Impact of tidal mixing with different scales of bottom roughness on the general circulation

The current study deals with a parameterization of diapycnal diffusivity in an ocean model. The parameterization estimates the diapycnal diffusivity depending on the location of tidal-related energy dissipation over rough topography. The scheme requires a bottom roughness map that can be chosen depending on the scales of topographic features. Here, we implement the parameterization on an ocean general circulation model, and we examine the sensitivity of the modeled circulations to different spatial scales of the modeled bottom roughness. We compare three simulations that include the tidal mixing scheme using bottom roughness calculated at three different ranges of spatial scales, with the largest scale varying up to 200 km. Three main results are discussed. First, the dependence of the topographic spectra with depth, characterized by an increase in spectral energy over short length scales in the deep ocean, influences the vertical profile of the diffusivity. Second, the changes in diffusivities lead to different equilibrium solutions in the Atlantic meridional overturning circulation and bottom circulation. In particular, the lower cell of the Atlantic overturning and the bottom water transport in the Pacific Ocean are stronger for stronger diffusivities at the corresponding basins and depths, and the strongest when using the small-scale roughness map. Third, a comparison of the density fields of the three simulations with the density field of World Ocean Atlas dataset, from which the models are initialized, shows that among the simulations with three different roughness maps, the one using small-scale bottom roughness map has the smallest density bias.

     

Modeling seasonal circulation, upwelling and tidal mixing in the Arafura and Timor Seas

The extensive shallow tropical seas off northern Australia, encompassing the Arafura and Timor Seas, have been identified as one of the most pristine marine environments on the planet. However, the remoteness and the absence of major industrial development that has contributed to this status have the additional consequence that relatively little is known about these systems. This study is the first to model oceanographic conditions across the tidally dominated Arafura and Timor Seas, and their seasonal variability. The results are based on a high-resolution (0.05°) ocean circulation model forced by realistic winds, waves and tides. The main focus of the study is on physical processes that influence the distributions of sediments and primary productivity across the system. Regions of high bottom stress and tidal mixing have been identified, including a large offshore area around Van Diemen Rise (Timor Sea). Lagrangian particle tracks have revealed a seasonal overturning cell that stretches across the Gulf of Carpentaria (Arafura Sea) with upwelling and downwelling on either side of the Gulf. The presence of coastal upwelling and downwelling is shown to provide a dynamically consistent explanation for the persistent turbid boundary layer observed around the shallow coastal waters of the Gulf.     

Upwelling and surface cold patches in the Yellow Sea in summer: Effects of tidal mixing on the vertical circulation

A three-dimensional, prognostic, wave–tide–circulation coupled numerical model is developed to study the effects of tidal mixing on the summertime vertical circulation in the Yellow Sea (YS). The distribution and mechanisms of upwelling are investigated by numerical means. Validated by historical tide gauge data, satellite sea surface temperature (SST) data, and cruise observation data, the model shows satisfactory performances in reproducing the dominant tidal system and three-dimensional sea temperature structure. Model results suggest that strong tidal mixing plays an important role in the formation of the vertical circulation in the YS. The Yellow Sea Cold Water Mass (YSCWM) is fringed by typical tidal mixing fronts (TMFs), which separate the cold, stratified water at the offshore side from the warm, well-mixed, shallow water at the other side. Considerable baroclinic gradient across the TMF makes the frontal zone the spot where the most active vertical circulation occurs; a secondary circulation is triggered with a distinct upwelling branch occurring mainly on the mixed side of the front. The numerical model produces systematic upwelling belts surrounding the YSCWM, and the upwelling is essentially induced by the TMF over sloping topography. The relative importance of tidal mixing and wind forcing for upwelling is further examined in numerical experiments. The southerly wind enhances the upwelling off the western coasts, but its overall influences in the whole YS are less important than tidal mixing. As shown by both satellite data and numerical modeling, the summertime SST field in the YS is featured by the stable existence of several site-selective surface cold patches (SCPs), most of which scatter in the waters off convex coastlines. One of the SCPs is found off Subei Bank, and the others are located off the eastern tip of Shandong Peninsula and off the three tips of Korean Peninsula. Two processes give rise to the SCP: on the one hand, TMF-induced upwelling supplies cold water from the deep layer; on the other hand, tidal mixing itself can stir the bottom water upward and homogenize the water column vertically. In the waters around the tips of peninsula in the YS, the tidal currents are extraordinarily strong, which provides a possible explanation for the site-selectivity of the SCPs.     

