Wave breaking on turbulent energy budget in the ocean surface mixed layer

As an important physical process at the air-sea interface, wave movement and breaking have a significant effect on the ocean surface mixed layer （OSML）. When breaking waves occur at the ocean surface, turbulent kinetic energy （TKE） is input downwards, and a sublayer is formed near the surface and turbulence vertical mixing is intensively enhanced. A one-dimensional ocean model including the Mellor-Yamada level 2.5 turbulence closure equations was employed in our research on variations in turbulent energy budget within OSML. The influence of wave breaking could be introduced into the model by modifying an existing surface boundary condition of the TKE equation and specifying its input. The vertical diffusion and dissipation of TKE were effectively enhanced in the sublayer when wave breaking was considered. Turbulent energy dissipated in the sublayer was about 92.0% of the total depth-integrated dissipated TKE, which is twice higher than that of non-wave breaking. The shear production of TKE decreased by 3.5% because the mean flow fields tended to be uniform due to wave-enhanced turbulent mixing. As a result, a new local equilibrium between diffusion and dissipation of TKE was reached in the wave-enhanced layer. Below the sublayer, the local equilibrium between shear production and dissipation of TKE agreed with the conclusion drawn from the classical law-of-the-wall （Craig and Banner, 1994）.     

Estimates of reynolds stress and TKE production in the seasonally stratified East China Sea

During the two cruises in March and July of 2011, the tidal cycling of turbulent properties and the T/S profiles at the same location in seasonally stratified East China Sea (ECS) were measured synchronously by a bottom-mounted fast sampling ADCP (acoustic Doppler current profiler) and a RBR CTD (RBR-620) profiler. While focusing on the tide-induced and stratification’s impact on mixing, the Reynolds stress and the turbulent kinetic energy (TKE) production rate were calculated using the ‘variance method’. In spring, the features of mixing mainly induced by tides were clear when the water column was well-mixed. Velocity shear and turbulent parameters intensified towards the seabed due to the bottom friction. The components of the velocity shear and the Reynolds stress displayed a dominant semi-diurnal variation related to velocity changes caused by the flood and ebb of M₂ tide. Stratification occurred in summer, and the water column showed a strongly stratified pycnocline with a characteristic squared buoyancy frequency of N² ～ (1–6) × 10^?3 s^?2. The components of the velocity shear and the Reynolds stress penetrated upwards very fast from the bottom boundary layer to the whole water column in spring, while in summer they only penetrated to the bottom of the pycnocline with a relatively slow propagation speed. In summer, the TKE production within the pycnocline was comparable with and sometimes larger than that in the well-mixed bottom layer under the pycnocline. Considering the associated high velocity shear, it is speculated that the mixing in the pycnocline is a result of the local velocity shear.     

Effects of Sediment-induced Stratification on Floc Breakup in an Idealized Tidal Estuary： A Numerical Modelling Study

Floc breakup dynamics are studied by a sediment transport numerical model in an idealized tidal estuary that has a constant water depth and rapid flocculation of cohesive sediments. The focus is placed on the effects of boundary layer stratification induced by a bottom nepheloid layer on floc breakup and size distribution in the water column. In a neutrally stratified estuary, the floc size distribution follows a parabolic function with maximum values at the surface and bottom. The sediment-induced stratification in the bottom boundary layer increases the median floc sizes. Furthermore, sediment-voided convection caused by the settling lutocline generates significant turbulent kinetic energy dissipation and reduces floc size at the depth where the convective mixing happens. Below that depth, a weak local maxima in the floc size is predicted due to presence of the lutocline. The effect of sediment-stratified bottom boundary layer on the floc breakup can be consistently approximated by a linear regression between the maximal floc size and flux Richardson number.     

Effects of sediment-induced stratification on floe breakup in an idealized tidal estuary: A numerical modelling study

Floe breakup dynamics are studied by a sediment transport numerical model in an idealized tidal estuary that has a constant water depth and rapid flocculation of cohesive sediments. The focus is placed on the effects of boundary layer stratification induced by a bottom nepheloid layer on floe breakup and size distribution in the water column. In a neutrally stratified estuary, the floe size distribution follows a parabolic function with maximum values at the surface and bottom. The sediment-induced stratification in the bottom boundary layer increases the median floe sizes. Furthermore, sediment-voided convection caused by the settling lutocline generates significant turbulent kinetic energy dissipation and reduces floe size at the depth where the convective mixing happens. Below that depth, a weak local maxima in the floe size is predicted due to presence of the lutocline. The effect of sediment-stratified bottom boundary layer on the floe breakup can be consistently approximated by a linear regression between the maximal floe size and flux Richardson number.     

