Turbulent-layer dynamics in homogeneous and stratified fluids

The dynamics of a layer of turbulence excited by a ribbed oscillating grate in homogeneous and stratified fluids is investigated experimentally. The time dependences of the thickness of the region encompassed by turbulence in a homogeneous fluid are obtained. On the basis of a semiempirical turbulence theory, it is shown that the time dependence of the coordinate of the turbulent-front position can be described by a power function. A satisfactory agreement between the experimental and theoretical dependences is obtained. Different regimes of turbulent-layer dynamics in a fluid with salinity stratification are investigated. The results of numerical calculations of turbulent-layer dynamics in a stratified fluid that satisfactorily agree with experimental data are presented. The data obtained can be used to estimate the efficiency of mixing within the oceanic depth.     

A study of SAR remote sensing of internal solitary waves in the north of the South China Sea: Ⅱ. Simulation of SAR signatures of internal solitary waves

A new model developed from the full-spectrum model of Lyzenga and Bennett （ 1988 ） is built up by us preliminarily through considering the impact of the ocean surface mixed layer turbulence on SAR remote sensing of internal solitary waves. In the partial differential equation of the action spectral density of the surface gravity-capillary waves the source function representing the contribution of the turbulence is added besides the usual source function representing the contribution of the wind. The source function is determined by applying the κ - ε model and adopting the Nasmyth spectrum of oceanic turbulence （ Nasmyth, 1970; Oakey, 1982; Fan, 2002） on the basis of the previous simulation results of internal tide transformation obtained in the companion paper （Fan et al. ,2008）. Either under relatively high wind speed, or under low wind speed, our model predicts significant large modulations of radar backscatter at all three bands （ L, C and X bands） for both VV and HH polarization. These results prove that considering the impact of ocean surface mixed layer turbulence on SAR remote sensing of internal solitary waves is reasonable and appropriate for settlement of the well-known problem of contemporary radar imaging models.     

Laboratory experiments for wave motions and turbulence flows in front of a breakwater

In this paper, laboratory data for free surface displacements and velocity fields in front of a caisson breakwater covered with wave-dissipating blocks, together with wave pressures acting on the caisson, are presented and discussed. The core of the breakwater is made of a concrete caisson with a vertical front wall. The caisson is protected by a thick layer of tetrapods and is supported by a rubble mound. The breakwater is placed on the 1/25 impermeable slope. Two types of incident waves are used in the experiments: nonbreaking waves and spilling-type breaking waves. In the breaking wave case, the incident wave breaks offshore before it reaches the breakwater. The velocity data are obtained by using both the Laser Doppler Velocimeter (LDV) and the Electromagnetic Current Meter (EMCM). The raw data are analyzed using a numerical-filtering scheme so that turbulent fluctuations are separated from the phase-dependent wave motions. The vertical profiles of the time-averaged (over a wave period) turbulent velocity components at several vertical cross-sections in front of the breakwater are then analyzed. The spatial variations of the time-averaged turbulence velocity suggest that turbulence is generated inside the protective armor layer and transported into the flow region in front of the breakwater. The wave pressures on the vertical face and on the bottom of the caisson are also reported.     

A study of SAR remote sensing of internal solitary waves in the north of the South China Sea:I.Simulation of internal tide transformation

For settlement of the well-known problem of contemporary radar imaging models,i.e.,the pmblem of a general underestimation of radar signatures of hydrodynamic features over oceanic internal waves and underwater bottom topography in tidal watels at at high radar frequency bands(X-band and C-band),the impact of the ocean surface mixed layer turbulence and the significance of strat-ified oceanic model on SAR remote sensing of internal solitary waves are proposed.In the north of the South China Sea by utilizing seme observed data of background field the nonlinearity coefficient,the dispersion coefficient,the horizontal variability coefficient and the phase speed in the generalized K-dV equation are determined approximately.Through simulations of internal tide transfor-mation the temporal evolution and spatial distribution of the vertical displacement and horizontal velocity of intereal wave field are obtained.The simulation results indicate that the maximum amplitudes of internal solitary waves occur at depth 35 m,but the maximum current speeds take place at depth 20 m in this area of the sea(about 20°30'N,114°E)in August.It was noticed that considering the effects of flood current and ebb current respectively is appropriate to investigate influence of the background shear flow on coefficients of the K-dV equation.The obtained results provide the possibility for the simulation of SAR signatures of inter-nal solitary waves under considering the impact of ocean surface mixed layer turbulence in the companion paper.     

