Bottom Drag Research Articles

Eddy saturation and frictional control of the Antarctic Circumpolar Current

AbstractThe Antarctic Circumpolar Current is the strongest current in the ocean and has a pivotal impact on ocean stratification, heat content, and carbon content. The circumpolar volume transport is relatively insensitive to surface wind forcing in models that resolve turbulent ocean eddies, a process termed “eddy saturation.” Here a simple model is presented that explains the physics of eddy saturation with three ingredients: a momentum budget, a relation between the eddy form stress and eddy energy, and an eddy energy budget. The model explains both the insensitivity of circumpolar volume transport to surface wind stress and the increase of eddy energy with wind stress. The model further predicts that circumpolar transport increases with increased bottom friction, a counterintuitive result that is confirmed in eddy‐permitting calculations. These results suggest an unexpected and important impact of eddy energy dissipation, through bottom drag or lee wave generation, on ocean stratification, ocean heat content, and potentially atmospheric CO2.

Numerically modelling tidal dissipation with bottom drag in the oceans of Titan and Enceladus

Icy satellites that contain subsurface oceans require sufficient thermal energy to prevent the liquid portion of their interiors from freezing. We develop a numerical finite difference model to solve the Laplace Tidal Equations on a sphere in order to simulate tidal flow and thermal energy dissipation in these oceans, neglecting the presence of an icy lid. The model is applied to Titan and Enceladus, where we explore how Rayleigh (linear) and bottom (quadratic) drag terms affect dissipation. The latter drag regime can only be applied numerically. We find excellent agreement between our results and recent analytical work. Obliquity tide Rossby-wave resonant features become independent of ocean thickness under the bottom drag regime for thick oceans. We show that for Titan, dissipation from this Rossby-wave resonance can act to dampen the rate of outward orbital migration by up to 40% for Earth-like values of bottom drag coefficient. Gravity-wave resonances can act to cause inward migration, although this is unlikely due to the thin oceans required to form such resonances. The same is true of all eccentricity tide resonances on Enceladus, such that dissipation becomes negligible for thick oceans under the bottom drag regime.

The effect of channel constriction on the potential for tidal stream power

Tidal channels with narrow constrictions are attractive sites for electricity generation due to energy dense, high velocity flow through the constricted zones. This work uses a 1D model to systematically examine the effect of constriction on channel potential (theoretical maximum power) and transport in channels connecting two large water bodies (Type I) and channels connecting a large water body to an embayment/lagoon (Type II). Type I channels showed a monotonic decrease in potential and transport with increasing constriction due to enhanced bottom drag from the resultant high velocity zone. The effect of constriction on potential and transport in Type II channels varies depending on the relative geometries of the channel and embayment. Type II channels may be geometrically modified to increase power and in some instances this would simultaneously produce a high velocity zone. The flow reduction required to achieve a channel’s potential was invariant to changes in constriction for Type I channels and also Type II channels if a “lagoon geometry factor” is less than about 4. A simple approximation for potential provided in the literature for unconstricted channels is extended for use with constricted channels and an approximation for the drag coefficient required to achieve potential is provided.

A correction to the enhanced bottom drag parameterisation of tidal turbines

Hydrodynamic modelling is an important tool for the development of tidal stream energy projects. Many hydrodynamic models incorporate the effect of tidal turbines through an enhanced bottom drag. In this paper we show that although for coarse grid resolutions (kilometre scale) the resulting force exerted on the flow agrees well with the theoretical value, the force starts decreasing with decreasing grid sizes when these become smaller than the length scale of the wake recovery. This is because the assumption that the upstream velocity can be approximated by the local model velocity, is no longer valid. Using linear momentum actuator disc theory however, we derive a relationship between these two velocities and formulate a correction to the enhanced bottom drag formulation that consistently applies a force that remains close to the theoretical value, for all grid sizes down to the turbine scale. In addition, a better understanding of the relation between the model, upstream, and actual turbine velocity, as predicted by actuator disc theory, leads to an improved estimate of the usefully extractable energy. We show how the corrections can be applied (demonstrated here for the models MIKE 21 and Fluidity) by a simple modification of the drag coefficient.