A non-breaking-wave-generated turbulence mixing scheme for a global ocean general circulation model

Ocean Dynamics - A novel vertical mixing scheme to describe the influence of the non-breaking surface waves in ocean general circulation models is proposed based on the second-order turbulence...     

Lateral tidal mixing in the Antarctic marginal seas

Tidal mixing plays an important role in the modification of dense water masses around the Antarctic continent. In addition to the vertical (diapycnal) mixing in the near-bottom layers, lateral mixing can also be of relevance in some areas. A numerical tide simulation shows that lateral tidal mixing is not uniformly distributed along the shelf break. In particular, strong mixing occurs all along the Ross Sea and Southern Weddell Sea shelf breaks, while other regions (e.g., the western Weddell Sea) are relatively quiet. The latter regions correspond surprisingly well to areas where indications for cross-shelf exchange of dense water masses have been found. The results suggest that lateral tidal mixing may account for the relatively small contribution of Ross Sea dense water masses to Antarctic Bottom Water.     

Influence of compound bedforms on hydraulic roughness in a tidal environment

The effect exerted by the seabed morphology on the flow is commonly expressed by the hydraulic roughness, a fundamental parameter in the understanding and simulation of hydro- and sediment dynamics in coastal areas. This study quantifies the hydraulic roughness of large compound bedforms throughout a tidal cycle and investigates its relationship to averaged bedform dimensions. Consecutive measurements with an acoustic Doppler current profiler and a multibeam echosounder were carried out in the Jade tidal channel (North Sea, Germany) along large compound bedforms comprising ebb-oriented primary bedforms with superimposed smaller secondary bedforms. Spatially averaged velocity profiles produced log-linear relationships which were used to calculate roughness lengths. During the flood phase, the velocity profiles were best described by a single log-linear fit related to the roughness created by the secondary bedforms. During the ebb phase, the velocity profiles were segmented, showing the existence of at least two boundary layers: a lower one scaling with the superimposed secondary bedforms and an upper one scaling with the ebb-oriented primary bedforms. The drag induced by the primary bedform during the ebb phase is suggested to be related to flow expansion, separation, and recirculation on the downstream side of the bedform. Three existing formulas were tested to predict roughness lengths from the local bedform dimensions. All three predicted the right order of magnitude for the average roughness length but failed to predict its variation over the tidal cycle.     

The effect of asymmetric dune roughness on tidal asymmetry in the Weser estuary

The bed of estuaries is often characterized by ripples and dunes of varying size. Whereas smaller bedforms adapt their morphological shape to the oscillating tidal currents, large compound dunes (here: asymmetric tidal dunes) remain stable for periods longer than a tidal cycle. Bedforms constitute a form roughness, that is, hydraulic flow resistance, which has a large-scale effect on tidal asymmetry and, hence, on hydrodynamics, sediment transport, and morphodynamics of estuaries and coastal seas. Flow separation behind the dune crest and recirculation on the steep downstream side result in turbulence and energy loss. Since the energy dissipation can be related to the dune lee slope angle, asymmetric dune shapes induce variable flow resistance during ebb and flood phases. Here, a noncalibrated numerical model has been applied to analyze the large-scale effect of symmetric and asymmetric dune shapes on estuarine tidal asymmetry evaluated by residual bed load sediment transport at the Weser estuary, Germany. Scenario simulations were performed with parameterized bed roughness of symmetric and asymmetric dune shapes and without dune roughness. The spatiotemporal interaction of distinct dune shapes with the main drivers of estuarine sediment and morphodynamics, that is, river discharge and tidal energy, is shown to be complex but substantial. The contrasting effects of flood- and ebb-oriented asymmetric dunes on residual bed load transport rates and directions are estimated to be of a similar importance as the controls of seasonal changes of discharge on these net sediment fluxes at the Lower Weser estuary. This corroborates the need to consider dune-induced directional bed roughness in numerical models of estuarine and tidal environments.     