Large eddy simulation of breaking waves

A numerical model is used to simulate wave breaking, the large scale water motions and turbulence induced by the breaking process. The model consists of a free surface model using the surface markers method combined with a three-dimensional model that solves the flow equations. The turbulence is described by large eddy simulation where the larger turbulent features are simulated by solving the flow equations, and the small scale turbulence that is not resolved by the flow model is represented by a sub-grid model. A simple Smagorinsky sub-grid model has been used for the present simulations. The incoming waves are specified by a flux boundary condition. The waves are approaching in the shore-normal direction and are breaking on a plane, constant slope beach. The first few wave periods are simulated by a two-dimensional model in the vertical plane normal to the beach line. The model describes the steepening and the overturning of the wave. At a given instant, the model domain is extended to three dimensions, and the two-dimensional flow field develops spontaneously three-dimensional flow features with turbulent eddies. After a few wave periods, stationary (periodic) conditions are achieved. The surface is still specified to be uniform in the transverse (alongshore) direction, and it is only the flow field that is three-dimensional.The turbulent structures are investigated under different breaker types, spilling, weak plungers and strong plungers. The model is able to reproduce complicated flow phenomena such as obliquely descending eddies. The turbulent kinetic energy is found by averaging over the transverse direction. In spilling breakers, the turbulence is generated in a series of eddies in the shear layer under the surface roller. After the passage of the roller the turbulence spreads downwards. In the strong plunging breaker, the turbulence originates to a large degree from the topologically generated vorticity. The turbulence generated at the plunge point is almost immediately distributed over the entire water depth by large organised vortices. Away from the bed, the length scale of the turbulence (the characteristic size of the eddies resolved by the model) is similar in the horizontal and the vertical direction. It is found to be of the order one half of the water depth.     

Simulation of the ocean surface mixed layer under the wave breaking

A one-dimensional mixed-layer model, including a Mellor-Yamada level 2.5 turbulence closure scheme, was implemented to investigate the dynamical and thermal structures of the ocean surface mixed layer in the northern South China Sea. The turbulent kinetic energy released through wave breaking was incorporated into the model as a source of energy at the ocean surface, and the influence of the breaking waves on the mixed layer was studied. The numerical simulations show that the simulated SST is overestimated in summer without the breaking waves. However, the cooler SST is simulated when the effect of the breaking waves is considered, the corresponding discrepancy with the observed data decreases up to 20% and the MLD calculated averagely deepens 3.8 m. Owing to the wave-enhanced turbulence mixing in the summertime, the stratification at the bottom of the mixed layer was modified and the temperature gradient spread throughout the whole thermocline compared with the concentrated distribution without wave breaking.     

Laboratory investigation of damping of gravity-capillary waves on the surface of turbulized liquid

Investigation of damping of gravity-capillary waves (GCWs) in the presence of turbulence is a classical hydrodynamic problem which has important geophysical applications, one of which is related with the problem of forming a radar and optical image of a ship wake on wavy water surface. In this work a new method for the laboratory study of surface wave damping in turbulized liquid is described and the results are presented. The damping of standing GCWs by turbulence on the water surface in a tank mounted on a vibration table is studied. GCWs and turbulence are excited using a two-frequency mode of vibration table oscillations. A high-frequency small amplitude signal is used for parametric GCW excitation; a low-frequency large amplitude signal is used for generating turbulence due to water flowing through a fixed perforated grid submerged into the tank. The coefficient of GCW damping is determined by measured threshold of parametric excitation of the waves; turbulence characteristics are determined by the PIV and PTV techniques. Dependences of GCW damping coefficients on their frequency at different turbulence intensities are obtained, estimates for turbulent viscosity are presented, and a comparison with empirical models proposed earlier is performed.     