Temporal evolution of the momentum balance terms and frictional adjustment observed over the inner shelf during a storm

Abstract. We investigate the rapidly changing equilibrium between the momentum sources and sinks during the passage of a single two-peak storm over the Catalan inner shelf (NW Mediterranean Sea). Velocity measurements at 24 m water depth are taken as representative of the inner shelf, and the cross-shelf variability is explored with measurements at 50 m water depth. During both wind pulses, the flow accelerated at 24 m until shortly after the wind maxima, when the bottom stress was able to compensate for the wind stress. Concurrently, the sea level also responded, with the pressure-gradient force opposing the wind stress. Before, during and after the second wind pulse, there were velocity fluctuations with both super- and sub-inertial periods likely associated with transient coastal waves. Throughout the storm, the Coriolis force and wave radiation stresses were relatively unimportant in the along-shelf momentum balance. The frictional adjustment timescale was around 10 h, consistent with the e-folding time obtained from bottom drag parameterizations. The momentum evolution at 50 m showed a larger influence of the Coriolis force at the expense of a decreased frictional relevance, typical in the transition from the inner to the mid-shelf.

Effect of model error representation in the Yellow and East China Sea modeling system based on the ensemble Kalman filter

To increase the accuracy of ocean predictions in the Yellow and East China Sea (YES), the satellite-borne sea surface temperature (SST) data have been assimilated to an operational ocean modeling system by applying an ensemble Kalman filter (EnKF). As the observed SST was assimilated continuously into the model with time, the ensemble spread decreased and the efficiency of data assimilation degenerated. To increase liability of the system and the ensemble spread, model uncertainties were represented stochastically by perturbing the model tendency parameters such as eddy viscosity, bottom drag coefficient, light attenuation depth, as well as atmospheric forcing. Data assimilation experiments were performed with forcing from a regional atmospheric model from September 2011 to February 2012. The assimilation results with and without the stochastically perturbed model parameters and atmospheric forcing were compared. The ensemble with the perturbations has larger spread and smaller root-mean-square deviation (RMSD) in temperature compared with the ensemble without the perturbations. The SST RMSD relative to anther supplementary SST dataset was reduced from 0.91 to 0.81 °C over the YES. The assimilation of the SST data improved the simulated SST compared with the observation at the ocean buoy stations, and also made the subsurface temperature profiles closer to the observed ones. The assimilation experiments showed that a stochastic representation of the model errors by the perturbations of the model parameters and atmospheric forcing increases the spread of the ensemble and improves the structure of background error covariance, which enhances the performance of the ensemble modeling system in the YES.

Surface gravity wave transformation across a platform coral reef in the Red Sea

AbstractThe transformation of surface gravity waves across a platform reef in the Red Sea is examined using 18 months of observations and a wave transformation model developed for beaches. The platform reef is 200 m across, 700 m long, and the water depth varies from 0.3 to 1.2 m. Assuming changes in wave energy flux are due to wave breaking and bottom drag dissipation, the wave transformation model with optimal parameters characterizing the wave breaking (γm = 0.25) and bottom drag (hydrodynamic roughness zo = 0.08 m) accounts for 75%–90% of the observed wave‐height variance at four sites. The observations and model indicate that wave breaking dominates the dissipation in a 20–30 m wide surf zone while bottom drag dominates the dissipation over the rest of the reef. Friction factors (drag coefficients) estimated from the observed wave energy balance range from fw = 0.5 to fw = 5 and increase as wave‐orbital displacements decrease. The observed dependence on wave‐orbital displacement is roughly consistent with extrapolation of an empirical relationship based on numerous laboratory studies of oscillatory flow. As a consequence of the dependence on wave‐orbital displacement, wave friction factors vary temporally due to changes in water depth and incident wave heights, and spatially across the reef as the waves decay.

