Near-surface flow structure over wind-generated water waves,part I: wave-induced flow characteristics

We report on an experimental study conducted to investigate the influence of small-scale wind waves on the airflow structure in the immediate vicinity of the air–water interface. PIV technique was used to measure the two-dimensional velocity fields at wind speeds of 3.7 and 4.4 m?s^?1 and at a fetch of 2.1 m. The flow structure was analyzed as a function of wave phase. In the near-surface region, significant variations were observed in the flow structure over the waveform. The phase-averaged profiles of velocity, vorticity, and Reynolds stress showed different behavior on the windward and leeward sides of the wave in the near-surface region. The influence of wave-induced velocity was restricted within a distance of three significant wave heights from the surface, which also showed opposite trends on the windward and leeward sides of the crest. The results also show that the turbulent Reynolds stress mainly supports downward momentum transfer whereas the wave-induced Reynolds stress is responsible for the upward momentum transfer from wave to wind. In the immediate vicinity of the air–water interface, the momentum is transferred from waves to wind along the windward side, whereas, the momentum transfer is from wind to waves along the leeward side.     

Airside velocity measurements over the wind-sheared water surface using particle image velocimetry

An experimental investigation of the airflow structure in the near surface region over the wind-sheared air–water interface is reported. The two-dimensional velocity fields in a plane perpendicular to the water surface were measured using particle image velocimetry (PIV) technique over a wind speed range from 1.5 to 4.4 m s⁻¹. The results show a reduction in the mean velocity magnitudes and the tangential stresses when gravity waves appear on the surface. An enhanced vorticity layer was observed immediately above the water surface that extended to a height of approximately 2 cm. The vorticity was enhanced by an order of magnitude, and the energy dissipation rate was enhanced by a factor of 7 in this layer at all wind speeds. The vertical profiles of Reynolds stress, energy production, and dissipation indicate the contribution of surface waves in the enhanced transfer of momentum and energy between the two fluids. The results in this study show that the flow dynamics in a layer immediately adjacent to the water surface whose thickness is of the order of the significant wave height is significantly different from that at greater heights. Thus, it is concluded that the quantitative investigation of the flow in the immediate vicinity of the interface is vital for an improved understanding of the heat, mass, and momentum exchange between air and water. The present study demonstrates that PIV is an effective technique to accurately measure the velocity fields in this region.     

A three-dimensional surface wave–ocean circulation coupled model and its initial testing

A theoretical framework to include the influences of nonbreaking surface waves in ocean general circulation models is established based on Reynolds stresses and fluxes terms derived from surface wave-induced fluctuation. An expression for the wave-induced viscosity and diffusivity as a function of the wave number spectrum is derived for infinite and finite water depths; this derivation allows the coupling of ocean circulation models with a wave number spectrum numerical model. In the case of monochromatic surface wave, the wave-induced viscosity and diffusivity are functions of the Stokes drift. The influence of the wave-induced mixing scheme on global ocean circulation models was tested with the Princeton Ocean Model, indicating significant improvement in upper ocean thermal structure and mixed layer depth compared with mixing obtained by the Mellor–Yamada scheme without the wave influence. For example, the model–observation correlation coefficient of the upper 100-m temperature along 35° N increases from 0.68 without wave influence to 0.93 with wave influence. The wave-induced Reynolds stress can reach up to about 5% of the wind stress in high latitudes, and drive 2–3 Sv transport in the global ocean in the form of mesoscale eddies with diameter of 500–1,000 km. The surface wave-induced mixing is more pronounced in middle and high latitudes during the summer in the Northern Hemisphere and in middle latitudes in the Southern Hemisphere.     

