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.     

Future wave climate over the west-European shelf seas

In this paper, we investigate changes in the wave climate of the west-European shelf seas under global warming scenarios. In particular, climate change wind fields corresponding to the present (control) time-slice 1961–2000 and the future (scenario) time-slice 2061–2100 are used to drive a wave generation model to produce equivalent control and scenario wave climate. Yearly and seasonal statistics of the scenario wave climates are compared individually to the corresponding control wave climate to identify relative changes of statistical significance between present and future extreme and prevailing wave heights. Using global, regional and linked global–regional wind forcing over a set of nested computational domains, this paper further demonstrates the sensitivity of the results to the resolution and coverage of the forcing. It suggests that the use of combined forcing from linked global and regional climate models of typical resolution and coverage is a good option for the investigation of relative wave changes in the region of interest of this study. Coarse resolution global forcing alone leads to very similar results over regions that are highly exposed to the Atlantic Ocean. In contrast, fine resolution regional forcing alone is shown to be insufficient for exploring wave climate changes over the western European waters because of its limited coverage. Results obtained with the combined global–regional wind forcing showed some consistency between scenarios. In general, it was shown that mean and extreme wave heights will increase in the future only in winter and only in the southwest of UK and west of France, north of about 44–45° N. Otherwise, wave heights are projected to decrease, especially in summer. Nevertheless, this decrease is dominated by local wind waves whilst swell is found to increase. Only in spring do both swell and local wind waves decrease in average height.     

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.     

Climate and extrema of ocean waves in the East China Sea

Wave climate plays an important role in the air-sea interaction over marginal seas. Extreme wave height provides fundamental information for various ocean engineering practices, such as hazard mitigation, coastal structure design, and risk assessment. In this paper, we implement a third generation wave model and conduct a high-resolution wave hindcast over the East China Sea to reconstruct a 15-year wave field from 1988 to 2002 for derivation of monthly mean wave parameters and analysis of extreme wave conditions. The numerical results of the wave field are validated through comparison with satellite altimetry measurements, low-resolution reanalysis, and the ocean wave buoy record. The monthly averaged wave height and wave period show seasonal variation and refined spatial patterns of surface waves in the East China Sea. The climatological significant wave height and mean wave period decrease from the open ocean in the southeast toward the continental area in the northwest, with the pattern generally following the bathymetry. Extreme analysis on the significant wave height at the buoy station indicates the hindcast data underestimate the extreme values relative to the observations. The spatial pattern of extreme wave height shows single peak emerges at the southwest of Ryukyu Island although a wind forcing with multi-core structure at the extreme is applied.     

Regional patterns of observed sea level change: insights from a 1/4° global ocean/sea-ice hindcast

A global eddy-admitting ocean/sea-ice simulation driven over 1958–2004 by daily atmospheric forcing is used to evaluate spatial patterns of sea level change between 1993 and 2001. In the present study, no data assimilation is performed. The model is based on the Nucleus for European Models of the Ocean code at the 1/4° resolution, and the simulation was performed without data assimilation by the DRAKKAR project. We show that this simulation correctly reproduces the observed regional sea level trend patterns computed using satellite altimetry data over 1993–2001. Generally, we find that regional sea level change is best simulated in the tropical band and northern oceans, whereas the Southern Ocean is poorly simulated. We examine the respective contributions of steric and bottom pressure changes to the total regional sea level changes. For the steric component, we analyze separately the contributions of temperature and salinity changes as well as upper and lower ocean contributions. Generally, the model results show that most regional sea level changes arise from temperature changes in the upper 750 m of the ocean. However, contributions of salinity changes and deep steric changes can be locally important. We also propose a map of ocean bottom pressure changes. Finally, we assess the robustness of such a model by comparing this simulation with a second simulation performed by MERCATOR-Ocean based on the same core model, but differing by its short length of integration (1992–2001) and its surface forcing data set. The long simulation presents better performance over 1993–2001 than the short simulation, especially in the Southern Ocean where a long adjustment time seems to be needed. In memory of my little brother Jean-Eudes, whose thirst for science filled out the rich discussions we had about my investigations and his job as user-service provider for MERCATOR-Ocean.     

Numerical simulation of internal solitary wave—induced reverse flow and associated vortices in a shallow,two-layer fluid benthic boundary layer

The wave-induced velocity and pressure fields beneath a large amplitude internal solitary wave of depression propagating over a smooth, flat, horizontal, and rigid boundary in a shallow two-layer fluid are computed numerically. A numerical ocean model is utilised, the set-up of which is designed and tuned to replicate the previously published experimental results of Carr and Davies (Phys Fluids 18(1):016,601–1–016,601–10, 2006). Excellent agreement is found between the two data sets and, in particular, the numerical simulation replicates the finding of a reverse flow along the bed aft of the wave. The numerically computed velocity and pressure gradients confirm that the occurrence of the reverse flow is a consequence of boundary layer separation in the adverse pressure gradient region. In addition, vortices associated with the reverse flow are seen to form near the bed.     

