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.     

Array measurements of the bottom boundary layer and the internal wave field on the continental slope

Abstract

An array of current meters was placed on the continental slope and rise for two months in the autumn of 1970. The bottom boundary layer was penetrated on the slope. On the smallest array scale, of the order of 1 kilometer, the array functioned as a directional internal wave antenna. Moving shoreward, the current spectra show strong suppression of the inertial peak and strong enhancement of the semidiurnal tide. The measured wave number spectra show that the tidal energy is almost completely baroclinic, and probably being generated in the region where the slope becomes “critical” for the tidal period. If this area is typical of worldwide conditions, a substantial fraction of the dissipation of surface tides takes place on the continental slopes by conversion to baroclinic waves. The bottom boundary layer has been modeled by an extension of the work of Ellison (1956) to a sloping boundary in a fluid of positive stability. An equivalent constant eddy coefficient has the value 3 cm²/sec as determined from the measurements.     

Effect of water depth and the bottom boundary layer upon internal wave generation over abrupt topography

The role of water depth and bottom boundary layer turbulence upon lee-wave generation in sill regions is examined. Their effect upon vertical mixing is also considered. Calculations are performed using a non-hydrostatic model in cross-section form with a specified tidal forcing. Initial calculations in deeper water and a sill height such that the sill top is well removed from the surrounding bed region showed that downstream lee-wave generation and associated mixing increased as bottom friction coefficient k increased. This was associated with an increase in current shear across the sill. However, for a given k, increasing vertical eddy viscosity A _v reduced vertical shear in the across sill velocity, leading to a reduction in lee-wave amplitude and associated mixing. Subsequent calculations using shallower water showed that for a given k and A _v, lee-wave generation was reduced due to the shallower water depth and changes in the bottom boundary layer. However, in this case (unlike in the deepwater case), there is an appreciable bottom current. This gives rise to bottom mixing which in shallow water extends to mid-depth and enhances the mid-water mixing that is found on the lee side of the sill. Final calculations with deeper water but small sill height showed that lee waves could propagate over the sill, thereby reducing their contribution to mixing. In this case, bottom mixing was the major source of mixing which was mainly confined to the near bed region, with little mid-water mixing.     

Mechanisms of bottom boundary fluxes in a numerical model of the Shetland shelf

Across-slope bottom boundary layer (BBL) fluxes on the shelf-edge connect this region to deeper waters. Two proposed ways in which across-slope BBL fluxes can occur, in regions that have a slope current aligned to the bathymetry, are the frictional veering of bottom currents termed the ‘Ekman drain’ and through local wind-forced downwelling (wind-driven surface Ekman flow with an associated bottom flow). We investigate the variability, magnitude and spatial scale of BBL fluxes on the Shetland shelf, which has a prominent slope current, using a high-resolution (～2 km) configuration of the MITgcm model. Fluxes are analysed in the BBL at the shelf break near the 200 m isobath and are found to have a seasonal variability with high/low volume transport in winter/summer respectively. By using a multivariate regression approach, we find that the locally wind-driven Ekman transport plays no explicit role in explaining daily bottom fluxes. We can better explain the variability of the across-slope BBL flux as a linear function of the speed and across-slope component of the interior flow, corresponding to an Ekman plus mean-flow flux. We estimate that the mean-flow is a greater contributor than the Ekman flux to the BBL flux. The spatial heterogeneity of the BBL fluxes can be attributed to the mean-flow, which has a much shorter decorrelation length compared to the Ekman flux. We conclude that both the speed and direction of the interior current determines the daily BBL flux. The wind does not explicitly contribute through local downwelling, but may influence the interior current and therefore implicitly the BBL fluxes on longer timescales.     

Turbulence structure of the boundary layer below marine clouds in the SOFIA experiment

The SOFIA (Surface of the Ocean: Flux and Interaction with the Atmosphere) experiment, included in the ASTEX (Atlantic Stratocumulus Transition EXperiment) field program, was conducted in June 1992 in the Azores region in order to investigate air-sea exchanges, as well as the structure of the atmospheric boundary layer and its capping low-level cloud cover. We present an analysis of the vertical structure of the marine atmospheric boundary layer (MABL), and especially of its turbulence characteristics, deduced from the aircraft missions performed during SOFIA. The meteorological situations were characteristic of a temperate latitude under anticyclonic conditions, i.e., with weak to moderate winds, weak surface sensible heat flux, and broken capping low-altitude cloud cover topped by a strong trade inversion. We show that the mixed layer, driven by the surface fluxes, is decoupled from the above cloud layer. Although weak, the surface buoyancy flux, and the convective velocity scale deduced from it, are relevant for scaling the turbulence moments. The mixed layer then follows the behavior of a continental convective boundary layer, with the exception of the entrainment process, which is weak in the SOFIA data. These results are confirmed by conditional sampling analysis, which shows that the major turbulence source lies in the buoyant moist updrafts at the surface.     