COMPOSICIÓN Y ESTRUCTURA DEL ENSAMBLAJE DE CRUSTÁCEOS BRACHYURA DE LA PLATAFORMA CONTINENTAL DE LA GUAJIRA COLOMBIANA Y SU RELACIÓN CON LA PROFUNDIDAD Y LAS CARACTERÍSTICAS DEL SEDIMENTO

Brachyura crustaceans composition and structure assemblage along be continental shelf of La Guajira and its variation according to depth gradient and sediment characteristics were determined. 44 bottom drag samples were taken at 10 and 50 m depth using a semi globe demersal net, during March and April 2005. 83 species belonging to 21 families were identified; the most important families due to their abundance of specimens and amount of species were Goneplacidae, Portunidae, and Mithracidae; and dominant species were Glyptoplax smithii, with, 12.53 % of total abundance; Portunus spinicarpus, 7.42 % and Nemausa cornuta, 6.84 %. The non-metric multidimensional scaling analysis (NMDS) did not show any well defined sampling station clusters, but meaningful statistical differences were found in the assemblage structure according to depth gradient and the different kinds of sediments. The ANOSIM tests and the ordination analysis (NMDS) pointed out that there is a single assemblage that varies gradually with depth, and to a lesser degree by physical sediments characteristics. The ordination (NMDS) also reveals that the assemblage is more heterogeneous at 10 m than at 50 m depth, possibly as a result of the larger environmental variability close to the coast, in comparison with the environmental stability that characterizes deeper zones.

Tsunami Penetration in Tidal Rivers, with Observations of the Chile 2015 Tsunami in Rivers in Japan

An extensive data set of water level measurements of the September 2015 Chilean tsunami in rivers in Japan and a new methodology for data processing are used to verify that tsunami dissipation in a river at each instant and locality depends on the tidally-modified wave-locked slope of the river surface. As deduced from the observations, a relatively small tsunami or ocean noise traveling at mild wave-locked slopes can propagate virtually without losses to the upstream locations where observed tidal ranges are a fraction of that downstream; though at the higher slopes, tidal and riverine currents combined efficiently damp the shorter waves. The observed correlations between the tsunami admittance upriver and the traveled wave-locked slopes are explained analytically under the fully-nonlinear shallow-water approximation. It is found that the wave-locked slope in a purely incident wave relates to the bottom drag in the same manner as a steady surface slope does for a stationary flow. For a small-amplitude tsunami in the study rivers, the wave-locked slope in a co-propagating tidal wave defines the background current and thereby friction experienced by the tsunami.

Study on the current structure of the thermohaline front in the southeastern entrance of the Yellow Sea during winter

A thermohaline front is located at the southeastern entrance of the Yellow Sea in winter, and it is generated by the intrusion of warm saline water into the Yellow Sea caused by a strong northerly wind. Recently, a westward transversal current traveling away from the west coast of Korea toward the open sea area along the front was reported. The westward transversal current is dominant in the surface layer during the temperature inversion period. The formation and structure of this current are examined using a numerical vertical ocean-slice model. When two different water masses meet, a front is formed and adjusted geostrophically. In this frontal zone, a horizontal pressure gradient flow by the vertically inclined isopycnal occurs under the thermal wind process in a baroclinic effect, and the cold fresh coastal water moves westward along the front in the upper layer. The barotropic effect across the front and the bottom friction effect strengthen the westward component of the velocity. The velocity of the bottom layer decreases remarkably in the increase of the bottom drag coefficient. This means that the bottom friction with the strong background tidal current causes a reduction in the current in the bottom layer.