Modeling studies of the upper ocean response to a tropical cyclone

A coupled ocean and boundary layer flux numerical modeling system is used to study the upper ocean response to surface heat and momentum fluxes associated with a major hurricane, namely, Hurricane Dennis (July 2005) in the Gulf of Mexico. A suite of experiments is run using this modeling system, constructed by coupling a Navy Coastal Ocean Model simulation of the Gulf of Mexico to an atmospheric flux model. The modeling system is forced by wind fields produced from satellite scatterometer and atmospheric model wind data, and by numerical weather prediction air temperature data. The experiments are initialized from a data assimilative hindcast model run and then forced by surface fluxes with no assimilation for the time during which Hurricane Dennis impacted the region. Four experiments are run to aid in the analysis: one is forced by heat and momentum fluxes, one by only momentum fluxes, one by only heat fluxes, and one with no surface forcing. An equation describing the change in the upper ocean hurricane heat potential due to the storm is developed. Analysis of the model results show that surface heat fluxes are primarily responsible for widespread reduction (0.5°–1.5°C) of sea surface temperature over the inner West Florida Shelf 100–300 km away from the storm center. Momentum fluxes are responsible for stronger surface cooling (2°C) near the center of the storm. The upper ocean heat loss near the storm center of more than 200 MJ/m² is primarily due to the vertical flux of thermal energy between the surface layer and deep ocean. Heat loss to the atmosphere during the storm’s passage is approximately 100–150 MJ/m². The upper ocean cooling is enhanced where the preexisting mixed layer is shallow, e.g., within a cyclonic circulation feature, although the heat flux to the atmosphere in these locations is markedly reduced.     

The wave climate of Liverpool Bay—observations and modelling

Directional wave measurements have been made in Liverpool Bay by means of wave buoys and acoustic instruments within the footprint of a phased-array high frequency (HF) radar system, which measures currents and waves. Several years of data have now been collected and are supplemented by an 11-year wave model hindcast. Wave parameters have been derived from the various instruments and compared: the directional waverider buoy is taken to provide the ground truth, confirming the good observations obtained from the ADCP; the HF radar wave data have a positive bias, while the model data have a negative bias. The variation of wave climate over various time-scales from seasonal and inter-annual to inter-decadal is examined. Significant wave–current interactions may occur in this area of shallow water and high tidal range and the measurements provide a good test of coupled hydrodynamic-wave models. The waves are mainly fetch-limited: largest events are due to depressions, which track across the UK from SW, generating westerly and WNW winds in the right rear quadrant. Hence, the future extreme wave events will be closely related to future North Atlantic storm tracks. Projections of 50-year return period wave heights differ between different instruments and model datasets. The future wave climate of Liverpool Bay is not expected to change much from the present day; although a slight increase in the severity of the most extreme events is projected, the frequency of extreme wind and wave events in general is slightly reduced. There is evidence for variability on decadal time-scales, with some correlation with the North Atlantic oscillation.     

Spatial characteristics of ocean surface waves

The spatial variability of open ocean wave fields on scales of O (10km) is assessed from four different data sources: TerraSAR-X SAR imagery, four drifting SWIFT buoys, a moored waverider buoy, and WAVEWATCH III^? model runs. Two examples from the open north-east Pacific, comprising of a pure wind sea and a mixed sea with swell, are given. Wave parameters attained from observations have a natural variability, which decreases with increasing record length or acquisition area. The retrieval of dominant wave scales from point observations and model output are inherently different to dominant scales retrieved from spatial observations. This can lead to significant differences in the dominant steepness associated with a given wave field. These uncertainties have to be taken into account when models are assessed against observations or when new wave retrieval algorithms from spatial or temporal data are tested. However, there is evidence of abrupt changes in wave field characteristics that are larger than the expected methodological uncertainties.     