Atmospheric boundary layer over steep surface waves

Turbulent air-sea interactions coupled with the surface wave dynamics remain a challenging problem. The needs to include this kind of interaction into the coupled environmental, weather and climate models motivate the development of a simplified approximation of the complex and strongly nonlinear interaction processes. This study proposes a quasi-linear model of wind-wave coupling. It formulates the approach and derives the model equations. The model is verified through a set of laboratory (direct measurements of an airflow by the particle image velocimetry (PIV) technique) and numerical (a direct numerical simulation (DNS) technique) experiments. The experiments support the central model assumption that the flow velocity field averaged over an ensemble of turbulent fluctuations is smooth and does not demonstrate flow separation from the crests of the waves. The proposed quasi-linear model correctly recovers the measured characteristics of the turbulent boundary layer over the waved water surface.     

Inclined internal tide waves at a narrow Mexican Pacific shelf

The dynamics of a semidiurnal internal tidal wave at a narrow Mexican Pacific shelf is discussed using the data of temperature obtained by an anchored instrument and data of field surveys. The internal tide on the shelf is dominated by an inclined wave, which propagates upward and onshore along a continental slope. Despite its reflection from the bottom and from the surface of the ocean, they remain inclined and totally destroyed over the course of one wavelength. Due to wave reflection from the inclined bottom, the horizontal and vertical wave number increase threefold when the wave goes into shallow waters. The wave undergoes nonlinear transformation and overturns forming several homogeneous temperature layers up to 20 m thick. The most intense disturbances of water layers are observed near the bottom, where the slope angle approaches its critical value. Because of nonlinear effects, the wave carries cool deep water out to the shallow depth and causes coastal upwelling. Intense solar warming together with vertical mixing results in a rapid rise of temperature in the 130-m water column that was observed.     

Numerical studies of large-amplitude internal waves shoaling and breaking at shelf slopes

Hydro carbon fields beyond the shelf break are presently being explored and developed, which has increased the scientific focus in this area. Measurements from the slopes reveal large variability in temperature and velocity, and some of the observed events are due to interactions between large-amplitude oscillations of the thermocline and the topography. The present study focuses on the strong currents that are generated near the seabed during shoaling and breaking of internal waves along shelf slopes. The parameter regime used is similar to the one for the Nordic Seas. The results show that, during shoaling of large internal waves along (gentle) slopes, the energy is transferred towards smaller scales and strong velocities (over 1 m s^− 1) can be generated. To resolve all scales involved is still not feasible, and therefore, the model results are sensitive to the grid size and the subgrid scale closure.     

On the generation of baroclinic rossby waves in the presence of a semi-circular boundary

Abstract

An analytical model is constructed for the generation of baroclinic Rossby waves by a vorticity source in the presence of a semi-circular boundary. The vorticity source is used to represent the effect of the Agulhas retroflection to the south of Southern Africa. The displacement of the interface between the two layers of the model ocean consists of quantized waves near the coast and a train of Rossby waves drifting westward further offshore.     

On leakage of energy from turbulence to internal waves in the oceanic mixed layer

In this paper, we address the question of energy leakage from turbulence to internal waves (IWs) in the oceanic mixed layer (OML). If this leakage is substantial, then not only does this have profound implications as far as the dynamics of the OML is concerned, but it also means that the equation for the turbulence kinetic energy (TKE) used in OML models must include an appropriate sink term, and traditional models must be modified accordingly. Through comparison with the experimental data on grid-generated turbulence in a stably stratified fluid, we show that a conventional two-equation turbulence model without any IW sink term can explain these observations quite well, provided that the fluctuating motions that persist long after the decay of grid-generated turbulence are interpreted as being due to IW motions generated by the initial passage of the grid through the stably stratified fluid and not during turbulence decay. We conclude that there is no need to postulate an IW sink term in the TKE equation, and conventional models suffice to model mixing in the OML.     

On propagation of Rayleigh waves in a thin transversely isotropic layer with rigid bottom surface

Summary The complete solution of the propagation of Rayleigh waves in a thin transversely isotropic layer with rigid bottom surface has been developed along with its frequency equation. The ratio of the possible vibrations at the free surface in the horizontal and vertical directions has been worked out and the proposed analysis has been applied to the case of Beryl and Ice Sheets which show definite behaviour of transverse isotropy.     