Gill’s model of the Antarctic Circumpolar Current, revisited: The role of latitudinal variations in wind stress

Gill’s (1968) model of the Antarctic Circumpolar Current (ACC) is reinterpreted for a stratified, reduced-gravity ocean, where the barotropic streamfunction is replaced by the pycnocline depth, and the bottom drag coefficient by the Gent and McWilliams eddy diffusivity. The resultant model gives a simple description of the lateral structure of the ACC that is consistent with contemporary descriptions of ACC dynamics. The model is used to investigate and interpret the sensitivity of the ACC to the latitudinal profile of the surface wind stress. A substantial ACC remains when the wind jet is shifted north of the model Drake Passage, even by several thousand kilometers. The integral of the wind stress over the circumpolar streamlines is found to be a useful predictor of the magnitude of the volume transport through the model Drake Passage, although it is necessary to correct for basin-wide zonal pressure gradients in order to obtain good quantitative agreement.

The Vertical Structure of Low-Frequency Motions in the Nearshore. Part II: Theory

AbstractField observations from a vertical stack of two-component current meters obtained from the 1994 Duck94 nearshore field experiment (presented in a companion paper by Lippmann, et al.) show significant vertical structure in energy, phase, and rotation of motions at low frequencies around 0.005 Hz. Low-frequency motions are typically modeled in the surfzone with the shallow-water (depth averaged) momentum equations that do not allow for any vertical structure. Following work from the shelf tidal community (Prandle), this study shows that the observations are consistent with the depth-varying momentum equations including shear stresses induced by a bottom boundary layer described by a constant eddy viscosity νt and bottom friction given by a constant drag coefficient and depth-averaged velocity . The bidirectional flow field is solved over arbitrary depth profiles varying only in the cross-shore direction h(x) in the presence of a vertically uniform mean alongshore current with cross-shore shear structure V(x). Analytic solutions are found to depend on νt, cd, h, ∂V/∂x, and the parameter , where σ and k are the radian frequency and alongshore wavenumber of the oscillating motion. Model behavior is explored by plotting solutions for a given parameter space as functions of the nondimensional depth H = λh and dimensionless friction parameter that combines the effects of bottom drag and vertical mixing. The behavioral changes in amplitude, phase shift, and rotational structure over the water column are qualitatively similar to those observed in the field.

Impact of topographic internal lee wave drag on an eddying global ocean model

The impact of topographic internal lee wave drag (wave drag hereafter) on several aspects of the low-frequency circulation in a high-resolution global ocean model forced by winds and air-sea buoyancy fluxes is examined here. The HYbrid Coordinate Ocean Model (HYCOM) is run at two different horizontal resolutions (one nominally 1/12° and the other 1/25°). Wave drag, which parameterizes both topographic blocking and the generation of lee waves arising from geostrophic flow impinging upon rough topography, is inserted into the simulations as they run. The parameterization used here affects the momentum equations and hence the structure of eddy kinetic energy. Lee waves also have implications for diapycnal mixing in the ocean, though the parameterization does not directly modify the density. Total near-bottom energy dissipation due to wave drag and quadratic bottom boundary layer drag is nearly doubled, and the energy dissipation due to quadratic bottom drag is reduced by about a factor of two, in simulations with an inserted wave drag compared to simulations having only quadratic bottom drag. With the insertion of wave drag, the kinetic energy is reduced in the abyss and in a three-dimensional global integral. Deflection by partial topographic blocking is inferred to be one reason why the near-bottom kinetic energy can increase in locations where there is little change in dissipation by quadratic bottom drag. Despite large changes seen in the abyss, the changes that occur near the sea surface are relatively small upon insertion of wave drag into the simulations. Both the sea surface height variance and geostrophic surface kinetic energy are reduced on global average by more than twice the seasonal variability in these diagnostics. Alterations in the intensified jet positions brought about by inserting wave drag are not distinguishable from the temporal variability of jet positions. Various statistical measures suggest that applying wave drag only within a fixed distance from the seafloor is not detrimental to the model performance relative to observations. However, the introduction of a novel diagnostic suggests that one way to improve the wave drag parameterization is to allow the vertical deposition of lee wave momentum flux to be spatially heterogeneous.