Measurements of Reynolds stress in a wind-driven lagoonal estuary

Acoustic Doppler current profilers (ADCPs) have been used to measure Reynolds stresses in tidally dominated environments where wave action was minimal. In this paper, we examine observations from a microtidal estuary where the effects of wind stress and surface waves dominate the velocity variance. Reynolds stress measurements in this setting require a technique for addressing surface gravity wave contamination. We present here a method of reducing the effect of wave motion on Reynolds stresses by subtracting coincident observations along the axis of the ADCP beam. Linear wave theory is used to account for the attenuation of wave orbital velocities with depth. Using this method, Reynolds stress values are brought in line with those predicted by drag laws at the surface and bottom. The apparent Reynolds stress that is removed by the along-axis subtraction is shown to be largely due to the interaction of a slight tilt (1°) in the ADCP and the wave orbital velocity. During periods of stronger wind and waves, there is evidence of enhanced near-surface turbulence and momentum flux, presumably due to breaking waves. During these events, our calculated Reynolds stress magnitudes still appear reasonable, although the directions are suspect. We develop a diagnostic technique that clearly demarcates this region when it occurs. Coincident density profile measurements are used with the ADCP data to compute gradient Richardson numbers throughout the water column. Enhanced Reynolds stresses appear to correspond to Richardson numbers less than one. Responsible editor: Alejandro Souza     

Observations of Reynolds Stresses in wind waves

Summary Data are presented concerning Reynolds Stresses in wind waves obtained from time series records of horizontal and vertical velocity components of motion beneath the ocean free surface. The stresses, of the order of 25 dyne cm^–2, are generally positive indicating horizontal momentum transfer downward through the dynamic wind wave regime. The magnitude of the observed stress increases with wind speed and sea state. The co-spectra show strong negative peaks which appear at the ambient wave frequencies and indicate that the correlations or eddy stresses of the gross wave motions are responsible for the momentum flux. This is a corroboration of results reported previously by the writer in this journal.     

Charnock dynamics: a model for the velocity structure in the wave boundary layer of the air–sea interface

We present a unified model of the air–sea boundary layer, which takes account of the air–sea momentum exchange across the sea surface. The recognition of the importance of the velocity shears in the water (which comprise a frictional shear and the Stokes shear due to the wave motion) in determining the sea surface roughness is a distinctive feature of the analysis, which leads to a prediction of the Charnock constant (α) in terms of two independent parameters, namely the wave age and the ratio of the Stokes shear to the Eulerian shear in the water. This expression is used to interpret the large observational variability of the Charnock constant. The 10-m drag coefficient can also be expressed using similar reasoning, and the introduction of a relation in which the ratio of the frictional shear in the water to the frictional shear in the air decreases with the friction velocity yields predictive relations for the variation of the 10-m drag coefficient at very high wind speeds both in the open ocean and in wind–wave tanks. The physical interpretation of this relation is that the production of spray essentially returns momentum from the ocean to the atmosphere, and this process becomes progressively more important as the wind speed increases.     

On the variability of the Charnock constant and the functional dependence of the drag coefficient on wind speed

A model for the air–sea interface, based on the coupled pair of similarity relations for “aerodynamically” rough flow in both fluids, is presented, which is applied to fetch-limited and high wind speed conditions which occur, for example, in hurricanes. It is shown that the specification of the maximum 10-m drag coefficient and the 10-m wind speed and the peak wave speed at which it occurs are sufficient to uniquely determine the drag law, which asymptotes at low wind speeds to a Charnock constant similar to that for the fully developed wind wave sea and is almost independent of the peak wave speed at the maximum in drag coefficient. A feature of the drag law is that it is of Charnock form, almost independent of the wave age, consistent with the transfer of momentum to the wave spectrum being due to the smaller rather than the dominant wavelengths. The analysis is also applied to a variable sea state in which either the surface wind or the surface Stokes drift vary, but the peak wave speed is kept constant. The corresponding variability in the Charnock constant is in general accord with observations.     