A study of SAR remote sensing of internal solitary waves in the north of the South China Sea: Ⅰ. Simulation of internal tide transformation

For settlement of the well-known problem of contemporary radar imaging models, i. e. , the problem of a general underestimation of radar signatures of hydrodynamic features over oceanic internal waves and underwater bottom topography in tidal waters at high radar frequency bands （ X-band and C-band）, the impact of the ocean surface mixed layer turbulence and the significance of strat- ified oceanic model on SAR remote sensing of internal solitary waves are proposed. In the north of the South China Sea by utilizing some observed data of background field the nonlinearity coefficient, the dispersion coefficient, the horizontal variability coefficient and the phase speed in the generalized K-dV equation are determined approximately. Through simulations of internal tide transfor- mation the temporal evolution and spatial distribution of the vertical displacement and horizontal velocity of internal wave field are obtained. The simulation results indicate that the maximum amplitudes of internal solitary waves occur at depth 35 m, but the maximum current speeds take place at depth 20 m in this area of the sea （about 20°30＇N, 114°E） in August. It was noticed that considering the effects of flood current and ebb current respectively is appropriate to investigate influence of the background shear flow on coefficients of the K-dV equation. The obtained results provide the possibility for the simulation of SAR signatures of internal solitary waves under considering the impact of ocean surface mixed layer turbulence in the companion paper.     

Observation of wave-enhanced turbulence in the near-surface layer of the ocean during TOGA COARE

Dissipation rate statistics in the near-surface layer of the ocean were obtained during the month-long COARE Enhanced Monitoring cruise with a microstructure sensor system mounted on the bow of the research vessel. The vibration contamination was cancelled with the Wiener filter. The experimental technique provides an effective separation between surface waves and turbulence, using the difference in spatial scales of the energy-containing surface waves and small-scale turbulence. The data are interpreted in the coordinate system fixed to the ocean surface. Under moderate and high wind-speed conditions, we observed the average dissipation rate of the turbulent kinetic energy in the upper few meters of the ocean to be 3–20 times larger than the logarithmic layer prediction. The Craig and Banner (J. Phys. Oceanogr. 24 (1994) 2546) model of wave-enhanced turbulence with the surface roughness length from the water side z₀ parameterized according to the Terray et al. (J. Phys. Oceanogr. 26 (1996) 792) formula z₀=cH_s provides a reasonable fit to the experimental dissipation profile, where z is the depth (defined here as the distance to the ocean surface), c≈0.6, and H_s is the significant wave height. In the wave-stirred layer, however, the average dissipation profile deviates from the model (supposedly because of extensive removing of the bubble-disturbed areas close to the ocean surface). Though the scatter of individual experimental dissipation rates (10-min averages) is significant, their statistics are consistent with the Kolmogorov's concept of intermittent turbulence and with previous studies of turbulence in the upper ocean mixed layer.     

