Internal waves and temperature fronts on slopes

Time series measurements from an array of temperature miniloggers in a line at constant depth along the sloping boundary of a lake are used to describe the ‘internal surf zone” where internal waves interact with the sloping boundary. More small positive temperature time derivatives are recorded than negative, but there are more large negative values than positive, giving the overall distribution of temperature time derivatives a small negative skewness. This is consistent with the internal wave dynamics; fronts form during the up-slope phase of the motion, bringing cold water up the slope, and the return flow may become unstable, leading to small advecting billows and weak warm fronts. The data are analysed to detect ‘events’, periods in which the temperature derivatives exceed a set threshold. The speed and distance travelled by ‘events’ are described. The motion along the slope may be a consequence of (a) instabilities advected by the flow (b) internal waves propagating along-slope or (c) internal waves approaching the slope from oblique directions. The propagation of several of the observed ‘events’ can only be explained by (c), evidence that the internal surf zone has some, but possibly not all, the characteristics of the conventional ‘surface wave’ surf zone, with waves steepening as they approach the slope at oblique angles.     

Frequency-Dependent Energy Dissipation of Irregular Breaking Waves

Results of field experiments and simulation are used to study the hypothesis that energy dissipation from irregular breaking waves can have a nonuniform distribution over the frequency. It was found that the wave energy dissipation in the outer surf zone is practically independent of the frequency and can be approximated by a constant. A quadratic or a selective (at the frequency band of second–third harmonics) dependence of energy dissipation on frequency was found to form in the inner part of the surf zone, where it is controlled by wave asymmetry and bed slope. The dissipation of the energy of breaking waves was shown to proceed in such a way as to compensate for the effect of processes of linear or nonlinear deformation of waves.     

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.     

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.

     

A field study of coastal dynamics on a muddy coast offshore of Cassino beach,Brazil

Mud deposits near sandy beaches, found throughout the world, are of scientific and societal interest as they form important natural sea defenses by efficiently damping storm waves. A multi-national field experiment to study these phenomena was performed offshore Cassino beach in southern Brazil starting in 2004. This experiment aimed to investigate the formation of an offshore mud deposit, to characterize wave attenuation over potentially mobile muddy bottoms, and to evaluate the performance of models for wave transformation over heterogeneous beds through the measurement of water waves, near-bottom currents, bathymetry, and changes in bottom sediment characteristics. The main instrumentation was a set of wave sensors deployed in a transect from the shoreline across sandy and muddy deposits offshore to a depth of 25 m. Additional sensors, including current meters and optical backscatter sensors, were concentrated at stations in the middle of the mud deposit and in the surf zone to document aspects of the wave boundary layer and lutocline dynamics. This fieldwork also involved the geological and geotechnical characterization of the mud deposit using seismic equipment, echo-sounders, cores, surficial sampling and an in-situ density meter. These sediment samples were subsequently analyzed for density, grain size distribution, mineralogy, rheology and sedimentary structures. In addition, video and radar monitoring equipment were installed to measure the long-term aspects of surf zone damping by fluid mud and any associated morphodynamic responses. This paper provides a summary of environmental conditions monitored during the experiment and describes the major findings of the various investigations. Although data collection was more difficult than anticipated and dramatic wave attenuation involving the onshore transport of fluid mud into the surf zone region was not observed during the instrumented interval, the new methodologies developed and comprehensive observations obtained during this effort are being used to improve our understanding of shoaling wave dynamics and sediment transport in the coastal zone in regions with significant cohesive sediment deposits.     