Interaction of waves,currents and tides,and wave-energy impact on the beach area of Sylt Island

Erosion due to waves is an important and actual problem for most coastal areas of the North Sea. The objective of this study was to estimate the impact of wave action on the coastline of Sylt Island. From a 2-year time series (November 1999 to October 2001) of hydrological and wave parameters generated with a coupled wave–current modelling system, a period comprising storm ‘Anatol’ (3–4 December 1999) is used to investigate the effects of waves on currents and water levels and the input of wave energy into the coastline. The wave-induced stress causes an increase of the current velocity of 1 m/s over sand and an additional drift along the coast of about 20 cm/s. This produces a water level increase of more than 20 cm in parts of the tidal basin. The model system also calculates the wave energy input into the coastline. Scenario runs for December 1999 with a water level increase of 50 cm and wind velocity increased by 10% show that the input of the wave energy into the west coast of Sylt Island increases by 30% compared to present conditions. With regard to the forecasted near-future (Woth et al., Ocean Dyn 56:3–15, 2006) increase of strong storm surges, the scenario results indicate an increased risk of coastal erosion in the surf zone of Sylt Island.     

LES of turbulent surface shear stress and pressure-gradient-driven flow on shallow continental shelves

Turbulent shear flows on shallow continental shelves (here shallow means that the interaction with the solid, no-slip bottom is important) are of great importance because tide- and wind-driven flows on the shelf are drivers of the transfer of momentum, heat, and mass (gas) across the air–sea interface. These turbulent flows play an important role because vertical mixing and current are vectors for the transport of sediment and bioactive material on continental shelves. Understanding the dynamics of this class of flows presents complications because of the presence of a free surface and also because the flow can be driven by a pressure gradient (a tidal current), a stress at the free surface (a wind-driven current), or a combination of both. In addition, the flow can be modified by the presence of a wave field that can induce Langmuir circulation (Langmuir, Science 87:119–123, 1938). Large eddy simulation is used to quantify the effects of pressure gradient and wind shear on the distinctive structures of the turbulent flow. From these computations, an understanding of the physics governing the turbulence of pressure-driven and wind-driven flows, how they can interact in a normal or a tangential direction, and the effect of wave forcing on these flows is obtained.     

Momentum transfer at the ocean–atmosphere interface: the wave basis for the inertial coupling approach

 The inertial coupling approach for the momentum transfer at the ocean–atmosphere interface, which is based on the assumption of a similarity hypothesis in which the ratio between the water and air reference velocities is equal to the square root of the ratio between the air and water densities, is reviewed using a wave model. In this model, the air and water reference velocities are identified, respectively, with the spectrally weighted phase velocity of the gravity waves and the Stokes velocity at the water roughness length, which are evaluated in terms of the dimensionless frequency limits in Toba's equilibrium spectrum. It is shown that the similarity hypothesis is approximately satisfied by the wave model over the range of wave ages encountered in typical sea states, and that the predicted values of the dimensionless surface drift velocity, the dimensionless water reference velocity, and the Charnock constant are in reasonable agreement with observational evidence. The application of the bulk relationship for the surface shear stress, derived from the inertial coupling hypothesis in general circulation modeling, is also discussed. Received: 6 January 2001 / Accepted: 28 June 2001     

Geophysical flows with anisotropic turbulence and dispersive waves: flows with stable stratification