The energy cycle of wind waves on the sea surface

The problems of wind-induced waves on the sea surface are considered. To this end, the empirical fetch laws that determine variations in the basic periods and heights of waves in relation to their fetch are used. The relation between the fetch and the physical time is found, as are the dependences of the basic characteristics of waves on the time of wind forcing. It is found that about 5% of wind energy dissipated in the near-water air layer contributes to the growth of wave heights, i.e. wave energy, although this quantity depends on the age of waves and the exponent in the fetch laws. With consideration for estimates of the probability distribution functions for the wind over the world ocean [11], it is found that the rate of wind-energy dissipation in the near-water air layer is on the order of 1 W/m². The calculations of wind waves [19] for the world ocean for 2007 have made it possible to assess the mean characteristics of the cycle of wave development and their seasonal variations. An analysis of these calculations [19] shows that about 20% of wind energy is transferred to the water surface. The remaining amount (80%) of wind energy is spent on the generation of turbulence in the near-water air layer. About 2%, i.e., one tenth of the energy transferred to water, is spent on turbulence generation due to the instability of the vertical velocity profile of the Stokes drift current and on energy dissipation in the surf zones. Of the remaining 18%, 5% is spent directly on wave growth and 13% is spent on the generation of turbulence during wave breaking and on a small-scale spectral region. These annually and globally mean estimates have a seasonal cycle with an amplitude on the order of 20% in absolute values but with a smaller amplitude in relative values. According to [19] and to the results of this study, the annually mean height of waves is estimated as 2.7 m and their age is estimated as 1.17.     

Dynamics of surf-zone turbulence in a strong plunging breaker

The characteristics of turbulence created by a plunging breaker on a 1 on 35 plane slope have been studied experimentally in a two-dimensional wave tank. The experiments involved detailed measurements of fluid velocities below trough level and water surface elevations in the surf zone using a fibre-optic laser-Doppler anemometer and a capacitance wave gage. The dynamical role of turbulence is examined making use of the transport equation for turbulent kinetic energy (the k-equation). The results show that turbulence under a plunging breaker is dominated by large-scale motions and has certain unique features that are associated with its wave condition. It was found that the nature of turbulence transport in the inner surf zone depends on a particular wave condition and it is not similar for different types of breakers. Turbulent kinetic energy is transported landward under a plunging breaker and dissipated within one wave cycle. This is different from spilling breakers where turbulent kinetic energy is transported seaward and the dissipation rate is much slower. The analysis of the k-equation shows that advective and diffusive transport of turbulence play a major role in the distribution of turbulence under a plunging breaker, while production and dissipation are not in local equilibrium but are of the same order of magnitude. Based on certain approximate analytical approaches and experimental measurements it is shown that turbulence production and viscous dissipation below trough level amount to only a small portion of the wave energy loss caused by wave breaking. It is suggested that the onshore sediment transport produced by swell waves may be tied in a direct way to the unique characteristics of turbulent flows in these waves.     

A linear model for the structure of turbulence beneath surface water waves

The structure of turbulence in the ocean surface layer is investigated using a simplified semi-analytical model based on rapid-distortion theory. In this model, which is linear with respect to the turbulence, the flow comprises a mean Eulerian shear current, the Stokes drift of an irrotational surface wave, which accounts for the irreversible effect of the waves on the turbulence, and the turbulence itself, whose time evolution is calculated. By analysing the equations of motion used in the model, which are linearised versions of the Craik–Leibovich equations containing a ‘vortex force’, it is found that a flow including mean shear and a Stokes drift is formally equivalent to a flow including mean shear and rotation. In particular, Craik and Leibovich’s condition for the linear instability of the first kind of flow is equivalent to Bradshaw’s condition for the linear instability of the second. However, the present study goes beyond linear stability analyses by considering flow disturbances of finite amplitude, which allows calculating turbulence statistics and addressing cases where the linear stability is neutral. Results from the model show that the turbulence displays a structure with a continuous variation of the anisotropy and elongation, ranging from streaky structures, for distortion by shear only, to streamwise vortices resembling Langmuir circulations, for distortion by Stokes drift only. The TKE grows faster for distortion by a shear and a Stokes drift gradient with the same sign (a situation relevant to wind waves), but the turbulence is more isotropic in that case (which is linearly unstable to Langmuir circulations).     