Using the Regional Ocean Modeling System (ROMS) to improve the ocean circulation from a GCM 20<Superscript>th</Superscript> century simulation

Global coupled climate models are generally capable of reproducing the observed trends in the globally averaged atmospheric temperature. However, the global models do not perform as well on regional scales. Here, we present results from a 20-year, high-resolution ocean model experiment for the Atlantic and Arctic Oceans. The atmospheric forcing is taken from the final 20 years of a twentieth-century control run with a coupled atmosphere–ocean general circulation model. The ocean model results from the regional ocean model are validated using observations of hydrography from repeat cruises in the Barents Sea. Validation is performed for average quantities and for probability distributions in space and time. The validation results reveal that, though the regional model is forced by a coupled global model that has a noticeable sea ice bias in the Barents Sea, the hydrography and its variability are reproduced with an encouraging quality. We attribute this improvement to the realistic transport of warm, salty waters into the Barents Sea in the regional model. These lateral fluxes in the ocean are severely underestimated by the global model. The added value with the regional model that we have documented here lends hope to advance the quality of oceanic climate change impact studies.     

Distribution of medium-scale acoustic gravity waves in polar regions according to satellite measurement data

The peculiarities of the distribution of medium-scale acoustic gravity waves (AGWs) in polar regions according to the data of measurements on board the Dynamics Explorer 2 satellite are studied. Over polar regions of both hemispheres at heights of 250–400 km, wave variations in neutral atmospheric parameters were systematically registered. These variations were identified as AGWs with horizontal wavelengths of 500–650 km. The relative amplitudes of polar AGWs in a neutral concentration reach 10%. Wave trains extend over the polar caps to thousands of kilometers and show a distinct spatial relationship with the auroral oval. A systematic direction is found in AGW propagation from the nighttime sector of the oval into the day-time sector, where wave activity is strictly limited. An assumption is formulated that this restriction is caused by dynamic interactions between AGWs and the zonal wind in the daytime sector of the auroral oval.     

Modelling ocean wave climate with a Bayesian hierarchical space–time model and a log-transform of the data

Long-term trends in the ocean wave climate because of global warming are of major concern to many stakeholders within the maritime industries, and there is a need to take severe sea state conditions into account in design of marine structures and in marine operations. Various stochastic models of significant wave height are reported in the literature, but most are based on point measurements without exploiting the flexible framework of Bayesian hierarchical space–time models. This framework allows modelling of complex dependence structures in space and time and incorporation of physical features and prior knowledge, yet remains intuitive and easily interpreted. This paper presents a Bayesian hierarchical space–time model with a log-transform for significant wave height data for an area in the North Atlantic ocean. The different components of the model will be outlined, and the results from applying the model to data of different temporal resolutions will be discussed. Different model alternatives have been tried and long-term trends in the data have been identified for all model alternatives. Overall, these trends are in reasonable agreement and also agree fairly well with previous studies. The log-transform was included in order to account for observed heteroscedasticity in the data, and results are compared to previous results where a similar model was employed without a log-transform. Furthermore, a discussion of possible extensions to the model, e.g. incorporating regression terms with relevant meteorological data, will be presented.     

Wave-induced topographic formstress in baroclinic channel flow

Large-scale zonal flow driven across submarine topography establishes standing Rossby waves. In the presence of stratification, the wave pattern can be represented by barotropic and baroclinic Rossby waves of mixed planetary topographic nature, which are locked to the topography. In the balance of momentum, the wave pattern manifests itself as topographic formstress. This wave-induced formstress has the net effect of braking the flow and reducing the zonal transport. Locally, it may lead to acceleration, and the parts induced by the barotropic and baroclinic waves may have opposing effects. This flow regime occurs in the circumpolar flow around Antarctica. The different roles that the wave-induced formstress plays in homogeneous and stratified flows through a zonal channel are analyzed with the BARBI (BARotropic-Baroclinic-Interaction ocean model, Olbers and Eden, J Phys Oceanogr 33:2719–2737, 2003) model. It is used in complete form and in a low-order version to clarify the different regimes. It is shown that the barotropic formstress arises by topographic locking due to viscous friction and the baroclinic one due to eddy-induced density advection. For the sinusoidal topography used in this study, the transport obeys a law in which friction and wave-induced formstress act as additive resistances, and windstress, the effect of Ekman pumping on the density stratification, and the buoyancy forcing (diapycnal mixing of the stratified water column) of the potential energy stored in the stratification act as additive forcing functions. The dependence of the resistance on the system parameters (lateral viscosity ε, lateral diffusivity κ of eddy density advection, Rossby radius λ, and topography height δ) as well as the dependence of transport on the forcing functions are determined. While the current intensity in a channel with homogeneous density decreases from the viscous flat bottom case in an inverse quadratic law ~δ ^–2 with increasing topography height and always depends on ε, a stratified system runs into a saturated state in which the transport becomes independent of δ and ε and is determined by the density diffusivity κ rather than the viscosity: κ/λ ² acts as a vertical eddy viscosity, and the transport is λ ²/κ times the applied forcing. Critical values for the topographic heights in these regimes are identified.     