The quasi-normal scale elimination (QNSE) is an analytical spectral theory of turbulence based upon a successive ensemble averaging of the velocity and temperature modes over the smallest scales of motion and calculating corresponding eddy viscosity and eddy diffusivity. By extending the process of successive ensemble averaging to the turbulence macroscale one eliminates all fluctuating scales and arrives at models analogous to the conventional Reynolds stress closures. The scale dependency embedded in the QNSE method reflects contributions from different processes on different scales. Two of the most important processes in stably stratified turbulence, internal wave propagation and flow anisotropization, are explicitly accounted for in the QNSE formalism. For relatively weak stratification, the theory becomes amenable to analytical processing revealing just how increasing stratification modifies the flow field via growing anisotropy and gravity wave radiation. The QNSE theory yields the dispersion relation for internal waves in the presence of turbulence and provides a theoretical reasoning for the Gargett et al. (J Phys Oceanogr 11:1258–1271, 1981) scaling of the vertical shear spectrum. In addition, it shows that the internal wave breaking and flow anisotropization void the notion of the critical Richardson number at which turbulence is fully suppressed. The isopycnal and diapycnal viscosities and diffusivities can be expressed in the form of the Richardson diffusion laws thus providing a theoretical framework for the Okubo dispersion diagrams. Transitions in the spectral slopes can be associated with the turbulence- and wave-dominated ranges and have direct implications for the transport processes. We show that only quasi-isotropic, turbulence-dominated scales contribute to the diapycnal diffusivity. On larger, buoyancy dominated scales, the diapycnal diffusivity becomes scale independent. This result underscores the well-known fact that waves can only transfer momentum but not a scalar and sheds a new light upon the Ellison–Britter–Osborn mixing model. It also provides a general framework for separation of the effects of turbulence and waves even if they act on the same spatial and temporal scales. The QNSE theory-based turbulence models have been tested in various applications and demonstrated reliable performance. It is suggested that these models present a viable alternative to conventional Reynolds stress closures.     

有限水域近水面气流演化特征试验研究

气流作为湖泊、湿地等有限水域的主要驱动力之一,其演化特征是研究水-气间能量与物质传递的基础,决定了水域水环境与水生态格局,具有重要研究意义.采用室内风洞水槽,通过设置不同试验风速,研究近水面气流与风速和吹程的响应关系与演化特征,并将光滑壁面条件下的气流特征作为试验对照组,分析时间域内风速垂向分布形式、摩阻风速、特征粗糙...     

Bed shear stress in the southern North Sea as an important driver for suspended sediment dynamics

This paper addresses the spatial and temporal patterns of drivers for sediment dynamics in coastal areas. The basic assumption is that local processes are dominating. The focus is put on the bed shear stress in the southern part of North Sea giving the basic control for deposition–sedimentation and resuspension–erosion. The wave-induced bed shear stress is formulated using a model based on the concept that the turbulent kinetic energy associated with surface waves is a function of orbital velocity, the latter depending on the wave height and period, as well as on the water depth. Parameters of surface waves are taken from simulations with the wave spectrum model WAM (wave model). Bed shear stress associated with currents is simulated with a 3D primitive equation model, Hamburg Shelf Ocean Model. Significant wave height, bed shear stress due to waves and currents, is subjected to empirical orthogonal functions (EOF) analysis. It has been found that the EOF-1 of significant wave height represents the decrease of significant wave height over the shallows and, due to fetch limitation, along the coastlines. Higher order modes are seesaw-like and, in combination, display a basin-scale rotational pattern centred approximately in the middle of the basin. Similar types of variability is also observed in the second and third EOF of bed shear stress. Surface concentrations of suspended matter derived from MERIS satellite data are analysed and compared against statistical characteristics of bed shear stress. The results show convincingly that the horizontal distribution of sediment can, to a larger extent, be explained by the local shear stress. However, availability of resuspendable sediments on the bottom is quite important in some areas like the Dogger Bank.     

The wave-induced boundary layer under long internal waves

The boundary layer formed under the footprint of an internal solitary wave is studied by numerical simulation for waves of depression in a two-layer model of the density stratification. The inviscid outer flow, in the perspective of boundary-layer theory, is based on an exact solution for the long wave-phase speed, yielding a family of fully nonlinear solitary wave solutions of the extended Korteweg–de Vries equation. The wave-induced boundary layer corresponding to this outer flow is then studied by means of simulation employing the Reynolds-averaged Navier–Stokes (RANS) formulation coupled with a turbulence closure model validated for wall-bounded flows. Boundary-layer characteristics are computed for an extensive range of environmental conditions and wave amplitudes. Boundary-layer transition, identified by monitoring the eddy viscosity, is correlated in terms of a boundary-layer Reynolds number. The frictional drag is evaluated for laminar, transitional, and turbulent cases, and correlations are presented for the friction coefficient plus relevant measures of the boundary-layer thickness.     

