A three-dimensional model study of near-inertial motion: generation and influence of an along-shelf flow

A three-dimensional baroclinic model of the Balearic Sea region is used to examine the processes influencing the distribution of near-inertial currents and waves in the region. Motion is induced by a spatially uniform wind impulse. By using a uniform wind, Ekman pumping due to spatial variability in the wind is removed with the associated generation of internal waves. However, internal waves can still be produced where stratification intersects topography. The generation and propagation of these waves, together with the spatial distribution of wind-forced inertial oscillations, are examined in detail. Diagnostic calculations show that in the near-coastal region inertial oscillations are inhibited by the coastal boundary. Away from this boundary the magnitude of the inertial oscillations increases, with currents showing a 180° phase shift in the vertical. The inclusion of an along-shelf flow modifies the inertial currents due to non-linear interaction between vorticity in the flow and the inertial oscillations. Prognostic calculations show that besides inertial oscillations internal waves are generated. In a linear model the addition of an along-shelf flow produces a slight reduction in the energy at the near-inertial frequency due to enhanced viscosity associated with the flow and changes in density field. The inclusion of non-linear effects modifies the currents due to inertial oscillations in a manner similar to that found in the diagnostic model. A change in the effective inertial frequency also influences the propagation of the internal waves. However, this does not appear to be the main reason for the enhanced damping of inertial energy, which is due to the along-shelf advection of water of a different density into a region and increased viscosity and mixing associated with the along-shelf flow.Responsible Editor: Phil Dyke     

Modeling the impact of wind and waves on suspended particulate matter fluxes in the East Frisian Wadden Sea (southern North Sea)

Suspended particulate matter (SPM) fluxes and dynamics are investigated in the East Frisian Wadden Sea using a coupled modeling system based on a hydrodynamical model [the General Estuarine Transport Model (GETM)], a third-generation wave model [Simulating Waves Nearshore (SWAN)], and a SPM module attached to GETM. Sedimentological observations document that, over longer time periods, finer sediment fractions disappear from the Wadden Sea Region. In order to understand this phenomenon, a series of numerical scenarios were formulated to discriminate possible influences such as tidal currents, wind-enhanced currents, and wind-generated surface waves. Starting with a simple tidal forcing, the considered scenarios are designed to increase the realism step by step to include moderate and strong winds and waves and, finally, to encompass the full effects of one of the strongest storm surges affecting the region in the last hundred years (Storm Britta in November 2006). The results presented here indicate that moderate weather conditions with wind speeds up to 7.5 m/s and small waves lead to a net import of SPM into the East Frisian Wadden Sea. Waves play only a negligible role during these conditions. However, for stronger wind conditions with speeds above 13 m/s, wind-generated surface waves have a significant impact on SPM dynamics. Under storm conditions, the numerical results demonstrate that sediments are eroded in front of the barrier islands by enhanced wave action and are transported into the back-barrier basins by the currents. Furthermore, sediment erosion due to waves is significantly enhanced on the tidal flats. Finally, fine sediments are flushed out of the tidal basins due to the combined effect of strong erosion by wind-generated waves and a longer residence time in the water column because of their smaller settling velocities compared to coarser sediments.

The role of remote wind forcing in the subinertial current variability in the central and northern parts of the South Brazil Bight

Data analysis of continental shelf currents and coastal sea level, together with the application of a semi-analytical model, are used to estimate the importance of remote wind forcing on the subinertial variability of the current in the central and northern areas of the South Brazil Bight. Results from both the data analysis and from the semi-analytical model are robust in showing subinertial variability that propagates along-shelf leaving the coast to the left in accordance with theoretical studies of Continental Shelf Waves (CSW). Both the subinertial variability observed in along-shelf currents and sea level oscillations present different propagation speeds for the narrow northern part of the SBB (~?6–7 m/s) and the wide central SBB region (~?11 m/s), those estimates being in agreement with the modeled CSW propagation speed. On the inner and middle shelf, observed along-shelf subinertial currents show higher correlation coefficients with the winds located southward and earlier in time than with the local wind at the current meter mooring position and at the time of measurement. The inclusion of the remote (located southwestward) wind forcing improves the prediction of the subinertial currents when compared to the currents forced only by the local wind, since the along-shelf-modeled currents present correlation coefficients with observed along-shelf currents up to 20% higher on the inner and middle shelf when the remote wind is included. For most of the outer shelf, on the other hand, this is not observed since usually, the correlation between the currents and the synoptic winds is not statistically significant.     