Internal Waves Generated by Tidal Flows over a Triangular Ridge with Critical Slopes

Direct numerical simulations are performed to investigate the generation of internal waves by tide-topography interaction in a lab-scale model. The bottom topography is a triangular ridge with two critical slopes. With increasing tidal forcing, subharmonic instabilities are identified, which cause internal wave beams to become unstable and turbulent. Kinetic energy densities in the upward going beams from the ridge top are stronger than those from the ridge bottom, whereas the reverse is true for the energy flux. This disparity between energy and energy flux is due to the existence of strong pressure disturbances near the ridge bottom. On each side of the critical ridge, there exists an amphidromic point, from which internal wave beams are emitted in opposite directions. The calculated energy conversion rate scales linearly with the square of the forcing amplitude and agrees within 13% of theoretical prediction, even when turbulence occurs. The fraction of radiated baroclinic energy becomes saturated in the range of low excursion parameter considered, which agrees with the behavior in large-scale systems wherein mixing parameterizations must be used. The present work enriches the studies on the generation of internal waves over a critical triangular ridge.     

Convection:a neglected pathway for downward transfer of wind energy in the oceanic mixed layer

Upper-ocean turbulent mixing plays a vital role in mediating air-sea fluxes and determining mixed-layer properties, but its energy source, especially that near the base of the mixed layer, remains unclear. Here we report a potentially significant yet rarely discussed pathway to turbulent mixing in the convective mixed layer. During convection, as surface fluid drops rapidly in the form of convective plumes, intense turbulence kinetic energy(TKE) generated via surface processes such as wave breaking is advected downward, enhancing TKE and mixing through the layer. The related power, when integrated over the global ocean except near the surface where the direct effect of breaking waves dominates, is estimated at O(1)TW, comparable to that required by maintaining the Meridional Overturning Circulation(MOC). The mechanism in question therefore deserves greater research attention, especially in view of the potential significance of its proper representation in climate models.     

The properties of dilute debris flow and hyper-concentrated flow in different flow regimes in open channels

Particle Image Velocimetry(PIV) technique was used to test the analogues of hyperconcentrated flow and dilute debris flow in an open flume. Flow fields, velocity profiles and turbulent parameters were obtained under different conditions. Results show that the flow regime depends on coarse grain concentration. Slurry with high fine grain concentration but lacking of coarse grains behaves as a laminar flow. Dilute debris flows containing coarse grains are generally turbulent flows. Streamlines are parallel and velocity values are large in laminar flows. However, in turbulent flows the velocity diminishes in line with the intense mixing of liquid and eddies occurring. The velocity profiles of laminar flow accord with the parabolic distribution law. When the flow is in a transitional regime, velocity profiles deviate slightly from the parabolic law. Turbulent flow has an approximately uniform distribution of velocity and turbulent kinetic energy. The ratio of turbulent kinetic energy to the kinetic energy of time-averaged flow is the internal cause determining the flow regime: laminar flow(k/K0.1); transitional flow(0.1 k/K1); and turbulent flow(k/K1). Turbulent kinetic energy firstly increases with increasing coarse grain concentration and then decreases owing to the suppression of turbulence by the high concentration of coarse grains. This variation is also influenced by coarse grain size and channel slope. The results contribute to the modeling of debris flow and hyperconcentrated flow.     

Energy dissipation through wind-generated breaking waves

Wave breaking is an important process that controls turbulence properties and fluxes of heat and mass in the upper oceanic layer.A model is described for energy dissipation per unit area at the ocean surface attributed to wind-generated breaking waves,in terms of ratio of energy dissipation to energy input,windgenerated wave spectrum,and wave growth rate.Also advanced is a vertical distribution model of turbulent kinetic energy,based on an exponential distribution method.The result shows that energy dissipation rate depends heavily on wind speed and sea state.Our results agree well with predictions of previous works.     