The 1st International Workshop on Waves,Storm Surges and Coastal Hazards incorporating the 15th International Workshop on Wave Hindcasting and Forecasting

Following the 1st International Workshop on Waves, Storm Surges and Coastal Hazards, which incorporated the 15th session of the long-standing the International Workshop on Wave Hindcasting and Forecasting, in September 2017 in Liverpool, United Kingdom, a topical collection has appeared in recent issues of Ocean Dynamics. Here, we give a brief overview of the 15 papers published in this topical collection as well as an overview of the widening scope of the conference in recent years. The continuing trend towards closer integration between the wave and ocean modeling communities is reflected in this workshop, culminating in the renaming of the workshop, while maintaining the connection with the three-decade long history of the wave workshop. This is also seen in this topical collection, with several papers exploring wave-generated storm surge, wave-tide contributions to coastal flooding, forcing a global ocean model with fluxes from a wave model and interaction between surface waves and sea ice.

     

Upper mantle P wave velocity structure of the northern part of China and Mongolia

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Wave disturbances in the ionosphere during a lasting solar activity minimum

Using the Kharkov incoherent scatter radar, observations of wave disturbances in electron concentration N in the ionosphere at heights of 120–600 km are conducted. The measurements were carried out in the periods of the spring and fall equinoxes and winter and summer solstices. The height-time dependences of the absolute ΔN and relative ΔN/N amplitudes of wave disturbances, as well as their spectral composition, were analyzed. It is shown that wave disturbances in the ionosphere with periods of 10–180 min were present at almost any time of the day and in all seasons. Their absolute and relative amplitudes varied from 6 × 10⁹ to 6 × 10¹⁰ m⁻³ and from 0.01 to 0.5, respectively. The maximum values of ΔN and ΔN/N were observed at a height of ∼200 km. The passage of the solar terminator changed substantially the wave disturbance parameters.     

A numerical study of the dynamics of the wave-driven circulation within a fringing reef system

The circulation driven by wave breaking, tides and winds within a fringing coral reef system (Ningaloo Reef) in Western Australia was investigated using the ocean circulation model ROMS two-way coupled to the wave model SWAN. Currents within the system were dominantly forced by wave breaking, with flow driven over the shallow reefs and towards the lagoon, which returned to the ocean through channels in the reef. Hindcast model simulations were compared against an extensive field dataset, revealing that the coupled wave–circulation model could accurately predict the waves and currents throughout this morphologically complex reef–lagoon system. A detailed momentum budget analysis showed that, over the reef, a dominant cross-shore balance was established between radiation stress gradients and a pressure (mean water level) gradient (similar to a beach). Within the lagoon, alongshore currents were primarily balanced by alongshore gradients in wave setup, which drove flow towards (and ultimately out) the channels. The importance of these wave-driven currents to Ningaloo Reef was quantified over a full seasonal cycle, during periods when wave and wind conditions significantly differed. These results showed that wave breaking still overwhelmingly dominated the circulation and flushing of Ningaloo Reef throughout the year, with winds playing an insignificant role.     

Why ripples become sweiis,and swells in shallow water decay rapidly

Abstract

In an ocean with a horizontal bottom where no wind is blowing it is shown that the spin (angular momentum) of the ocean is conserved. Thus, when energy is dissipated, at least one of three things will happen: i) Wave spectra may move towards lower frequencies. ii) The directional distribution may be changed towards long-crested waves. iii) Shear currents may be generated. By neglecting ii) and iii), the frequency shift of a spectrum is calculated due to molecular dissipation. When all energy transforming phenomena as e.g. wave breaking and turbulence generation are taken into account, the conservation of spin seems to be able to explain the frequency shift of wave spectra. In shallow water it is shown that there is energy transfer from the waves to shear currents.     

Statistics of breaking waves and its applications to estimation of air-sea fluxes (I)

Wave breaking statistics, such as the whitecap coverage and average volume of broken seawater, are evaluated in terms of wave parameters by use of wave breaking model (Yuan et al., 1988) taking the fifth order Stokes’s wave as the analog of the original wave field. Based on the observed fact that breaking waves play an important role in the exchange of mass, momentum and energy between the atmosphere and the ocean, the influence of wave breaking on air-sea fluxes of heat and moisture is investigated. Theoretical expressions of bubble-volume flux and sea spray spectrum at the sea surface and models for bubble-induced and spray droplet-induced heat and moisture fluxes are established. This work can be taken as the basis for further understanding the mechanism of air-sea coupling and parameterization models.     

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.