear can exist in both the vertical and horizontal. In contrast to existing formulations, where the wave at leading order responds to a depth-uniform current field, the present formulation allows for an arbitrary degree of vertical shear, leading to a description of the vertical structure of waves in terms of solutions to a Rayleigh stability equation. The resulting formulation leads to a conservation law for wave action, and forcing terms for the description of the mean flow formulated using the Craik-Leibovich vortex formalism. A special case for strong current with linear shear is discussed. Results are provided to compare with the existing formulations. Applications to numerical model is left for further development. [Preview Abstract] |
Sunday, November 20, 2011 4:53PM - 5:06PM |
E3.00002: Shallow Water Model Using Adaptive Wavelet Collocation Method Shanon Reckinger, Oleg V. Vasilyev, Baylor Fox-Kemper The adaptive wavelet collocation method is applied to the shallow water model. This method solves the equations on temporally and spatially varying meshes, which allows higher effective resolution to be obtained with less computational cost. The grid adaptation is achieved by using the ability of wavelet multiresolution analysis to identify and isolate localized dynamically dominant flow structures, e.g., vortices, and to track these structures on adaptive computational meshes. In addition to studying how the shallow water model behaves on non-uniform, time varying grids, this work also sets out to improve the representation of continental topology through an extension of the Brinkman penalization method. This numerical technique works by altering the governing equations in such a way that no slip boundary conditions are enforced. When coupled with the adaptive wavelet collocation method, the flow near a complex boundary can be well defined. In addition the bathymetry is represented in wavelet compressed form, thus allowing active control of the roughness, length scales, etc., plus efficient representation of the detailed bathymetry, with automatic refinement in regions of active interaction of bathymetry and flow structures. The applications presented here include wind-driven flow in a square basin, North Atlantic circulation, and a tsunami simulation. [Preview Abstract] |
Sunday, November 20, 2011 5:06PM - 5:19PM |
E3.00003: A new triad resonance in two-layer density stratified fluids Mohammad-Reza Alam In a two-layer density stratified fluid it is known, due to Ball (1964), that two oppositely traveling surface waves may form a triad resonance with an interfacial wave. In the case of a real ocean with a relatively weak stratification, the two surface waves have close wavelengths and the resonant interfacial wave has the wavelength of about half of surface waves. Ball (1964) claims ``there are no other interactions" between two surface waves and one interfacial wave. Contrary to this, here we present a new class of triad resonance that obtains between two co-propagating surface waves (with close wavelengths) and a much longer interfacial wave. We present, via theoretical analysis and direct simulation, that for weak stratifications this new class of resonance results in a cascade of (near) resonance interaction that spreads the energy of initial waves to a number of lower and higher frequency waves. The resonance discussed here is in fact more likely to affect the evolution of a spectrum because waves within a typical spectrum are usually co-propagating than oppositely traveling. The significance of the resonance studied here is, particularly, more highlighted in the littoral zones, where the spectrum refracts toward a uni-directional wave train. [Preview Abstract] |
Sunday, November 20, 2011 5:19PM - 5:32PM |
E3.00004: Numerical study of non-breaking and breaking surface waves over viscous mud flow Yi Hu, Xin Guo, Yi Liu, Lian Shen, Robert A. Dalrymple It is well known that water surface waves can be drastically damped over a muddy seabed. To understand the mechanism of wave-mud interaction, we perform DNS of the NS equations for wave propagation over mud, which is modeled as Newtonian fluid with larger density and much higher viscosity than water. A level set method is used to capture water surface and water-mud interface. From the simulations, the velocity and vorticity and the energy budget terms in water and mud are analyzed. The energy flux from water to mud and the dissipation in mud are found to play an important role in the energy budget. For non-breaking waves, despite the wave nonlinearity, the wave dissipation rate is found to be comparable to the predictions of existing theories. For breaking waves, before the impingement of plunging jet on the wave surface and then after about 2.5 wave periods when most of the wave energy is lost, dissipation in mud dominates that in water. During the wave breaking itself, the dissipation rate in water increases sharply and exceeds that in mud. In the presence of mud, the intensity of breaking is reduced compared with the non-mud case. [Preview Abstract] |
Sunday, November 20, 2011 5:32PM - 5:45PM |
E3.00005: Temporal decay of water waves over a mud layer in a small tank Younes Nouri, Robert A. Dalrymple, Khatoon Melick Several field observations have recorded drastic dissipation of water waves traveling over a soft muddy bottom. However, current understanding of mechanisms of interaction of waves and mud layer is still at a preliminary level. Here, the temporal decay in amplitude of standing water waves over a layer of kaolinite mud in a small tank was examined to study role of mud layer thickness, density and rheological properties, as well as initial wave amplitude. An important parameter was found to be the history of the mud prior to the tests. The data set provides a suitable benchmark for verification of theoretical and numerical models of waves-mud interaction. [Preview Abstract] |
Sunday, November 20, 2011 5:45PM - 5:58PM |