A two-dimensional horizontal wave propagation and mud mass transport model

The present study offers a two-dimensional horizontal wave propagation and morphodynamic model for muddy coasts. The model can be applied on a general three-dimensional bathymetry of a soft muddy coast to calculate wave damping, fluid mud mass transport and resulting bathymetry change under wave actions. The wave propagation model is based on time-dependent mild slope equations including the wave energy dissipation due to the wave-mud interaction of bottom mud layers as well as the combined effects of the wave refraction, diffraction and breaking. The constitutive equations of the visco-elastic–plastic model are adopted for the rheological behavior of fluid mud. The mass transport velocity within the fluid mud layer is calculated combining the Stokes’ drift, the mean Eulerian velocity and the gravity-driven mud flow. The results of the numerical model are compared against a series of conducted wave basin experiments, wave flume experiments and field observations. Comparisons between the computed results with both the field and laboratory data reveal the capability of the proposed model to predict the wave transformation and mud mass transport.     

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.     

Laboratory experiment on the 3D tide-induced Lagrangian residual current using the PIV technique

The 3D structure of the tide-induced Lagrangian residual current was studied using the particle image velocimetry (PIV) technique in a long shallow narrow tank in the laboratory. At the mouth of the tank, a wave generator was used to make periodic wave which represents the tide movement, and at the head of the tank, a laterally sloping topography with the length of one fifth of the water tank was installed, above which the tide-induced Lagrangian residual current was studied. Under the weakly nonlinear condition in the present experiment setup, the results show that the Lagrangian residual velocity (LRV) field has a three-layer structure. The residual current flows inwards (towards the head) in the bottom layer and flows outwards in the middle layer, while in the surface layer, it flows inwards along the shallow side of the sloping topography and outwards along the deep side. The depth-averaged and breadth-averaged LRV are also analyzed based on the 3D LRV observations. Our results are in good agreement with the previous experiment studies, the analytical solutions with similar conditions and the observational results in real bays. Moreover, the volume flux comparison between the Lagrangian and Eulerian residual currents shows that the Eulerian residual velocity violates the mass conservation law while the LRV truly represents the inter-tidal water transport. This work enriches the laboratory studies of the LRV and offers valuable references for the LRV studies in real bays.     

Mean meridional circulations of the stratosphere and mesosphere

Observations from the Nimbus 6 pressure modulator radiometer (PMR) have been used to estimate monthly mean planetary wave fluxes of heat and momentum in the stratosphere and mesosphere. While the eddy heat fluxes play an important role in the mean meridional circulation of the winter stratosphere they are shown to be less important in the upper mesosphere. Incorporation of the observed momentum fluxes into the Oxford two-dimensional circulation model has shown that they are incapable of providing the momentum transport necessary to balance the zonal flow accelerations induced by the mean meridional motion. Other unspecified transfer processes represented by Rayleigh frictional damping of the zonal fow are shown to dominate. In contrast the observed fluxes in the stratosphere achieve the necessary redistribution of momentum. Moreover their interannual variability profoundly influences the stratospheric circulation, as demonstrated in the model by the use of two different annual sets of observed momentum fluxes. The desirability of calculating the planetary wave behaviour within the model is indicated.     

A depth-dependent study of the topographic rectification of tidal currents

Abstract

A depth-dependent model for the topographic rectification of tidal currents in a homogeneous rotating fluid is used to examine the dependence of the rectified mean flow on various tidal, topographic and frictional parameters. Friction is parameterized through a vertically-uniform, time-independent vertical eddy viscosity and a bottom stress law applied near the top of the constant stress layer. The model neglects the interaction of mean and tidal currents, assumes uniformity along isobaths, and is closed with the assumption of zero depth-averaged mean flow across isobaths.

In the limit of depth-independence, the model reduces to that considered by Huthnance (1973) and Loder (1980) which, for weak friction, favours anticyclonic mean circulation around shallow regions and Lagrangian flow which is significantly reduced from the Eulerian. With the inclusion of vertical structure, the magnitude of the anticyclonic flow is amplified suggesting that depth-independent models may underestimate the along-isobath flow. For strong friction the direction of the mean flow depends on the orientation of the tidal ellipse relative to the isobaths. The depthindependent model again underestimates the magnitude of the along-isobath flow, but this can be offset with an appropriate reduction of the bottom friction coefficient.