Application of a circulation and transport model system to the dispersal of herring larvae in the North Sea

A model system consisting of a three-dimensional circulation and transport model is used to simulate the dispersal of herring larvae in the North Sea. The driving forces of the circulation model are theM₂-tide, time dependent wind stress and air pressure fields, as well as monthly climatological density fields interpolated on a daily basis. The transport model includes advection as well as diffusion and uses a tracer technique to pursue the larvae in the time and space domain. Furthermore, the transport model incorporates a simulation of active vertical movement of the larvae as vertical migration has a marked effect on the drift route of the larvae.Simulated North Sea currents are compared to observed currents gained during the Autumn Circulation Experiment (ACE) which took place from August 1987 to March 1988. The variability in observed currents at the location of the moorings is found to be larger than in the simulated currents. On a larger scale, the simulated circulation in the northern North Sea shows a close correspondence to the inferred circulation from a quasi-synoptic hydrographic survey. The quality of the predictions of larval transport and distribution patterns by the model system is tested using sequential larvae distributions observed during ACE. Common features and discrepancies of observed and simulated distributions are discussed and conclusions for further field investigations and modelling studies are drawn.     

Observation and simulation of a floe drift near the North Pole

The drift trajectory of a floe near the North Pole (87° N, 175° W) was observed during 8–19 August, 2010 based on the fourth Chinese National Arctic Research Expedition. The trajectory of the floe showed circular motions superimposed on straight drift. Each cycle had a period of about 12?h. The circular motion is inertial oscillation. The largest amplitude of inertial oscillation speed can reach 20?cm/s. After removing the inertial oscillation, the floe drift direction is about 40° on average to the right of the observed 10-m wind which is much larger than previous reports on the angle between sea-ice velocity and the geostrophic wind, and floe drift moves with a speed of about 1.4?% of the observed 10-m wind speed throughout the whole observation period. A simple dynamic sea ice-ocean coupled model and a three-dimensional sea ice-ocean coupled model are employed to simulate the floe drift. Both numerical models are with the widely used quadratic water-drag formulation, i.e., the stress is proportional to the square of the ice velocity relative to the ocean surface current. The inertial oscillation of the floe is successfully simulated by the simple passive drag model, while the floe drift amplitudes simulated from the three-dimensional model are relatively small.     

Inertial oscillations in the Irish Sea

An inertial current with a maximum speed of about 0.20 m s¹ was observed in June 1981, by a current meter 17 m below the surface of the thermally stratified waters of the western Irish Sea. The dynamics of the surface waters have been modelled using contemporary wind data recorded at the site to drive a horizontally unbounded surface slab 20 m deep with a velocity decay time of about three inertial periods (1.86 days). From thermistor chain data, inertial frequency potential energy was observed to radiate beneath the thermocline, descending at a rate of about 0.06 cm s¹. The energy available for internal mixing from the observed oscillation may have been as much as 80 J m², compared with 150 J m² from wind-induced surface mixing. The mean surface mixing power in summer is about7.1 × 10⁴W m², while the mean shear-induced mixing power could be as much as2.0 × 10⁴W m². The likely occurrence of strong inertial events has been estimated using the wind record fcr 10 successive summers at Dublin airport. Large oscillations with speeds 0.20m s¹, or mixed layer kinetic energy(MLKE) > 400 J m², have an average duration of about 28 h. They occur about once every 2 months between mid-May and mid-August but seem to be more frequent from then until mid-September. Moderate oscillations (MLKE > 200 J m²) are more evenly distributed, occurring about once every 2 weeks. Small oscillations (MLKE > 40 J m²) occur nearly 50% of the time.     

Application of third generation shallow water wave models in a tidal environment

Wave modeling was performed in the German Bight of the North Sea during November 2002, using the spectral wave models, namely the K-model and Simulating WAves Nearshore (SWAN), both developed for applications in environments of shallow water depths. These models mainly differ with respect to their dissipation source term expressions and in exclusion or inclusion of nonlinear wave–wave interactions. The K-model uses nonlinear dissipation and bottom dissipation, and neglects quadruplet wave–wave interaction whereas, SWAN includes, besides bottom dissipation, dissipation by white-capping and depth induced wave breaking and triad wave–wave interaction. The boundary spectra were extracted from the WAM model results of a North Sea hindcast of the HIPOCAS project, wind fields, tidal current and water level variations from the results of models used in the Belawatt project. The purpose of this study was to test the performance of both wave models to see whether they were able to predict near-shore wave conditions accurately. The runs were performed with and without tidal current and level variations to determine their effect on the waves. Comparisons of model results with buoy measurements show that taking into account tides and currents improve the spectral shape especially in areas of high current speeds. Whereas SWAN performed better in terms of spectral shape, especially in case of two peaked spectra, the K-model showed better results in terms of integrated parameters.Responsible Editor: Hans Burchard     