The impact of the spatial variability in bottom roughness on tidal dynamics and energetics, a case study: the M 2 surface tide in the North European Basin

A modified version of the 3D finite-element hydrostatic model QUODDY-4 is used to quantify the changes in the dynamics and energetics of the M ₂ surface tide in the North European Basin, induced by the spatial variability in bottom roughness. This version differs from the original one, as it introduces a module providing evaluation of the drag coefficient in the bottom boundary layer (BBL) and by accounting for the equilibrium tide. The drag coefficient is found from the resistance laws for an oscillatory rotating turbulent BBL over hydrodynamically rough and incompletely rough underlying surfaces, describing how the wave friction factor as well as other resistance characteristics depend on the dimensionless similarity parameters for the BBL. It is shown that the influence of the spatial variability in bottom roughness is responsible for some specific changes in the tidal amplitudes, phases, and the maximum tidal velocities. These changes are within the model noise, while the changes in the averaged (over a tidal cycle) horizontal wave transport and the averaged dissipation of barotropic tidal energy may be of the same orders of magnitude as are the above energetic characteristics as such. Thus, contrary to present views, ignoring the spatial variability in bottom roughness at least in the North European Basin is only partially correct: it is valid for the tidal dynamics, but is liable to break down for the tidal energetics.     

The impact of the spatial variability in bottom roughness on tidal dynamics and energetics,a case study: the M 2 surface tide in the North European Basin

A modified version of the 3D finite-element hydrostatic model QUODDY-4 is used to quantify the changes in the dynamics and energetics of the M ₂ surface tide in the North European Basin, induced by the spatial variability in bottom roughness. This version differs from the original one, as it introduces a module providing evaluation of the drag coefficient in the bottom boundary layer (BBL) and by accounting for the equilibrium tide. The drag coefficient is found from the resistance laws for an oscillatory rotating turbulent BBL over hydrodynamically rough and incompletely rough underlying surfaces, describing how the wave friction factor as well as other resistance characteristics depend on the dimensionless similarity parameters for the BBL. It is shown that the influence of the spatial variability in bottom roughness is responsible for some specific changes in the tidal amplitudes, phases, and the maximum tidal velocities. These changes are within the model noise, while the changes in the averaged (over a tidal cycle) horizontal wave transport and the averaged dissipation of barotropic tidal energy may be of the same orders of magnitude as are the above energetic characteristics as such. Thus, contrary to present views, ignoring the spatial variability in bottom roughness at least in the North European Basin is only partially correct: it is valid for the tidal dynamics, but is liable to break down for the tidal energetics.

     

Experiments with a numerical model of coastal currents and tidal mixing fronts

A three-dimensional numerical model is used to simulate the development of disturbances on shelf-sea coastal currents and fronts. The model, which has a free surface, uses a finite difference grid ☐ scheme based on sigma coordinates. It has a semi-implicit scheme for the barotropic flow and a hydrid advection scheme to retain sharp fronts. The results demonstrate that (i) eddy formation follows changes at the inflow of a coastal current, (ii) a simple radiation boundary condition at the outflow produces nearly identical results for different outflow boundary positions, (iii) eddy growth, with matching behaviour of surface and bottom fronts, follows a small displacement on a tidal mixing front and (iv) effects of friction and mixing can significantly alter the behaviour of the front and the relative strength of the cyclonic and anticyclonic eddies formed.     

Far-field effects of tidal energy extraction in the Minas Passage on tidal circulation in the Bay of Fundy and Gulf of Maine using a nested-grid coastal circulation model

The Bay of Fundy in eastern Canada has the highest tides in the world. Harnessing the tidal energy in the region has long been considered. In this study, the effects of tidal in-stream energy extraction in the Minas Passage on the three-dimensional (3D) tidal circulation in the Bay of Fundy (BoF) and the Gulf of Maine (GoM) are examined using a nested-grid coastal ocean circulation model based on the Princeton Ocean Model (POM). The nested-grid model consists of a coarse-resolution (~4.5 km) parent sub-model for the GoM and a high-resolution (~1.5 km) child sub-model for the BoF. The tidal in-stream energy extraction in the model is parameterized in terms of nonlinear Rayleigh friction in the momentum equation. A suite of numerical experiments are conducted to determine the ranges of extractable tidal in-stream energy and resulting effects on the 3D tidal circulation over the Bay of Fundy and the Gulf of Maine (BoF-GoM) in terms of the Rayleigh friction coefficients. The 3D model results suggest that the maximum energy extraction in the Minas Passage increases tidal elevations and tidal currents throughout the GoM and reduces tidal elevations and circulation in the upper BoF, especially in the Minas Basin. The far-field effect of tidal energy extraction in the Passage on the 3D tidal circulation in the BoF-GoM is examined in two cases of harnessing tidal in-stream energy from (a) the entire water column and (b) the lower water column within 20 m above the bottom in the Passage. The 3D model results demonstrate that tidal in-stream energy extraction from the lower water column has less impact on the tidal elevations and circulation in the BoF-GoM than the energy extraction from the whole water column in the Minas Passage.     