The cross-isobath mean flows are one to two orders of magnitude weaker than the along-isobath flows and generally have more vertical structure. There is also a significant Stokes drift in the cross-isobath direction. Although there is some tendency for the cross-isobath mean bottom current to be down the cross-isobath mean pressure gradient, it appears that it is not generally possible to infer this current from depth-independent models.     

Hydrodynamic response of a fringing coral reef to a rise in mean sea level

Ningaloo Reef, located along the northwest coast of Australia, is one of the longest fringing coral reefs in the world extending ~300 km. Similar to other fringing reefs, it consists of a barrier reef ~1–6 km offshore with occasional gaps, backed by a shallow lagoon. Wave breaking on the reef generates radiation stress gradients that produces wave setup across the reef and lagoon and mean currents across the reef. A section of Ningaloo Reef at Sandy Bay was chosen as the focus of an intense 6-week field experiment and numerical simulation using the wave model SWAN coupled to the three-dimensional circulation model ROMS. The physics of nearshore processes such as wave breaking, wave setup and mean flow across the reef was investigated in detail by examining the various momentum balances established in the system. The magnitude of the terms and the distance of their peaks from reef edge in the momentum balance were sensitive to the changes in mean sea level, e.g. the wave forces decreased as the mean water depth increased (and hence, wave breaking dissipation was reduced). This led to an increase in the wave power at the shoreline, a slight shift of the surf zone to the lee side of the reef and changes in the intensity of the circulation. The predicted hydrodynamic fields were input into a Lagrangian particle tracking model to estimate the transport time scale of the reef-lagoon system. Flushing time of the lagoon with the open ocean was computed using two definitions in renewal of semi-enclosed water basins and revealed the sensitivity of such a transport time scale to methods. An increase in the lagoon exchange rate at smaller mean sea-level rise and the decrease at higher mean sea-level rise was predicted through flushing time computed using both methods.     

Numerical modelling of wind effects on breaking waves in the surf zone

Wind effects on periodic breaking waves in the surf zone have been investigated in this study using a two-phase flow model. The model solves the Reynolds-averaged Navier–Stokes equations with the k ? ?? turbulence model simultaneously for the flows both in the air and water. Both spilling and plunging breakers over a 1:35 sloping beach have been studied under the influence of wind, with a focus during wave breaking. Detailed information of the distribution of wave amplitudes and mean water level, wave-height-to-water-depth ratio, the water surface profiles, velocity, vorticity, and turbulence fields have been presented and discussed. The inclusion of wind alters the air flow structure above water waves, increases the generation of vorticity, and affects the wave shoaling, breaking, overturning, and splash-up processes. Wind increases the water particle velocities and causes water waves to break earlier and seaward, which agrees with the previous experiment.     

Tidal-induced buoyancy flux and mean transverse circulation

A weakly nonlinear model is used to examine the mean transverse circulation (cross-isobath) driven by tidal-induced buoyancy flux. The mean Eulerian flows driven by both the barotropic and baroclinic tide are presented for a semi-infinite wedge. The mean flow driven by the barotropic tide is significant only near the apex where the thickness of the frictional boundary layer is comparable to the water depth. The mean flow there is characterized by a single-cell circulation with offshore flow near the bottom, and its magnitude can reach a few percentage or a significant fraction of the tidal velocity in oceanic applications. The mean flow driven by the baroclinic tide, on the other hand, is characterized by pairs of half-open (on the seaward side) counter-rotating cells, the number of which equals the vertical mode number. For a baroclinic tide propagating onshore, the mean flow near the top and bottom surfaces is always directed offshore and its magnitude can reach a large fraction of the tidal velocity. Taken together, the model thus predicts a mean offshore flow near the bottom while higher up in the water column the mean flow direction is less definite due to the contribution from different tidal components. The model results are consistent with some current measurements over the Georges Bank.     