On the sensitivity of the sedimentary system in the East Frisian Wadden Sea to sea-level rise and wave-induced bed shear stress

The paper addresses the individual and collective contribution of different forcing factors (tides, wind waves, and sea-level rise) to the dynamics of sediment in coastal areas. The results are obtained from simulations with the General Estuarine Transport Model coupled with a sediment transport model. The wave-induced bed shear stress is formulated using a simple model based on the concept that the turbulent kinetic energy (TKE) associated with wind waves is a function of orbital velocity, the latter depending on the wave height and water depth. A theory is presented explaining the controls of sediment dynamics by the TKE produced by tides and wind waves. Several scenarios were developed aiming at revealing possible trends resulting from realistic (observed or expected) changes in sea level and wave magnitude. The simulations demonstrate that these changes not only influence the concentration of sediment, which is very sensitive to the magnitude of the external forcing, but also the temporal variability patterns. The joint effect of tides and wave-induced bed shear stress revealed by the comparison between theoretical results and simulations is well pronounced. The intercomparison between different scenarios demonstrates that the spatial patterns of erosion and deposition are very sensitive to the magnitude of wind waves and sea-level rise. Under a changing climate, forcing the horizontal distribution of sediments adjusts mainly through a change in the balance of export and import of sediment from the intertidal basins. The strongest signal associated with this adjustment is simulated North of the barrier islands where the evolution of sedimentation gives an integrated picture of the processes in tidal basins.     

A comparison of gravity wave phase velocities calculated from the impedance equation and pressure data

Abstract

Marked oscillations in wind speed, wind direction and pressure with periods of between 5 and 15 minutes were recorded on a number of occasions and it is assumed that they were produced by atmospheric gravity waves. Gossard and Munk (1954) have shown that the phase velocity of a gravity wave can be calculated using wind and pressure fluctuation data from a single station by means of the “impedance equation”. It is also possible to measure the phase velocity of a gravity wave using an array of microbarovariographs. In this investigation, the phase velocity of gravity waves calculated using these two different methods are compared and the feasibility of deriving wave characteristics from single point measurements is discussed. The results show that, while in a few isolated cases the two velocities agree reasonably well, the application of the impedance equation to data from a single station is limited due to the superposition of local wind systems upon the wave-induced perturbations.     

Observation-based evaluation of surface wave effects on currents and trajectory forecasts

Knowledge of upper ocean currents is needed for trajectory forecasts and is essential for search and rescue operations and oil spill mitigation. This paper addresses effects of surface waves on ocean currents and drifter trajectories using in situ observations. The data set includes colocated measurements of directional wave spectra from a wave rider buoy, ocean currents measured by acoustic Doppler current profilers (ADCPs), as well as data from two types of tracking buoys that sample the currents at two different depths. The ADCP measures the Eulerian current at one point, as modelled by an ocean general circulation model, while the tracking buoys are advected by the Lagrangian current that includes the wave-induced Stokes drift. Based on our observations, we assess the importance of two different wave effects: (a) forcing of the ocean current by wave-induced surface fluxes and the Coriolis–Stokes force, and (b) advection of surface drifters by wave motion, that is the Stokes drift. Recent theoretical developments provide a framework for including these wave effects in ocean model systems. The order of magnitude of the Stokes drift is the same as the Eulerian current judging from the available data. The wave-induced momentum and turbulent kinetic energy fluxes are estimated and shown to be significant. Similarly, the wave-induced Coriolis–Stokes force is significant over time scales related to the inertial period. Surface drifter trajectories were analysed and could be reproduced using the observations of currents, waves and wind. Waves were found to have a significant contribution to the trajectories, and we conclude that adding wave effects in ocean model systems is likely to increase predictability of surface drifter trajectories. The relative importance of the Stokes drift was twice as large as the direct wind drag for the used surface drifter.