Density Perturbation and Energy Flux of Internal Waves from Velocity Data

Internal waves play a crucial role in ocean mixing, and density perturbation and energy flux are essential quantities to investigate the generation and propagation of internal waves. This paper presents a methodology for calculating density perturbation and energy flux of internal waves only using a velocity field that is based on linearized equations for internal waves. The method was tested by numerical simulations of internal waves generated by tidal flowing over a Gaussian topography in a stratified fluid. The density perturbations and energy fluxes determined using our method that only used velocity data agreed with density perturbations and energy fluxes determined by the equation of state based on temperature data. The mean relative error (MRE) and root mean square error (RMSE) between the two methods were lower than 5% and 10% respectively. In addition, an experiment was performed to exam our method using the velocity field measured by Particle Image Velocimetry (PIV), and the setup of the experiment is consistent with the numerical model. The results of the experiments calculated by the methods using PIV data were also generally equal to those of the numerical model.     

Laboratory Experiments on an Internal Solitary Wave over a Triangular Barrier

Laboratory experiments were conducted to investigate the evolution of interfacial internal solitary waves(ISWs) incident on a triangular barrier. ISWs with different amplitudes were generated by gravitational collapse. The ISW energy dissipation and turbulence processes were calculated as waves passed over the triangular barrier. Experimental results showed that ISWs were reflecting back off the triangular barrier, and shoaling ISWs led to wave breaking and mixing when waves propagated over the obstacle. Wave instability created the dissipation of energy as it was transmitted from waves to turbulence. The rate of ISW energy dissipation, the maximum turbulent dissipation, and the buoyancy diffusivity linearly increased with the increase in the incident wave energy.     

Study on surface wave-induced mixing of transport flux residue under typhoon conditions

The transport flux residue of surface waves plays an important role in a variety of ocean phenomena, for example, the change in sea surface temperature(SST) and upper mixed layer profile that were studied in a series of recent papers. In the previous studies, its effect was discussed rigorously and fragmented based on numerical modeling. Here we propose a relatively comprehensive and simplified exposition of the wave transport flux residue, and focus on its influence under typhoon conditions with strong background current. An analogue Reynolds Number is presented for tentative comparison with wave-generated turbulence mixing, especially in the coastal area. Numerical results indicate that both overwhelming dynamical mixing processes can remarkably change the coastal environment, and should not be ignored consciously for further marine hazards assessment.     

Study on numerical simulation and dynamic mechanism of winter-time circulation in the eastern China seas

An MOM2 based 3-dimentional prognostic baroclinic Z-ordinate model was established to study the circulation in eastern China seas, considering the topography, inflow and outflow on the open boundary, wind stress, temperature and salinity exchange on the sea surface. The results were consistent with observation and showed that the Kuroshio intrudes in large scale into the East China Sea continental shelf East China, during which its water is exchanged ceaselessly with outer sea water along Ryukyu Island. The Tsushima Warm Current is derived from several sources, a branch of the Kuroshio, part of the Taiwan Warm Current, and Yellow Sea mixed water coming from the west of Cheju Island. The water from the west of Cheju Island contributes approximately 13% of the Isushima Warm Current total transport through the Korea Strait. The circulation in the Bohai Sea and Yellow Sea is basically cyclonic circulation, and is comprised of coastal currents and the Yellow Sea Warm Current. Besides simulation of the real circulation, numerical experiments were conducted to study the dynamic mechanism. The numerical experiments indicated that wind directly drives the East China Sea and Yellow Sea Coastal Currents, and strengthens the Korea Coastal Current and Yellow Sea Warm Current. In the no wind case, the kinetic energy of the coastal current area and main YSWC area is only 1% of that of the wind case.Numerical experiments also showed that the Tsushima Warm Current is of great importance to the formation of the Korea Coastal Current and Yellow Sea Warm Current.     

Test and evaluation of a moored microstructure recorder

A new moored microstructure recorder （MMR） is designed, developed, tested, and evaluated. The MMR directly measures the high-frequency shear of velocity fluctuations, with which we can estimate the dissipation rate of turbulent kinetic energy. We summarize and discuss methods for estimating the turbulent kinetic energy dissipation rate. Instrument body vibrations contaminate the shear signal in an ocean field experiment, and a compensating correction successfully removes this contamination. In both tank test and ocean field experiment, the dissipation rate measured with the MMR agreed well with that measured using other instruments.     