E3.00006: Numerical Study of turbulent coherent structures and bubble entrainment under surfzone breaking waves Gangfeng Ma, James Kirby, Fengyan Shi Wave breaking in the surf zone entrains large volumes of bubbles into the water column. These bubbles are involved in intense interactions with mean flow and turbulence, producing a complex two phase bubbly flow field. It is necessary to describe the dynamics of breaking waves as two-phase flow with air bubbles of appropriate size distribution. The present study employ a three- dimensional large eddy simulation coupled with a two-phase bubbly flow model to investigate the detailed interactions between coherent structures and bubble entrainment in a laboratory scale breaking wave. Our results show that the vortical structures under the wave front are characterized by counter-rotating vortices. These vortices are initially carried downward by the downbursts, and then subject to stretching and bending to form obliquely descending eddies. To study the effects of coherent structures on turbulence and momentum transport, we conduct a TKE budget analysis. It is found that the TKE and Reynolds stress transport are closely related to obliquely descending eddies behind wave crest. Using the two-phase bubbly flow model, we are able to simulate the bubble entrainment and transport after wave breaking. Our results support the conclusion that the obliquely descending eddies have great effects on bubble entrainment and downward dispersion. [Preview Abstract] |
Sunday, November 20, 2011 5:58PM - 6:11PM |
E3.00007: Large-wave simulation of spilling breaking and undertow current over constant slope beach Athanassios Dimas, Gerasimos Kolokythas, Aggelos Dimakopoulos The three-dimensional, free-surface flow, developing by the propagation of nonlinear breaking waves over a constant slope bed, is numerically simulated. The main objective is to investigate the effect of spilling breaking on the characteristics of the induced undertow current by performing large-wave simulations (LWS) based on the numerical solution of the Navier-Stokes equations subject to the fully nonlinear free-surface boundary conditions and the appropriate bottom, inflow and outflow boundary conditions. The equations are properly transformed so that the computational domain becomes time-independent. In the present study, the case of incoming waves with wavelength to inflow depth ratio \textit{$\lambda $}/$d\approx $6.6 and wave steepness $H$/\textit{$\lambda $}$\approx $0.025, over bed of slope tan\textit{$\beta $} = 1/35, is investigated. The LWS predicts satisfactorily breaking parameters - height and depth - and wave dissipation in the surf zone, in comparison to experimental data. In the corresponding LES, breaking height and depth are smaller and wave dissipation in the surf zone is weaker. For the undertow current, it is found that it is induced by the breaking process at the free surface, while its strength is controlled by the bed shear stress. Finally, the amplitude of the bed shear stress increases substantially in the breaking zone, becoming up to six times larger than the respective amplitude at the outer region. [Preview Abstract] |
Sunday, November 20, 2011 6:11PM - 6:24PM |
E3.00008: An Experimental Study of Spilling Breakers in the Presence of Wind and Surfactants X. Liu, D. Wang, J. H. Duncan Spilling breaking waves in the presence of light-wind and surfactants are studied experimentally in a wind-wave tank. The breaking waves are mechanically generated with a single wave maker motion that produces a weak spilling breaker in clean water without wind. The crest-profiles of the waves along the center plane of the tank are measured with a cinematic laser-induced fluorescence (LIF) technique. It is found that with a wind speed lower than 2.3 m/s, the wave breaking is initiated with the formation of a bulge-capillary-wave pattern on the forward face of the wave crest. This pattern is dominated by surface tension and is qualitatively similar to the pattern found without wind and surfactants, Duncan et al.\ (1999). The slope of the back face of the wave crest decreases rapidly with increasing wind speed and the geometrical parameters describing the bulge are found to be linearly proportional to the surface wind drift speed. The physics of the effect of surfactants on these parameters is explained by a longitudinal wave theory. [Preview Abstract] |
Sunday, November 20, 2011 6:24PM - 6:37PM |
E3.00009: Evolution of deep-water waves under wind forcing and wave breaking effects: Numerical simulations and experimental assessment Zhigang Tian, Wooyoung Choi The performance of wave breaking and wind forcing models on the evolution of deep-water waves is evaluated with laboratory experiments. In the experiments, non-breaking and breaking wave groups are generated by the dispersive focusing technique and different wind conditions are considered. Surface elevations are measured with high-speed imaging. For numerical studies, an eddy viscosity model is employed to simulate energy dissipation due to wave breaking. Wind forcing is modeled by introducing a pressure distribution over the water surface in the dynamic boundary condition. The models are incorporated into a wave evolution model, which is solved numerically using a pseudo-spectrum method for the evolution of the wind forced breaking wave groups. Comparisons between the experimental and numerical results and discussions of the numerical model performance will be presented. [Preview Abstract] |
Sunday, November 20, 2011 6:37PM - 6:50PM |
E3.00010: Statistics of unidirectional random breaking water-waves Lev Shemer, Anna Sergeeva Quasi-random wave groups were studied experimentally in a 300 m long Large Wave Chanel in Hannover. Multiple realizations of several spectral shapes each having random phases of individual harmonics were excited by a computer-controlled wavemaker. Wave field evolution along the tank was recorded by 28 wave gauges and the variation of waves' statistical parameters with the distance from the wavemaker was analyzed. An attempt was made to identify individual breaking events based on the spectrum variation between consecutive wave gauges. It was concluded that energy decay in the high frequency part of the spectrum can serve as a reliable criterion for breaking localization in each realization. The data processing based on the adopted criterion resulted in constructing separate ensembles of events with and without breaking. Statistical processing of those ensembles enabled to assess the effect of breaking on such wave field characteristics as probability of appearance of extremely steep (rogue, or freak) waves, as well on skewness and kurtosis. [Preview Abstract] |
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