海底边界层异常(地震海洋学)反射地震特征的地球物理分析

通过对南海北部与西部大量反射地震剖面海水层部分进行再处理,与以往地震海洋学主要关注海水层内部的反射结构不同,本文重点对海底附近水体的各种复杂反射地震特征进行分类、分析与总结.与传统对海底边界层的定义不同,我们将海底边界附近的水体称之为海底边界层.本文利用传统地震相分析方法,分析海底边界层各种复杂反射地震结构的几何形态、内部反射结构、连续性、振幅以及视频率特征,结合过去相关的地震海洋学研究成果、海底边界层理论与其它各种海底附近作用/过程,不仅对中尺度涡旋、内孤立波和背风波在地震剖面上的反射地震特征进行了归类与分析,并推断最新发现的一些反射地震特征可能揭示的各种海洋作用/过程,例如不同的地震相特征可能反映了海底湍流边界层,海底沉积物再悬浮,天然气渗漏羽状流和麻坑内部异常上升流相关海底界面作用过程.结果分析表明,地震海洋学方法不仅能够对海洋内波、涡旋等物理海洋现象进行研究,同时也能够对海底附近各种复杂海洋作用/过程进行成像,从而拓展了地震海洋学的研究领域,一定程度上也能为过去不能有效对海底边界面发生的各种冷泉热液活动、生物和沉积等作用过程进行现场观测提供新的探测方法和研究视角.     

Structure of the inner core boundary

Abstract

A model of the inner-core boundary (ICB) is constructed which is consistent with current ideas of the dynamic and thermodynamic state of the core and which is capable of reflecting seismic waves with period of one second. This requires the mass fraction of solid below the ICB to grow to an appreciable fraction in roughly one kilometer. This rapid growth of solid with depth is a result of downward fluid flow from the outer core which is a part of the convective motions which sustain the geodynamo. The solid which crystallizes from this descending fluid after it crosses the ICB continually coats the dendrites which occur there. The gradual cooling of the outer core causes the ICB to advance by growth of dendrites at their tips. The balance of these two effects gives an equilibrium profile for the mass fraction of solid with depth below the ICB which is capable of yielding sharp reflection of seismic waves.     

Nonlinear aspects of long shelf waves

Abstract

Continental shelf waves are examined in the long wavelength limit, and the effects of weak topographic dispersion calculated. These dispersive effects are then balanced against nonlinear terms and a Korteweg-de Vries equation is derived to describe the evolution of the wave amplitude. Two particular cases are worked in detail.     

Sediment transport on the Palos Verdes shelf,California

Sediment transport and the potential for erosion or deposition have been investigated on the Palos Verdes (PV) and San Pedro shelves in southern California to help assess the fate of an effluent-affected deposit contaminated with DDT and PCBs. Bottom boundary layer measurements at two 60-m sites in spring 2004 were used to set model parameters and evaluate a one-dimensional (vertical) model of local, steady-state resuspension, and suspended-sediment transport. The model demonstrated skill (Brier scores up to 0.75) reproducing the magnitudes of bottom shear stress, current speeds, and suspended-sediment concentrations measured during an April transport event, but the model tended to underpredict observed rotation in the bottom-boundary layer, possibly because the model did not account for the effects of temperature–salinity stratification. The model was run with wave input estimated from a nearby buoy and current input from four to six years of measurements at thirteen sites on the 35- and 65-m isobaths on the PV and San Pedro shelves. Sediment characteristics and erodibility were based on gentle wet-sieve analysis and erosion-chamber measurements. Modeled flow and sediment transport were mostly alongshelf toward the northwest on the PV shelf with a significant offshore component. The 95th percentile of bottom shear stresses ranged from 0.09 to 0.16 Pa at the 65-m sites, and the lowest values were in the middle of the PV shelf, near the Whites Point sewage outfalls where the effluent-affected layer is thickest. Long-term mean transport rates varied from 0.9 to 4.8 metric tons m⁻¹ yr⁻¹ along the 65-m isobaths on the PV shelf, and were much higher at the 35-m sites. Gradients in modeled alongshore transport rates suggest that, in the absence of a supply of sediment from the outfalls or PV coast, erosion at rates of ∼0.2 mm yr⁻¹ might occur in the region southeast of the outfalls. These rates are small compared to some estimates of background natural sedimentation rates (∼5 mm yr⁻¹), but do not preclude higher localized rates near abrupt transitions in sediment characteristics. However, low particle settling velocities and strong currents result in transport length-scales that are long relative to the narrow width of the PV shelf, which combined with the significant offshore component in transport, means that transport of resuspended sediment towards deep water is as likely as transport along the axis of the effluent-affected deposit.     