Dam breach simulations with multiple breach locations under wind and wave actions

Multiple breaches of a dam resulting from wind-generated waves and wave overtopping are studied for a hypothetical long non-cohesive earthen dam with an uneven crest. Both wind speed and direction affect breach locations and outflow for a particular reservoir surface geometry. Locations on the dam with longer fetches along the wind direction are more subject to wave overtopping and breaching than other locations. Higher wind speeds lead to wave overtopping and dam breaches under larger freeboards than lower wind speeds. For a specified inflow hydrograph and spillway configuration, there exists a location at which the smallest estimated peak outflow occurs among all possible breach locations and the pool drops too quickly for additional breaches to develop. Using this location for a fuse plug or a pilot channel could minimize downstream impact, perhaps as an interim or emergency measure for a dam with inadequate spillway capacity.     

Correction of inertial oscillations by assimilation of HF radar data in a model of the Ligurian Sea

This article aims at analyzing if high-frequency radar observations of surface currents allow to improve model forecasts in the Ligurian Sea, where inertial oscillations are a dominant feature. An ensemble of ROMS models covering the Ligurian Sea, and nested in the Mediterranean Forecasting System, is coupled with two WERA high-frequency radars. A sensitivity study allows to determine optimal parameters for the ensemble filter. By assimilating observations in a single point, the obtained correction shows that the forecast error covariance matrix represents the inertial oscillations, as well as large- and meso-scale processes. Furthermore, it is shown that the velocity observations can correct the phase and amplitude of the inertial oscillations. Observations are shown to have a strong effect during approximately half a day, which confirms the importance of using a high temporal observation frequency. In general, data assimilation of HF radar observations leads to a skill score of about 30% for the forecasts of surface velocity.     

Observations over an annual cycle and simulations of wind-forced oscillations near the critical latitude for diurnal-inertial resonance

Sea breezes are characteristic features of coastal regions that can extend large distances from the coastline. Oscillations close to the inertial period are thought to account for around half the kinetic energy in the global surface ocean and play an important role in mixing. In the vicinity of 30°N/S, through a resonance between the diurnal and inertial frequencies, diurnal winds could force enhanced anti-cyclonic rotary motions that contribute to near-inertial energy.Observations of strong diurnal anti-cyclonic currents in water of depth 175 m off the Namibian coastline at 28.6°S are analysed over the annual cycle. Maxima in the diurnal anti-cyclonic current and wind stress amplitudes appear to be observed during the austral summer. Both the diurnal anti-cyclonic current and wind stress components have approximately constant phase throughout the year. These observations provide further evidence that these diurnal currents may be wind forced. Realistic General Ocean Turbulence Model (GOTM) 1-D simulations of diurnal wind forcing, including the first order coast-normal surface slope response to diurnal wind forcing, represent the principal features of the observed diurnal anti-cyclonic current but do not replicate the observed vertical diurnal current structure accurately. Cross-shelf 2-D slice simulations suggest that the first order surface slope response approximation applies away from the coast (>140 km). However, nearer to the coast, additional surface slope variations associated with spatial variations in the simulated velocity field (estimated from Bernoulli theory) appear to be significant and also result in transfer of energy to higher harmonics. Evidence from 3-D simulations at similar latitude in the northern hemisphere suggests that 3-D variations, including propagating near-inertial waves, may also need to be considered.     

Storm observations by remote sensing and influences of gustiness on ocean waves and on generation of rogue waves