Hydrokinematic regions within the swash zone

A method for delimiting the swash zone and regions within is presented. Two regions are recognized and distinguished by their differing flow kinematics. The outer swash region involves wave-swash interactions and related processes, whereas the inner swash region consists of pure swash motion (i.e., free from interaction with subsequent waves). The boundary between these two hydrokinematic regions can be determined from shoreline elevation time series. The vertical extent of the outer swash was found to scale directly with inner surf zone wave variance and beach slope. Since the vertical extent of the entire swash zone also varies directly with the former, the relative extents of the outer and inner swash are approximately constant for the range of beach slopes investigated here. The efficacy of a previously utilized method for determining the location of instruments in the swash zone, based on the percentage of time the bed is inundated, is established here for the first time. A new method for determining the location of an instrument station within either of the hydrokinematic regions is also presented, and requires only a single pressure sensor time series. The data discussed here include over 140 runup time series collected from five different sandy beaches with beach face gradients ranging from 0.03 to 0.12. The results are expected to be generally applicable to swell-dominated sandy beaches, where swash is driven by a combination of short and long waves in the inner surf zone. The applicability of the results at either extreme of the reflective–dissipative continuum remains to be established.     

Net sediment transport in tidal basins: quantifying the tidal barotropic mechanisms in a unified framework

Net sediment transport in tidal basins is a subtle imbalance between large fluxes produced by the flood/ebb alternation. The imbalance arises from several mechanisms of suspended transport. Lag effects and tidal asymmetries are regarded as dominant, but defined in different frames of reference (Lagrangian and Eulerian, respectively). A quantitative ranking of their effectiveness is therefore missing. Furthermore, although wind waves are recognized as crucial for tidal flats’ morphodynamics, a systematic analysis of the interaction with tidal mechanisms has not been carried out so far. We review the tide-induced barotropic mechanisms and discuss the shortcomings of their current classification for numerical process-based models. Hence, we conceive a unified Eulerian framework accounting for wave-induced resuspension. A new methodology is proposed to decompose the sediment fluxes accordingly, which is applicable without needing (semi-) analytical approximations. The approach is tested with a one-dimensional model of the Vlie basin, Wadden Sea (The Netherlands). Results show that lag-driven transport is dominant for the finer fractions (silt and mud). In absence of waves, net sediment fluxes are landward and spatial (advective) lag effects are dominant. In presence of waves, sediment can be exported from the tidal flats and temporal (local) lag effects are dominant. Conversely, sand transport is dominated by the asymmetry of peak ebb/flood velocities. We show that the direction of lag-driven transport can be estimated by the gradient of hydrodynamic energy. In agreement with previous studies, our results support the conceptualization of tidal flats’ equilibrium as a simplified balance between tidal mechanisms and wave resuspension.     

Nearshore circulation over transverse bar and rip morphology with oblique wave forcing

There is a paucity of field data to describe the transition in nearshore circulation between alongshore, meandering and rip current systems. A combination of in‐situ current meters and surf zone drifters are used to characterize the nearshore circulation over a transverse bar and rip morphology at Pensacola Beach, Florida in the presence of relatively low energy oblique waves. Current speeds vary in response to the relative wave height ratio (H_s/h), which defines the degree and extent of breaking over the shoal. In the absence of wave breaking the nearshore circulation was dominated by an alongshore current driven by the oblique waves. As waves begin to break across the shoal (0.2<H_s/ h<0.5) the nearshore circulation is characterized by a meandering alongshore current. As conditions became more dissipative (H_s/h>0.5), the meandering current is replaced by an unsteady rip circulation that moves offshore between the shoals before turning alongshore in the direction of wave advance outside the surf zone. The increase in wave dissipation is associated with an increase in very low frequency (VLF) variations in the current speed across the shoal and in the rip channel that caused the circulation to oscillate between an offshore and an alongshore flow. The unsteady nature of the nearshore circulation is responsible for 55% of all surf zone exits under these more dissipative conditions. In contrast, only 29% of the drifters released from the shoal exited the surf zone and bypassed the adjacent shoal with the alongshore‐meandering current. While the currents had a low velocity (maximum of ~0.4 m s^‐1) and would not pose a significant hazard to the average swimmer, the results of this study suggest that the transverse bar and rip morphology is sufficient to create an alongshore variation in wave dissipation that forces alongshore meandering and low‐energy rip circulation systems under oblique wave forcing. Copyright © 2013 John Wiley & Sons, Ltd.     