     

Seasonal variations of the Hawaiian Lee Countercurrent induced by the meridional migration of the trade winds

Seasonal variations of the Hawaiian Lee Countercurrent (HLCC) are investigated using satellite observations of sea surface height and wind stress as well as eddy-resolving ocean model simulations. The HLCC is strong from summer to winter and weak in spring between the dateline and the Hawaiian Islands. In response to the seasonal migration of the northeast trade winds in the meridional direction, the wind curl dipole lee of Hawaii varies in strength, exciting westward-propagating Rossby waves. The analyses of both observations and simulations show that the propagation of Rossby waves south of the HLCC, driven by the southern pole of the wind curl dipole in the lee of the islands, contributes the most to the seasonal variations of the HLCC. Unlike the wind-driven seasonal variations, our analysis suggests that other mechanisms such as mode water intrusion or air–sea interaction may cause the interannual variations of the HLCC.     

Inversion of travel times obtained during active seismic refraction experiments CELEBRATION 2000, ALP 2002 and SUDETES 2003

A series of kinematic inversions based on robust non-linear optimization approach were performed using travel time data from a series of seismic refraction experiments: CELEBRATION 2000, ALP 2002 and SUDETES 2003. These experiments were performed in Central Europe from 2000 to 2003. Data from 8 profiles (CEL09, CEL10, Alp01, S01, S02, S03, S04 and S05) were processed in this study. The goal of this work was to find seismic velocity models yielding travel times consistent with observed data. Optimum 2D inhomogeneous isotropic P-wave velocity models were computed. We have developed and used a specialized two-step inverse procedure. In the first “parametric” step, the velocity model contains interfaces whose shapes are defined by a number of parameters. The velocity along each interface is supposed to be constant but may be different along the upper and lower side of the interface. Linear vertical interpolation is used for points in between interfaces. All parameters are searched for using robust non-linear optimization (Differential Evolution algorithm). Rays are continuously traced by the bending technique. In the second “tomographic” step, small-scale velocity perturbations are introduced in a dense grid covering the currently obtained velocity model. Rays are fixed in this step. Final velocity models yield travel time residuals comparable to typical picking errors (RMS ∼ 0.1 s). As a result, depth-velocity cross-sections of P waves along all processed profiles are obtained. The depth range of the models is 35–50 km, the velocity varies in the range 3.5–8.2 km/s. Lowest velocities are detected in near-surface depth sections crossing sedimentary formations. The middle crust is generally more homogeneous and has typical P wave velocity around 6 km/s. Surprisingly the lower crust is less homogeneous and the computed velocity is in the range 6.5–7.5 km/s. The MOHO is detected in the depth ≈30–45 km.     

兰新第二双线铁路防风明洞实验段风荷载数值模拟研究

介绍了高速铁路防风明洞的基本作用及设计方法;利用计算流体动力学原理中的数学模型及控制方程,对兰新第二双线铁路防风明洞大风作用下的风荷载进行了分析;通过计算工况的假定以及边界条件的合理设定,采用有限体积法建立防风明洞数值分析模型,并模拟计算了平地路段、浅路堑地段和路堤地段三大类工况和70、60、50、40m/s4种风速情况。研究结果表明：①开孔情况下,明洞各部位所受风荷载随着风速增大而增大;②明洞迎风侧均为正压,平地地段与路堤地段所受正压较接近,最大值出现在风速为70m/s时,迎风边墙正压为3202Pa;③明洞拱顶及背风侧均为负压,浅路堑地段所受负压最大值出现在风速为70m/s时,拱顶负压为-3550Pa;④各地段背风侧所受负压均小于-1500Pa,背风墙脚与背风边墙受力基本相同;⑤各地段各风速情况下,拱顶处负压均为最大;⑥开孔情况下的明洞各部位风荷载,普遍小于不开孔情况;⑦明洞开孔附近有回流风速,并随着外界风速增大而增大。