General velocity formula of boundary layer above mobile sediment bed induced by asymmetric waves

Sediment movement in the wave boundary layer above a mobile sediment bed is complex.A velocity formula for the boundary layer is proposed for sheet flow induced by asymmetric waves above a mobile sediment bed.The formula consists of a free stream velocity and a defect function which contains a phase-lead,boundary layer thickness and mobile sediment bed.Phase-lag of sediment movement is considered in the formula for the mobile sediment bed.The formula needs six dependent variables about asymmetric wave and sediment characteristics.Asymmetry effects on parameters(orbital amplitude,roughness height,bed shear stress,and boundary layer thickness)are properly considered such that the formula can yield velocity differences among onshore,offshore,acceleration,and deceleration stages.The formula estimates the net boundary layer velocity resulting from the mobile sediment bed and asymmetric boundary layer thickness.In addition,a non-constant phase-lead also contributes to the net boundary layer velocity in asymmetric oscillatory sheet flow.Results of the formula are as good as that of a two-phase numerical model.Sheet flow transport induced by asymmetric waves,and the offshore net sediment transport rate with a large phase-lag under velocity-skewed waves,can be adequately estimated by the formula with a power sediment concentration function.     

Large-scale impacts of bottom trawling on shelf primary productivity

Disturbance of the seabed resulting from bottom trawling affects ecosystem processes, such as the rate and magnitude of nutrient regeneration. The potential responses of the plankton community arising from such effects can be modelled, provided that reliable data on the effects on nutrient fluxes are available. In a north Cretan outer continental shelf and upper slope fishing ground (Heraklion Bay, Crete, Eastern Mediterranean) we applied a new field instrument which can simulate the passage of trawl groundropes across the sea floor and made direct seasonal measurements of the rate of dissolved and particulate nutrient releases resulting from seabed disturbance. These observational data were then integrated in a 3D ecosystem model. Results revealed that bottom trawling may trigger off considerable productivity pulses, in addition to pulses from the natural seasonal cycle.     

Tidal currents,energy flux and bottom boundary layer thickness in the Clyde Sea and North Channel of the Irish Sea

A high-resolution three-dimensional model of the Clyde Sea and the adjacent North Channel of the Irish Sea is used to compute the major diurnal and semidiurnal tides in the region, the associated energy fluxes and thickness of the bottom boundary layer. Initially, the accuracy of the model is assessed by performing a detailed comparison of computed tidal elevations and currents in the region, against an extensive database that exists for the M₂, S₂, N₂, K₁ and O₁ tides. Subsequently, the model is used to compute the tidal energy flux vectors in the region. These show that the major energy flux is confined to the North Channel region, with little energy flux into the Clyde Sea. Comparison with the observed energy flux in the North Channel shows that its across-channel distribution and its magnitude are particularly sensitive to the phase difference between elevation and current. Consequently, small changes in the computed values of these parameters due to slight changes of the order of the uncertainty in the open-boundary values to the model, can significantly influence the computed energy flux. The thickness of the bottom boundary layer in the region is computed using a number of formulations. Depending upon the definition adopted, the empirical coefficient C used to determine its thickness varies over the range 0.1 to 0.3, in good agreement with values found in the literature. In the North Channel, the boundary layer thickness occupies the whole water depth, and hence tidal turbulence produced at the sea bed keeps the region well mixed. In the Clyde Sea, the boundary layer thickness is a small fraction of the depth, and hence the region stratifies.Responsible Editor: Phil Dyke     

边界层参数化方案对边界层热力和动力结构特征影响的比较

本文利用高分辨率中尺度WRF模式,通过改变边界层参数化方案进行多组试验,评估该模式对美国北部森林地区边界层结构的模拟能力,同时比较了五种不同边界层参数化方案模拟得出的边界层热力和动力结构.结果表明：除个别方案外,配合不同边界层方案的WRF模式都能成功模拟出白天对流边界层强湍流混合特征和夜间稳定边界层内强逆温、逆湿和低空急流等热力和动力结构.非局地YSU、ACM2方案在白天表现出强的湍流混合和卷夹,相比于局地MYJ、UW方案,模拟的对流边界层温度更高、湿度更低、混合层高度更高、感热通量更大,更接近实际观测,这表明在不稳定层结下考虑非局地大涡输送更为合理,但局地方案在风速和风向的预报上存在一定优势.TEMF方案得到的白天局地湍流混合强度为所有方案中最弱,混合层难以发展,无法体现对流边界层内气象要素垂直分布均匀的特点.对于夜间稳定边界层的模拟,不同参数化方案之间的差异较小,但是YSU方案在一定程度上高估了机械湍流,导致局地湍流混合偏强,从而影响了其对稳定边界层的模拟能力.