Flow resistance and hydraulic geometry in bedrock rivers with multiple roughness length scales

Many models of incision by bedrock rivers predict water depth and shear stress from discharge; conversely, palaeoflood discharge is sometimes reconstructed from flow depth markers in rock gorges. In both cases, assumptions are made about flow resistance. The depth–discharge relation in a bedrock river must depend on at least two roughness length scales (exposed rock and sediment cover) and possibly a third (sidewalls). A conceptually attractive way to model the depth–discharge relation in such situations is to partition the total shear stress and friction factor, but it is not obvious how to quantify the friction factor for rough walls in a way that can be used in incision process models. We show that a single flow resistance calculation using a spatially averaged roughness length scale closely approximates the partitioning of stress between sediment and rock, and between bed and walls, in idealized scenarios. Both approaches give closer fits to the measured depth–discharge relations in two small bedrock reaches than can be achieved using a fixed value of Manning's n or the Chézy friction factor. Sidewalls that are substantially rougher or smoother than the bed have a significant effect on the partitioning of shear stress between bed and sidewalls. More research is needed on how best to estimate roughness length scales from observable or measurable channel characteristics. © 2019 John Wiley & Sons, Ltd.     

A general mixing equation with applications to Icelandic basalts

The mixing equation applied by Vollmer [1] to Pb and Sr isotope ratios is shown to be a general equation applicable to consideration of element and isotope ratios. The mixing equation is hyperbolic and has the form:Ax + Bxy + Cy + D = 0where the coefficients are dependent on the type of plot considered: i.e. ratio-ratio, ratio-element, or element-element. Careful use of this equation permits testing whether mixing is a viable process, places constraints on end member compositions, allows distinction between mixing of sources and mixing of magmas, and should allow distinction between recent mixing and long-term evolution of sources.The available chemical data for postglacial basalts from Iceland and along the Reykjanes Ridge are not consistent with either mixing of magmas or simple mixing of an enriched ocean island source with a depleted ocean ridge source. If the available analyses for basalts are representative of the source regions, the data are consistent with at least two models neither of which can be properly tested with the available data.(1) There are two separate mixing trends: one beneath Iceland with the alkali basalt source and a depleted Iceland source as end members; the second along the Reykjanes Ridge with a heterogeneous ocean ridge basalt source and a source similar to that for intermediate basalts on Iceland as end members. The depleted Iceland source and the depleted ocean ridge source are not the same.(2) The chemistry of the basalts is not determined by mixing. Instead the basalts are derived from a multiplicity of sources with a similar history which have been isolated for hundreds of millions of years.     

Correcting circulation biases in a lower-resolution global general circulation model with data assimilation

In this study, we aim at developing a new method of bias correction using data assimilation. This method is based on the stochastic forcing of a model to correct bias by directly adding an additional source term into the model equations. This method is presented and tested first with a twin experiment on a fully controlled Lorenz ’96 model. It is then applied to the lower-resolution global circulation NEMO-LIM2 model, with both a twin experiment and a real case experiment. Sea surface height observations are used to create a forcing to correct the poorly located and estimated currents. Validation is then performed throughout the use of other variables such as sea surface temperature and salinity. Results show that the method is able to consistently correct part of the model bias. The bias correction term is presented and is consistent with the limitations of the global circulation model causing bias on the oceanic currents.     

Impact of small-scale structures on estuarine circulation

We present a novel and challenging application of a 3D estuary-shelf model to the study of the collective impact of many small-scale structures (bridge pilings of 1 m × 2 m in size) on larger-scale circulation in a tributary (James River) of Chesapeake Bay. We first demonstrate that the model is capable of effectively transitioning grid resolution from ~?400 m down to ~?1 m near the pilings without introducing undue numerical artifact. We then show that despite their small sizes and collectively small area as compared to the total channel cross-sectional area, the pilings exert a noticeable impact on the large-scale circulation, and also create a rich structure of vortices and wakes around the pilings. As a result, the water quality and local sedimentation patterns near the bridge piling area are likely to be affected as well. However, when evaluating over the entire waterbody of the project area, the near field effects are weighed with the areal percentage which is small compared to that for the larger unaffected area, and therefore the impact on the lower James River as a whole becomes relatively insignificant. The study highlights the importance of the use of high resolution in assessing the near-field impact of structures.     