The Effect of Internal Gravity Waves on Fluctuations in Meteorological Parameters of the Atmospheric Boundary Layer

Variations in the intensity of turbulence during wave activity in the stable atmospheric boundary layer over a homogeneous steppe surface have been analyzed. Eight wave activity episodes recorded with a Doppler sodar in August 2015 at the Tsimlyansk Scientific Station of the Obukhov Institute of Atmospheric Physics have been studied. These episodes include seven trains of Kelvin–Helmholtz waves and one train of buoyancy waves. Variations in the rms deviation of the vertical wind-velocity component, the temperature structure parameter, and vertical heat and momentum fluxes have been estimated for each episode of wave activity. It has been found that Kelvin–Helmholtz waves slightly affect the intensity of turbulence, while buoyancy waves cause the temperature structure parameter and the vertical fluxes to increase by more than an order of magnitude.     

The wind-field structure in a stably stratified atmospheric boundary layer over a rough surface

Both wind turning with height and ageostrophic flow in a stably stratified atmospheric boundary layer are analyzed using a three-parameter turbulence model. For a quasi-steady state of the boundary layer, the cross-isobaric flow is determined only by turbulent stress at the surface in the direction of geostrophic wind. The “operative” prediction models, in which the first-order turbulence closure schemes are used, tend to overestimate the boundary-layer depth and underestimate the angle between the surface and geostrophic winds when compared to “research” models (schemes of high-level turbulence closure). The true value of the angle between the surface and geostrophic winds is significant for the presentation of a large-scale flow. A nocturnal low-level jet is a mesoscale phenomenon reflected in data obtained from measurements in a stably stratified atmospheric boundary layer. It is found that such jets are of great importance in transporting humidity, momentum, and air pollution. In this study, the difference between jet flows over a homogeneous underlying surface and over a spatially localized large-scale aerodynamic roughness is shown.     

Transfer function of the differential wave gauge

The transfer function of a differential wave slope meter having the form of a two-element resonance array is determined. The measured spectrum depends on the coherence of the wave field and on the differential wave gauge's measuring base. Theoretical calculations of the transfer function are supported by experimentally derived data. Some recommendations are suggested on how to conduct measurements in the field and under laboratory conditions. Measurement accuracies are compared and limits of applicability are defined for a method of measuring sea surface slope by means of the differential wavemeter. The results presented may be effectively used to perform measurements of surface and internal waves, turbulence, etc.Translated by V. Puchkin.     

Mixing processes relevant to phytoplankton dynamics in lakes

Active turbulence in lakes is confined to the surface mixed layer, to boundary layers on the lake sides and bottom, and to turbulent patches in the interior. The density stratification present in most lakes fundamentally alters the pathways connecting external mechanical energy inputs, for example by wind, with its ultimate fate as dissipation to heat; the density stratification supports internal waves and intrusions that distribute the input energy throughout the lake. Intrusions may be viewed as internal waves with zero horizontal wavenumber and are formed each time localised mixing occurs in a stratified fluid. Intrusions are also formed in the epilimnion by differential heating or cooling and by differential deepening. The fraction of lake volume below the diurnal mixed layer that is subject to active turbulence is very small, probably of the order of 1% or less in small to medium‐sized lakes. By contrast, in the surface mixed layer, turbulence is less intermittent and maintains phytoplankton in suspension and controls their exposure to the underwater solar flux. Nutrient transport to individual cells depends not only on the cell Reynolds number but also on the Peclet number, which, if large, implies enhanced mass transfer above purely diffusive values.     

Large Eddy Simulation for Plunge Breaker and Sediment Suspension

Breaking waves are a powerful agent for generating turbulence that plays an important role in many fluid dynamical processes, particularly in the mixing of materials. Breaking waves can dislodge sediment and throw it into suspension, which will then be carried by wave-induced steady current and tidal flow. In order to investigate sediment suspension by breaking waves, a numerical model based on large-eddy-simulation (LES) is developed. This numerical model can be used to simulate wave breaking and sediment suspension. The model consists of a free-surface model using the surface marker method combined with a two-dimensional model that solves the flow equations. The turbulence and the turbulent diffusion are described by a large-eddy-simulation (LES) method where the large turbulence features are simulated by solving the flow equations, and a subgrid model represents the small-scale turbulence that is not resolved by the flow model. A dynamic eddy viscosity subgrid scale stress model has been used for the     