The impact of the gustiness on surface waves under storm conditions is investigated with focus on the appearance of wave groups with extreme high amplitude and wavelength in the North Sea. During many storms characterized by extremely high individual waves measured near the German coast, especially in cold air outbreaks, the moving atmospheric open cells are observed by optical and radar satellites. According to measurements, the footprint of the cell produces a local increase in the wind field at sea surface, moving as a consistent system with a propagation speed near to swell wave-traveling speed. The optical and microwave satellite data are used to connect mesoscale atmospheric turbulences and the extreme waves measured. The parameters of open cells observed are used for numerical spectral wave modeling. The North Sea with horizontal resolution of 2.5?km and with focus on the German Bight was simulated. The wind field “storm in storm,” including moving organized mesoscale eddies with increased wind speed, was generated. To take into account the rapid moving gust structure, the input wind field was updated each 5?min. The test cases idealized with one, two, and four open individual cells and, respectively, with groups of open cells, with and without preexisting sea state, as well the real storm conditions, are simulated. The model results confirm that an individual-moving open cell can cause the local significant wave height increase in order of meters within the cell area and especially in a narrow area of 1–2?km at the footprint center of a cell (the cell's diameter is 40–90?km). In a case of a traveling individual open cell with 15?m·s^?1 over a sea surface with a preexisting wind sea of and swell, a local significant wave height increase of 3.5?m is produced. A group of cells for a real storm condition produces a local increase of significant wave height of more than 6?m during a short time window of 10–20?min (cell passing). The sea surface simulation from modeled wave spectra points out the appearance of wave groups including extreme individual waves with a period of about 25?s and a wavelength of more than 350?m under the cell's footprint. This corresponds well with measurement of a rogue wave group with length of about 400?m and a period of near 25?s. This has been registered at FiNO-1 research platform in the North Sea during Britta storm on November 1, 2006 at 04:00 UTC. The results can explain the appearance of rogue waves in the German Bight and can be used for ship safety and coastal protection. Presently, the considered mesoscale gustiness cannot be incorporated in present operational wave forecasting systems, since it needs an update of the wind field at spatial and temporal scales, which is still not available for such applications. However, the scenario simulations for cell structures with appropriate travel speed, observed by optical and radar satellites, can be done and applied for warning messages.     

山体遮挡对滇池风生流的影响初探

用二维风生流数值模型模拟滇池湖流运动。滇池在主导风向西南风作用下,假定湖面风场是均匀的,数值模拟的湖流流态与实测湖流结果相差很大。而考虑山体遮挡影响,根据实测湖流期间现有的风情资料,在湖面上构造一非均匀风场,数值模拟结果与实测值基本一致。山体遮挡对滇池风生流的影响是不容忽视的。建议进一步进行湖流和湖面风向、风速监测,并建立过山气流数学模型,深入研究山体遮挡对湖泊风生流的影响。     

Variations in wind direction and speed from arctic to the Caspian Sea as a manifestation of modern climate changes

The regularities in present-day variations in the wind speed vector are examined at 18 stations along the section from Kola Peninsula to the Caspian Sea. Data on long-term variations in the major climate-forming factors and climatic parameters are generalized. The statistically significant tendency toward a considerable decline in the wind speed with a maximum module and the most frequent wind speeds of zonal, mostly western, directions (this tendency has been revealed earlier for the eastern coast of the middle and southern Caspian Sea) was found to hold for the greater part of the European Russia. Possible causes of present-day climate changes and their manifestations at the regional level are analyzed. A possible mechanism of present-day climate changes is proposed     

Effects of wave-induced forcing on a circulation model of the North Sea

The effect of wind waves on water level and currents during two storms in the North Sea is investigated using a high-resolution Nucleus for European Modelling of the Ocean (NEMO) model forced with fluxes and fields from a high-resolution wave model. The additional terms accounting for wave-current interaction that are considered in this study are the Stokes-Coriolis force, the sea-state-dependent energy and momentum fluxes. The individual and collective role of these processes is quantified and the results are compared with a control run without wave effects as well as against current and water-level measurements from coastal stations. We find a better agreement with observations when the circulation model is forced by sea-state-dependent fluxes, especially in extreme events. The two extreme events, the storm Christian (25–27 October 2013), and about a month later, the storm Xaver (5–7 December 2013), induce different wave and surge conditions over the North Sea. Including the wave effects in the circulation model for the storm Xaver raises the modelled surge by more than 40 cm compared with the control run in the German Bight area. For the storm Christian, a difference of 20–30 cm in the surge level between the wave-forced and the stand-alone ocean model is found over the whole southern part of the North Sea. Moreover, the modelled vertical velocity profile fits the observations very well when the wave forcing is accounted for. The contribution of wave-induced forcing has been quantified indicating that this represents an important mechanism for improving water-level and current predictions.     