Baroclinic,Kelvin and inertia-gravity waves in the barostrat instability experiment

The differentially heated rotating annulus is a laboratory experiment historically designed for modelling large-scale features of the mid-latitude atmosphere. In the present study, we investigate a modified version of the classic baroclinic experiment in which a juxtaposition of convective and motionless stratified layers is created by introducing a vertical salt stratification. The thermal convective motions are suppressed in a central region at mid-depth of the rotating tank, therefore double-diffusive convection rolls can develop only in thin layers located at top and bottom, where the salt stratification is weakest. For high enough rotation rates, the baroclinic instability destabilises the flow in the top and the bottom shallow convective layers, generating cyclonic and anticyclonic eddies separated by the stable stratified layer. Thanks to this alternation of layers resembling the convective and radiative layers of stars, the planetary’s atmospheric troposphere and stratosphere or turbulent layers at the sea surface above stratified waters, this new laboratory setup is of interest for both astrophysics and geophysical sciences. More specifically, it allows to study the exchange of momentum and energy between the layers, primarily by the propagation of internal gravity waves (IGW). PIV velocity maps are used to describe the wavy flow pattern at different heights. Using a co-rotating laser and camera, the wave field is well resolved and different wave types can be found: baroclinic waves, Kelvin and Poincaré type waves. The signature of small-scale IGW can also be observed attached to the baroclinic jet. The baroclinic waves occur at the thin convectively active layer at the surface and the bottom of the tank, though decoupled they show different manifestation of nonlinear interactions. The inertial Kelvin and Poincaré waves seem to be mechanically forced. The small-scale wave trains attached to the meandering jet point to an imbalance of the large-scale flow. For the first time, the simultaneous occurrence of different wave types is reported in detail for a differentially heated rotating annulus experiment.     

Difference between the Lagrangian trajectories and Eulerian residual velocity fields in the southwestern Yellow Sea

The responses to tidal and/or wind forces of Lagrangian trajectories and Eulerian residual velocity in the southwestern Yellow Sea are investigated using a high-resolution circulation model. The simulated tidal harmonic constants agree well with observations and existing studies. The numerical experiment reproduces the long-range southeastward Eulerian residual current over the sloping bottom around the Yangtze Bank also shown in previous studies. However, the modeled drifters deployed at the northeastern flank of the Yangtze Bank in the simulation move northeastward, crossing over this strong southeastward Eulerian residual current rather than following it. Additional sensitivity experiments reveal that the influence of the Eulerian tidal residual currents on Lagrangian trajectories is relatively weaker than that of the wind driven currents. This result is consistent with the northeastward movement of ARGOS surface drifters actually released in the southwestern Yellow Sea. Further experiments suggest that the quadratic nature of the bottom friction is the crucial factor, in the southwestern Yellow Sea, for the weaker influence of the Eulerian tidal residual currents on the Lagrangian trajectories. This study demonstrates that the Lagrangian trajectories do not follow the Eulerian residual velocity fields in the shallow coastal regions of the southwestern Yellow Sea.     

Wave breaking and bubble formation associate energy dissipation and wave setup

Ocean Dynamics - In this work, theoretical development of void fraction effect over wave energy dissipation and wave setup in a surf zone is made. The formulation incorporates simple energy...