Turbulent structure in water under laboratory wind waves

The structure of the turbulent boundary layer underneath laboratory wind waves was studied by using a combination of a high-sensitivity thermometer array with a two-component sonic flowmeter. The temperature fluctuations are used to detect movements of water parcels, with temperature as a passive quantity. The turbulence energy was dominant in the frequency range (0.01 0.1 Hz), which was much smaller than the wind-wave frequency (2 5 Hz), and in which the turbulence was anisotropic. There was a frequency range (0.2 2 Hz for velocity, 0.2 5 Hz for temperature fluctuation) where the turbulence was isotropic and had a –5/3 slope in the energy spectrum. These points are the same as those in previous works. However, by analyses of the time series by using a variable-interval time-averaging technique (VITA), it has been found that conspicuous events in this main turbulence energy band are the downward bursting from the vicinity of the water surface. Thus the structure of the water layer underneath the wind waves has characters which are similar to the familiar turbulent boundary layer over a rough solid wall, as already conceived. It has been found that, at the same time, the turbulence energy can be related to quantities of the wind waves (the root mean squared water level fluctuation and the wave peak frequency), for different wind and wave conditions. That is, the turbulence underneath the wind waves develops under a close coupling with the wind waves.     

Simulation of additive transport from the land surface on the basis of experimental data on heat transfer in the atmospheric surface layer

A method is proposed to study the transport of a passive additive in the atmospheric surface layer with the use of the atmospheric transfer function. This method makes it possible to estimate the spatial distribution of the concentration of a passive additive in the atmospheric surface layer from the additive’s surface source without experimentally determining the vertical profile of the transport coefficient or without resorting to various hypotheses for the character of its behavior. The transfer function, which contains the information on the wind-field structure, can be obtained from simple one-point measurements of surface-and air-temperature fluctuations and from subsequent spectral processing of the data. The effects of the wind-velocity profile and turbulence on the spatial distribution of additive concentration are assessed. This method allows one to simplify experiments during development and verification of the models of atmospheric diffusion. This method may also be useful in emergency situations to predict the propagation of hazardous additives.     

Observational and numerical modeling methods for quantifying coastal ocean turbulence and mixing

In this review paper, state-of-the-art observational and numerical modeling methods for small scale turbulence and mixing with applications to coastal oceans are presented in one context. Unresolved dynamics and remaining problems of field observations and numerical simulations are reviewed on the basis of the approach that modern process-oriented studies should be based on both observations and models. First of all, the basic dynamics of surface and bottom boundary layers as well as intermediate stratified regimes including the interaction of turbulence and internal waves are briefly discussed. Then, an overview is given on just established or recently emerging mechanical, acoustic and optical observational techniques. Microstructure shear probes although developed already in the 1970s have only recently become reliable commercial products. Specifically under surface waves turbulence measurements are difficult due to the necessary decomposition of waves and turbulence. The methods to apply Acoustic Doppler Current Profilers (ADCPs) for estimations of Reynolds stresses, turbulence kinetic energy and dissipation rates are under further development. Finally, applications of well-established turbulence resolving particle image velocimetry (PIV) to the dynamics of the bottom boundary layer are presented. As counterpart to the field methods the state-of-the-art in numerical modeling in coastal seas is presented. This includes the application of the Large Eddy Simulation (LES) method to shallow water Langmuir Circulation (LC) and to stratified flow over a topographic obstacle. Furthermore, statistical turbulence closure methods as well as empirical turbulence parameterizations and their applicability to coastal ocean turbulence and mixing are discussed. Specific problems related to the combined wave-current bottom boundary layer are discussed. Finally, two coastal modeling sensitivity studies are presented as applications, a two-dimensional study of upwelling and downwelling and a three-dimensional study for a marginal sea scenario (Baltic Sea). It is concluded that the discussed methods need further refinements specifically to account for the complex dynamics associated with the presence of surface and internal waves.