A quasi single-phase model for debris flows and its comparison with a two-phase model

A depth-averaged quasi single-phase mixture model is proposed for debris flows over inclined bed slopes based on the shallow water hydrosediment-morphodynamic theory with multi grain sizes. The stresses due to fluctuations are incorporated based on analogy to turbulent flows, as estimated using the depth-averaged k-? turbulence model and a modification component. A fully conservative numerical algorithm, using wellbalanced slope limited centred scheme, is deployed to solve the governing equations. The present quasi single-phase model using four closure relationships for the bed shear stresses is evaluated against USGS experimental debris flow and compared with traditional quasi single-phase models and a recent physically enhanced two-phase model. It is found that the present quasi single-phase model performs much better than the traditional models, and is attractive in terms of computational cost while the two-phase model performs even better appreciably.     

The suspended sediment concentration distribution in the Bohai Sea, Yellow Sea and East China Sea

The distribution of the suspended sediment concentration (SSC) in the Bohai Sea, Yellow Sea and East China Sea (BYECS) is studied based on the observed turbidity data and model simulation results. The observed turbidity results show that (i) the highest SSC is found in the coastal areas while in the outer shelf sea areas turbid water is much more difficult to observe, (ii) the surface layer SSC is much lower than the bottom layer SSC and (iii) the winter SSC is higher than the summer SSC. The Regional Ocean Modeling System (ROMS) is used to simulate the SSC distribution in the BYECS. A comparison between the modeled SSC and the observed SSC in the BYECS shows that the modeled SSC can reproduce the principal features of the SSC distribution in the BYECS. The dynamic mechanisms of the sediment erosion and transport processes are studied based on the modeled results. The horizontal distribution of the SSC in the BYECS is mainly determined by the current-wave induced bottom stress and the fine-grain sediment distribution. The current-induced bottom stress is much higher than the wave-induced bottom stress, which means the tidal currents play a more significant role in the sediment resuspension than the wind waves. The vertical mixing strength is studied based on the mixed layer depth and the turbulent kinetic energy distribution in the BYECS. The strong winter time vertical mixing, which is mainly caused by the strong wind stress and surface cooling, leads to high surface layer SSC in winter. High surface layer SSC in summer is restricted in the coastal areas.     

Distribution of vertical turbulent mixing parameter caused by internal tidal waves and solitary waves in the South Yellow Sea

Many observations show that in the Yellow Sea internal tidal waves (ITWs) possess the remarkable characteristics of internal Kelvin wave, and in the South Yellow Sea (SYS) the nonlinear evolution of internal tidal waves is one of the mechanisms producing internal solitary waves (ISWs), which is different from the generation mechanism in the case where the semidiurnal tidal current flows over topographic drops. In this paper, the model of internal Kelvin wave with continuous stratification is given, and an elementary numerical study of nonlinear evolution of ITWs is made for the SYS, using the generalized KdV model (GKdV model for short) for a continuous stratified ocean, in which the different effects of background barotropic ebb and flood currents are considered. Moreover, the parameterization of vertical turbulent mixing caused by ITWs and ISWs in the SYS is studied, using a parameterization scheme which was applied to numerical experiments on the breaking of ISWs by Vlasenko and Hutter in 2002. It is found that the vertical turbulent mixing caused by internal waves is very strong within the upper layer with depth less than about 30m, and the vertical turbulent mixing caused by ISWs is stronger than that by ITWs.     

Study on Hydrography and Small-Scale Process over Zhoushan Sea Area

This paper mainly analyzes the tidal characteristics and small-scale mixing process near Zhoushan Islands. First, the spectral analysis and wavelet analysis are adopted for the measured tide level data and tidal current data from the Zhoushan sea area, which indicate that the main tidal cycle near Hulu Island and Taohua Island is semi-diurnal cycle, the diurnal cycle is subordinate. Both their intensities are changed periodically, meanwhile, the diurnal tide becomes stronger when semi-diurnal tide becomes weak. The intensity of baroclinic tidal current weakens at first and then strengthens from top to bottom. Then, in this paper, the Gregg-Henyey(G-H) parameterization method is adopted to calculate the turbulent kinetic energy dissipation rate based on the measured temperature and tidal current data. The results of which shown that the turbulent kinetic energy dissipation rate around Hulu Island is higher than that around Taohua Island. In most cases, the turbulent kinetic energy dissipation rate during spring tide is larger than that during the neap tide; the turbulent kinetic energy dissipation rate in the surface layer and the bottom layer are higher than that in the intermediate water; the changes of turbulent kinetic energy dissipation rate and tidal current are basically synchronous. The modeled turbulent kinetic energy dissipation rate gets smaller with the increase of the stratification, however, gets larger with the increase of shearing.     