Alteration of bottom roughness by benthic organisms in a sandy coastal environment

This work deals with the potential influence of benthic communities on the sediment dynamics of the coastal zone, and specifically with the modifications to bottom roughness caused by communities and their effects on wave propagation across the coastal profile. Time-series of video observations of the sea bottom on the Ebro delta coast were analysed in order to estimate the bottom roughness associated with physical and biological morphological components and the sediment reworking rates caused by epifaunal organisms. Biological roughness was mainly caused by ophiuroids and tanatocenosis of bivalve and gastropod shells, which changed their abundance during the study period. The total biological roughness (K_bio) ranged between 0.27 and 0.81 cm and represented a significant part (<20%) of the total form drag roughness. Flattening of ripples caused by bioturbation was observed under low-energy conditions. Surface sediment perturbation and bioturbation rates were also estimated. Based on these observations a wave propagation model was applied in order to carry out a sensitivity analysis of the significance of biological roughness on wave dissipation in the study area under different wave conditions.     

On the influence of stratification and tidal forcing upon mixing in sill regions

A cross-sectional non-hydrostatic model with idealized topography was used to examine the processes influencing tidal mixing in the region of sills. Initial calculations with appropriate parameters for the sill at the entrance to Loch Etive showed that the model could reproduce the main features of the observed mixing in the region. In particular, the hydraulic jump in the sill region was reproduced, as was an intense mid-water jet that was observed to separate from the lee side of the sill. Shear instabilities associated with the jet appeared to be a source of mixing within the thermocline. In addition, internal lee waves were generated on the lee side of the sill, with the observed amplification because of trapping during the flood stage. Their magnitude and hence the mixing increased with increasing Froude number (F _r). In the case of vertically varying buoyancy frequency, its value near the sill top determined the F _r number, with its value below influencing internal waves magnitude at depth. At high F _r values particularly with strong currents, short waves and overturning occurred.     

Impact of the chemical composition of bottom sediments on internal phosphorus load

Examples of the impact of the content of organic matter and compounds of Al and Fe in freshwater sediments on the phosphorus release from the bottom are studied. The relationships between the phosphorus release from bottom sediments and organic matter concentration in sediments of 22 lakes of the world are obtained and discussed as a result of generalization of actual data.     

Modelling the tidal mixing fronts and seasonal stratification of the Northwest European Continental shelf

We investigate mixing processes under stratified conditions on the Northwest European Continental shelf using a numerical model (POLCOMS). Our results indicate that convection induced by vertical shearing of horizontal density gradients (‘shear-induced convection’) is a regularly occurring feature in the bottom and surface boundary layers in this open shelf-sea situation. Two types of turbulence models are investigated to study their capability for reproducing the observed location of tidal mixing fronts, and the physical processes occurring in seasonally stratified waters. The first model is a one-equation variant of the Mellor–Yamada model, whereas the second model combines a more recent second-momentum closure with a two-equation model. It is found that generally mean frontal positions (as estimated from ICES data) are predicted more accurately by the two-equation model. The one-equation model reproduces the mean frontal locations to 18.1 km (<3 grid spacings) and the two-equation model to 17.1 km; although in the Celtic Sea the accuracy is ∼33 and ∼12 km, respectively. Comparison with historical tide gauges, current metres, CTD stations, and thermistor chain data from the North Sea Project all show an improvement in accuracy when the two-equation model is used. This is particularly apparent in the model's ability to reproduce the spring–neap variability during stratification. We find that in the presence of shear-induced convection the routinely applied clipping of the turbulent length-scale, previously thought to be a minor ingredient in a turbulence model, has a dramatic effect on the results: if the length-scale clipping is not applied, substantial over-mixing is observed to occur. The causes and possible remedies of this effect are investigated. Overall our results demonstrate a sensitivity to the details of the turbulence model that is significantly greater than previously thought.