Effect Of Wave Breaking In Vertical Diffusion Coefficient

Bedload and suspended load contributions to breaker bar morphodynamics

Improving the Turbulence Coupling between High Resolution Numerical Weather Prediction Models and Lagrangian Particle Dispersion Models

We investigate the influences of the diffusion coefficients for heat and salt in the deep ocean upon the stability of the Atlantic thermohaline circulation through a parameter space investigation that employs the GFDL Modular Ocean Model (MOM). The ocean general circulation model is configured to represent an idealized Atlantic basin and steadily (including an annual cycle) forced under the assumption of mixed boundary conditions. The impact on the results of the use of mixed boundary conditions is examined through additional sensitivity experiments to demonstrate that this choice of boundary conditions does not affect the main conclusions. The two primary sets of the experiments that we describe consist of sensitivity analyses for both horizontal and vertical diffusion coefficients; Bryan-Lewis type diffusion coefficient profiles are applied in such a way that one diffusion coefficient profile is varied while the other diffusion coefficient profile is fixed. We are thereby able to demonstrate that the choice of the horizontal diffusion coefficient plays a crucial role in determining the stability of the thermohaline circulation which is such that the thermohaline circulation exhibits very intense oscillations on a multi-millennium timescale when the horizontal diffusion coefficient of the deep ocean is set to a sufficiently small value. We demonstrate that the critical value required to realize an oscillatory solution of the thermohaline circulation lies well within the range of observed large-scale ocean diffusion coefficients, whereas the value of vertical diffusion coefficients affect not the bifurcation structure but the period of the millennial timescale oscillation.

<strong class="journal-contentHeaderColor">Abstract.</strong> Accurate description of the wind energy input into ocean waves is crucial to ocean wave modeling and a physics-based consideration on the effect of wave breaking is absolutely necessary to obtain such an accurate description. This study evaluates the performance of an improved formula recently proposed by Xu and Yu (2020), who took into account not only the effect of breaking but also the effect of air-flow separation on the leeside of steep wave crests in a reasonably consistent way. Numerical results are obtained through coupling an enhanced atmospheric wave boundary layer model with the ocean wave model WaveWatch III (v5.16). The coupled model has been extended to be valid in both deep and shallow waters. Duration-limited waves under controlled normal conditions and storm waves under practical hurricane conditions are studied in details to verify the improved model. Both the representative wave parameters and the parameters characterizing the wave spectrum are discussed. It is shown that the improved source-term package for the wind energy input and the wave energy dissipation leads to more accurate results under all conditions. It performs evidently better than other standard source-term options of ST2, ST4 and ST6 embedded in WaveWatch III. It is also demonstrated that the improvement is particularly important for waves at their early development stage and waves in shallow waters.

Displacements of mechanical waves superposed onto wind waves were measured with a laser displacement gauge in a wind-wave tank. The effects of wave breaking, especially the spilling breaking type, on the wave-variance spectra are investigated. In the absence of wave breaking, the quasi-equilibrium spectrum consists of an f−7/3 subrange in the capillary regime, and its spectral density increases with increasing wind speed. When intense spilling breaking occurs, the water surface is saturated with small-scale features that cause not only an increase in the spectral density but also a reduction in the slope of the spectrum at high frequencies. Velocity components under the water surface were measured with a laser Doppler velocimeter. The energy spectra of the vertical and longitudinal velocity components in breaking waves are practically identical in the frequency range near the dominant wave frequency. At higher frequencies, the spectra generally follow Kolmogorov's −5/3 law. In the intermediate frequency range, we observed a higher spectral density for the vertical velocity component than for its longitudinal counterpart. These results suggest that turbulence energy is transferred from the vertical component to the longitudinal component in breaking waves. The acceleration of the water motion becomes as large as gravitational acceleration when intense wave breaking takes place. The flow field in breaking waves is highly dissipative.

The effect of wave breaking on the wave energy spectral shape is examined. The Stokes wave-breaking criterion is first extended to random waves and a breaking wave model is established in which the elevation of breaking waves is expressed in terms of that of the original ideal waves, which are assumed to be stationary and Gaussian. Based on this model, a simple but approximate expression for the spectrum of breaking waves is derived and applied to the case in which a deep water unidirectional wave train enters a region of adverse current steady in time and uniformly distributed in depth.