Large eddy simulation of the rotation effect on the ocean turbulence kinetic energy budget in the surface mixed layer

A non-hydrostatic, Boussinesq, and three-dimensional large eddy simulation(LES) model was used to study the impact of the Earth's rotation on turbulence and the redistribution of energy in turbulence kinetic energy(TKE) budget. A set of numerical simulations was conducted,(1) with and without rotation,(2) at different latitudes(10°N, 30°N, 45°N, 60°N, and 80°N),(3) with wave breaking and with Langmuir circulation, and(4) under different wind speeds(5, 10, 20, and 30 m/s). The results show that eddy viscosity decreases when rotation is included, indicating that rotation weakens the turbulence strength. The TKE budget become tight with rotation and the effects of rotation grow with latitude. However, rotation become less important under Langmuir circulation since the transport term is strong in the vertical direction. Finally, simulations were conducted based on field data from the Boundary Layer and Air-Sea Transfer Low Wind(CBLAST-Low) experiment. The results, although more complex, are consistent with the results obtained from earlier simulations using ideal numerical conditions.     

Interaction of Waves, Surface Currents, and Turbulence： the Application of Surface-Following Coordinate Systems

Surface waves comprise an important aspect of the interaction between the atmosphere and the ocean, so a dynamically consistent framework for modelling atmosphere-ocean interaction must take account of surface waves, either implicitly or explicitly. In order to calculate the effect of wind forcing on waves and currents, and vice versa, it is necessary to employ a consistent formula- tion of the energy and momentum balance within the airflow, wave field, and water column. It is very advantageous to apply sur- face-following coordinate systems, whereby the steep gradients in mean flow properties near the air-water interface in the cross-interface direction may be resolved over distances which are much smaller than the height of the waves themselves. We may account for the waves explicitly by employing a numerical spectral wave model, and applying a suitable theory of wave–mean flow interaction. If the mean flow is small compared with the wave phase speed, perturbation expansions of the hydrodynamic equations in a Lagrangian or generalized Lagrangian mean framework are useful: for stronger flows, such as for wind blowing over waves, the presence of critical levels where the mean flow velocity is equal to the wave phase speed necessitates the application of more general types of surface-following coordinate system. The interaction of the flow of air and water and associated differences in temperature and the concentration of various substances (such as gas species) gives rise to a complex boundary-layer structure at a wide range of vertical scales, from the sub-millimetre scales of gaseous diffusion, to several tens of metres for the turbulent Ekman layer. The bal- ance of momentum, heat, and mass is also affected significantly by breaking waves, which act to increase the effective area of the surface for mass transfer, and increase turbulent diffusive fluxes via the conversion of wave energy to turbulent kinetic energy.     

Turbulence and Fossil Turbulence in Oceans and Lakes

Turbulence is defined as an eddy-like state of fluid motion where the inertial-vortex forces of the eddies are larger than any of the other forces that tend to damp the eddies out. Energy cascades of irrotational flows from large scales to small are non-turbulent, even if they supply energy to turbulence. Turbulent flows are rotational and cascade from small scales to large, with feedback. Viscous forces limit the smallest turbulent eddy size to the Kolmogorov scale. In stratified fluids, buoyancy forces limit large vertical overturns to the Ozmidov scale and convert the largest turbulent eddies into a unique class of saturated, non-propagating, internal waves, termed fossil-vorticity-turbulence. These waves have the same energy but different properties and spectral forms than the original turbulence patch. The Gibson (1980, 1986) theory of fossil turbulence applies universal similarity theories of turbulence and turbulent mixing to the vertical evolution of an isolated patch of turbulence in a stratified fluid as its growth is constrained and fossilized by buoyancy forces. Quantitative hydrodynamic-phase-diagrams (HPDs) from the theory are used to classify microstructure patches according to their hydrodynamic states. When analyzed in HPD space, previously published oceanic datasets showed their dominant microstructure patches are fossilized at large scales in all layers. Laboratory and field measurements suggested phytoplankton species with different swimming abilities adjust their growth strategies by pattern recognition of tur-bulence-fossil-turbulence dissipation and persistence times that predict survival-relevant surface layer sea changes. New data collected near a Honolulu waste-water outfall showed the small-to-large evolution of oceanic turbulence microstructure from active to fossil states, and revealed the ability of fossil-density-turbulence patches to absorb, and vertically radiate, internal wave energy, information, and enhanced turbulent-mixing-rates toward the sea surface so that the submerged waste-field could be detected from a space satellite (Bondur and Filatov, 2003).