Synergy of satellite remote sensing and numerical modeling for monitoring of suspended particulate matter

Monitoring and modeling of the distribution of suspended particulate matter (SPM) is an important task, especially in coastal environments. Several SPM models have been developed for the North Sea. However, due to waves in shallow water and strong tidal currents in the southern part of the North Sea, this is still a challenging task. In general there is a lack of measurements to determine initial distributions of SPM in the bottom sediment and essential model parameters, e.g., appropriate exchange coefficients. In many satellite-borne ocean color images of the North Sea a plume is visible, which is caused by the scattering of light at SPM in the upper ocean layer. The intensity and length of the plume depends on the wave and current climate. It is well known that the SPM plume is especially obvious shortly after strong storm events. In this paper a quasi-3-D and a 3-D SPM transport model are presented. Utilizing the synergy of satellite-borne ocean color data with numerical models, the vertical exchange coefficients due to currents and waves are derived. This results in models that for the first time are able to reproduce the temporal and spatial evolution of the plume intensity. The SPM models consist of several modules to compute ocean dynamics, the vertical and horizontal exchange of SPM in the water column, and exchange processes with the seabed such as erosion, sedimentation, and resuspension. In the bottom layer, bioturbation via benthos and diffusion processes is taken into account.Responsible Editor: Jörg-Olaf Wolff     

On the modifications of near-inertial waves at fronts: implications for energy transfer across scales

In the ocean, wind-generated kinetic energy (KE) manifests itself primarily in balanced currents and near-inertial waves. The dynamics of these flows is strongly constrained by the Earth’s rotation, causing the KE in balanced currents to follow an inverse cascade but also preventing wave-wave interactions from fluxing energy in the near-inertial band to lower frequencies and higher vertical wavenumbers. How wind-generated KE is transferred to small-scale turbulence and dissipated is thus a non-trivial problem. This article presents a review of recent theoretical calculations and numerical simulations that demonstrate how some surprising modifications to internal wave physics by the lateral density gradients present at ocean fronts allow for strong interactions between balanced currents and near-inertial waves that ultimately result in energy loss for both types of motion.     

Evidence and effects of a wave-driven nonlinear current in the equatorial electrojet

Ionospheric two-stream waves and gradientdrift waves nonlinearly drive a large-scale (D.C.) current in the E-region ionosphere. This current flows parallel to, and with a comparable magnitude to, the fundamental Pedersen current. Evidence for the existence and magnitude of wave-driven currents derives from a theoretical understanding of E-region waves, supported by a series of nonlinear 2D simulations of two-stream waves and by data collected by rocket instruments in the equatorial electrojet. Wave-driven currents will modify the large-scale dynamics of the equatorial electrojet during highly active periods. A simple model shows how a wave-driven current appreciably reduces the horizontally flowing electron current of the electrojet. This reduction may account for the observation that type-I radar echoes almost always have a Doppler velocity close to the acoustic speed, and also for the rocket observation that electrojet regions containing gradientdrift waves do not appear also to contain horizontally propagating two-stream waves. Additionally, a simple model of a gradient-drift instability shows that wavedriven currents can cause nonsinusoidal electric fields similar to those measured in situ.     

洪泽湖风生流对风场和水位变化响应特征

深入认识大型湖泊在不同风速、风向和水位下三维风生流结构特征对于湖泊污染控制、生态恢复及资源的开发利用具有重要意义.本文在构建笛卡尔坐标系下洪泽湖三维水动力模型的基础上,利用2次全湖30个点位流场监测数据验证了模型精度.基于1975-2020年长系列风场观测数据,确定了洪泽湖典型风速风向.在此基础上,模拟了16种不同风向,13种不同风速和20种不同水位工况条件下洪泽湖三维风生流结构.结果表明：水动力模型可以较好地刻画洪泽湖三维湖流变化特征.洪泽湖风生流结构随风向变化呈现出较大空间差异.风生流流速随着风速的升高呈加速上升趋势,其中表层水体流速上升幅度远高于其他水层.在2.4 m/s东风驱动下,溧河洼、成子湖和南部湖区垂向平均流速随着水位上升呈先升高后降低的趋势,3个湖区分别在12.7、12.4和12.2 m水位下流速达到最大值.     

Time-varying storm surges on Lorentz’s Wadden Sea networks

We present an idealized network model for storm surges in the Wadden Sea, specifically including a time-dependent wind forcing (wind speed and direction). This extends the classical work by H.A. Lorentz who only considered the equilibrium response to a steady wind forcing. The solutions obtained in the frequency domain for the linearized shallow-water equations in a channel are combined in an algebraic system for the network. The velocity scale that is used for the linearized friction coefficient is determined iteratively. The hindcast of the storm surge of 5 December 2013 produces credible time-varying results. The effects of storm and basin parameters on the peak surge elevation are the subject of a sensitivity analysis. The formulation in the frequency domain reveals which modes in the external forcing lead to the largest surge response at coastal stations. There appears to be a minimum storm duration, of about 3–4 h, that is required for a surge to attain its maximum elevation. The influence of the water levels at the North Sea inlets on the Wadden Sea surges decreases towards the shore. In contrast, the wind shearing generates its largest response near the shore, where the fetch length is at its maximum.