A second-order turbulence closure model, similar to Mellor and Yamada's (1974) level-3 model, is implemented. This is used to investigate the role of the different turbulent processes and the resulting dynamical and thermal structures, for oceanic upper layers subjected to a variety of unsteady atmospheric forcings. From the distributions obtained for current and temperature, turbulence levels, the production, transfer and dissipation terms in the turbulent kinetic energy and temperature variance budgets, the physics of the oceanic mixed layer and thermocline can be discussed and comparisons made with the models of Mellor and Durbin (1975), Warn-Varnas and Piacsek (1979) and Kundu (1980) and some experimental data. Most often, shear production and viscous dissipation of turbulent kinetic energy dominate within the mixed layer. Gravitational production or destruction and turbulent diffusion, however, play a crucial role in thermocline evolution. Under strong winds, current shear and turbulence diffusion at the base of the mixed zone control the erosion mechanism, while the effect of surface wave breaking seems rather limited. After a significant wind-speed reduction, turbulence regresses upward, leaving behind quasi-free inertial current oscillations. Surface cooling enhanced turbulence and mixing, whereas solar heating results in a diminished turbulent zone and a diurnal secondary thermocline. The time variability of atmospheric forcings appears as a determinant factor for the oceanic mixed layer.

Water wave breaking and the resulting surf-zone turbulence play a role in sediment transport, wave damping, and mixing processes. The vortex structures associated with wave breaking carry large amount of turbulent momentum and turbulent kinetic energy and therefore have a crucial effect on the safety of vessels and structures located in the surf zone. In this study, turbulent vortical structures under a broken solitary waves is studied using a three-dimensional Smoothed Particle Hydrodynamics (SPH) method. A broken solitary wave is of interest since the generation and evolution of the three-dimensional vortex structures under a broken wave can be isolated from the case of a periodic wave train, which has undertow and residual turbulence induced from previously broken waves. Further, a solitary wave is a first approximation to a tsunami wave. The numerical model predicts water surface evolution very well in comparison with the experimental results of Ting (2006). The numerical results show organized coherent structures trailing the wave and characterized by reversed horseshoe (hairpin) vortices, traveling downward, which appear to be the previously found obliquely descending eddies. These horseshoe coherent structures transport momentum and turbulent kinetic energy downward into the water column and likely have a significant role in bed and beach erosion. Different terms of vorticity equations are studied and it is concluded that vortex stretching and vortex bending play an important role on the generation and evolution of reversed horseshoe structures.

The present paper reports a numerical study of fully developed turbulent flow over a flat plate with a step change from a smooth to a rough surface. The Reynolds number based on momentum thickness for the smooth flow was Reθ=5950. The focus of the study was to investigate the capability of the Reynolds-averaged Navier–Stokes (RANS) equations to predict the internal boundary layer (IBL) created by the flow configuration. The numerical solution used a two-layer k−ε model to implement the effects of surface roughness on the turbulence and mean flow fields via the use of a hydrodynamic roughness length y0. The prediction for the mean velocity field revealed a development zone immediately downstream of the step in which the mean velocity profile included a lower region affected by the surface roughness below and an upper region with the characteristics of the smooth-wall boundary layer above. In this zone, both the turbulence kinetic energy and Reynolds shear stress profiles were characterized by a significant reduction in magnitude in the outer region of the flow that is unaffected by the rough surface. The turbulence kinetic energy profile was used to estimate the thickness of the IBL, and the resulting growth rate closely matched the experimental results. As such, the IBL is a promising test case for assessing the ability of RANS models to predict the discrete roughness configurations often encountered in industrial and environmental applications.

Past studies have shown that there is a wave-enhanced, near-surface mixed-layer in which the dissipation rate is greater than that derived from the “law of the wall”. In this study, turbulence in water columns under wind breaking waves is investigated numerically and analytically. Improved estimations of dissipation rate are parameterized as surface source of turbulent kinetic energy (TKE) for a more accurate modelling of vertical profile of velocity and TKE in the water column. The simulation results have been compared with the experimental results obtained by Cheung and Street (1988) and Kitaigorodskii et al. (1983), with good agreement. The results show that the numerical full model can well simulate the near-surface wave-enhanced layer and suggest that the vertical diffusive coefficients are highly empirical and related to the TKE diffusion, the shear production and the dissipation. Analytical solutions of TKE are also derived for near surface layer and in deep water respectively. Near the surface layer, the dissipation rate is assumed to be balanced by the TKE diffusion to obtain the analytical solution; however, the balance between the dissipation and the shear production is applied at the deep layer. The analytical results in various layers are compared with that of the full numerical model, which confirms that the wave-enhanced layer near the surface is a diffusion-dominated region. The influence of the wave energy factor is also examined, which increases the surface TKE flux with the wave development. Under this region, the water behavior transits to satisfy the classic law of the wall. Below the transition depth, the shear production dominantly balances the dissipation.

Wave transport in the South Australian Basin

Owing to the interactions among the complex terrain, bottom materials, and the complicate hydrodynamics, typhoon waves show special characteristics as big waves appeared at the high water level (HWL) and small waves emerged at low and middle water levels (LWL and MWL) in radial sand ridges (RSR). It is assumed that the mud damping, sandy bed friction and wave breaking effects have a great influence on the typhoon wave propagation in this area. Under the low wave energy, a mud layer will form and transport into the shallow area, thus the mud damping effects dominate at the LWL and the MWL. And high Collins coefficient (c around 1) can be applied to computing the damping effects at the LWL and the MWL. But under the high wave energy, the bottom sediment will be stirred and suspended, and then the damping effects disappear at the HWL. Thus the varying Collins coefficient with the water level method (VCWL) is implemented into the SWAN to model the typhoon wave process in the Lanshayang Channel (LSYC) of the RSR, the observed wave data under “Winnie” (“9711”) typhoon was used as validation. The results show that the typhoon wave in the RSR area is able to be simulated by the VCWL method concisely, and a constant wave breaking coefficient (γ) equaling 0.78 is better for the RSR where wide tidal flats and gentle bed slopes exist.

: The primary focus of this research is to use large-eddy simulation (LES) and large-wave simulation (LWS) to obtain improved physical understanding of wind-wave-ocean interactions, based on which we aim to develop effective models of wind input and whitecapping dissipation for phase-resolving, nonlinear wave-field simulation at large scales. Our ultimate goal is to establish a numerical capability for predicting deterministically large-scale nonlinear wave-field in real marine environments with the presence of significant wind and wave breaking effects.

Waves and currents are essential elements in the design of an artificial surfing reef (ASR). ASRs are primarily designed to optimize the surfing conditions (i.e., increase the surfability of the incoming waves) possibly in combination with the shoreline protection from erosion. The currents generated by waves breaking on the ASR play an important role in the surfability through the wave-current interaction (WCI). Depending on the design, the WCI may negatively affect the surfability by causing the waves to break prematurely due to the current-induced wave steepening. In addition, wave breaking tends to become more irregular due to the temporal variability of the underlying currents. To mitigate the negative effects of wave breaking induced currents on the surfability, three ASR layouts are examined through detailed laboratory experiments. The layouts differ in the alongshore separation distance between two symmetrical reef sides. The ensuing flow circulations are examined in detail with both in situ current meters and video observations of surface drifters. This is done for regular incident waves, bichromatic incident waves, and irregular incident waves, all with equal energy. A data analysis shows that for a given layout the mean flow patterns for regular, bichromatic, and irregular waves are qualitatively similar, with oblique rip currents exiting at either side of the reef and strong flow circulations onshore of the gap in between the two reef sides. Increasing the separation distance leads to a significant reduction of the obliquely exiting rip currents at the outer sides of the reef, but an increase in the flow circulation onshore of the gap. This has a positive effect on the surfability by reducing the negative effects associated with the WCI on the wave breaking, thus, providing longer rides.

This paper reports new experimental results on the mean velocity, excess fractional density, and turbulence structures of conservative and particulate density currents. Experiments were conducted in a laboratory flume consisting of a ramp followed by a horizontal bed. Instantaneous point velocity along the body of a continuous, developed underflow was measured using two 16 MHz Acoustic Doppler Velocity Probes (ADV). Mean velocity, turbulent kinetic energy (TKE) and Reynolds stress components have been derived from the instantaneous velocity data. The normalized mean velocity, Reynolds stress, and TKE profiles have been derived and plotted in different groups corresponding to saline and particulate gravity currents over sloping and horizontal beds. The Reynolds‐averaged velocity shows excellent similarity collapse in these plots, while the Reynolds stress and the TKE profiles display good similarity in the wall‐bounded shear flow region. Vertical profiles of the TKE display two peaks separated by a zone of low turbulence around the position of the maximum velocity. The ratio of the maximum to the layer‐averaged TKE is found to be approximately 1.5. The TKE at the low turbulence zone between the peaks is approximately 50% of the depth‐averaged value.