Numerical modelling of longitudinal dispersion in tidal flows with submerged vegetation

ABSTRACTThree-dimensional simulations are performed to investigate flow and transport mechanisms through submerged vegetation under the influence of tidal oscillations. A global minimum least squares method is proposed to compute the spatially-averaged lateral and vertical diffusivities. Our results indicate that the longitudinal dispersion coefficients have sinusoidal behaviour and oscillate with a similar frequency as the tidal forcing. The dispersion coefficients are reduced at high water and enhanced at low water, which may be attributed to increased vertical shear and turbulence due to stronger bottom drag in the presence of vegetation. The effects of varying tidal amplitude and frequency are investigated. The revealed regularity of variation in the dispersion process suggests that an empirical formulation describing the longitudinal dispersion coefficient may be found. Our findings are applicable for specific types of vegetation with intermediate submergence, such as mangrove pneumatophores planted in estuaries.

Hydrodynamic effect of a large offshore mussel suspended aquaculture farm

Hydrodynamic effect of a mussel suspended aquaculture farm on tidal currents off Gouqi Island, outside the Changjiang Estuary, China, was examined using observational data. The surface friction induced by suspended mussel aquaculture facilities in the top 3.5m was much stronger than bottom friction. As a result, tidal current velocity was reduced by 75–90% in the top layer and by about 45% at the bottom. The mean surface hydraulic roughness z0s̅ and surface drag coefficient C500̅, were estimated to be around 1.392–1.890m and 0.0875–0.1694, respectively. On the contrary, the mean bottom hydraulic roughness z0b̅ and bottom drag coefficient C100̅ within the farm, were estimated to be around 0.093–0.098m and 0.0226–0.0252, respectively. The observed surface friction velocity u⁎s have the same order of magnitude with the bottom friction velocity u⁎b. However, the surface hydraulic roughness z0s is about 20 times greater than that at the bottom. The local surface drag coefficient C500̅ is 3.5–7.5 times of that at the local bottom. The aquaculture facilities not only inhibited the horizontal tidal currents, but also appeared to have induced downwelling, which was shown by the vertical profiles of salinity, temperature, and chlorophyll-a (chl-a) fluorescence. Surface chl-a fluorescence was depleted to below 1.0μgL−1 inside the farm area, which was 80% less than the outside. The reduction of horizontal velocity and the presence of downwelling can significantly decrease food supply for filter-feeding mussels.

Stability constraints for oceanic numerical models: implications for the formulation of time and space discretizations

Except for vertical diffusion (and possibly the external mode and bottom drag), oceanic models usually rely on explicit time-stepping algorithms subject to Courant–Friedrichs–Lewy (CFL) stability criteria. Implicit methods could be unconditionally stable, but an algebraic system must be solved at each time step and other considerations such as accuracy and efficiency are less straightforward to achieve. Depending on the target application, the process limiting the maximum allowed time-step is generally different. In this paper, we introduce offline diagnostics to predict stability limits associated with internal gravity waves, advection, diffusion, and rotation. This suite of diagnostics is applied to a set of global, regional and coastal numerical simulations with several horizontal/vertical resolutions and different numerical models. We show that, for resolutions finer that 1/2°, models with an Eulerian vertical coordinate are generally constrained by vertical advection in a few hot spots and that numerics must be extremely robust to changes in Courant number. Based on those results, we review the stability and accuracy of existing numerical kernels in vogue in primitive equations oceanic models with a focus on advective processes and the dynamics of internal waves. We emphasize the additional value of studying the numerical kernel of oceanic models in the light of coupled space–time approaches instead of studying the time schemes independently from spatial discretizations. From this study, we suggest some guidelines for the development of temporal schemes in future generation multi-purpose oceanic models.

Parameterization of eddy fluxes based on a mesoscale energy budget

It has recently been proposed to formulate eddy diffusivities in ocean models based on a mesoscale eddy kinetic energy (EKE) budget. Given an appropriate length scale, the mesoscale EKE can be used to estimate an eddy diffusivity based on mixing length theory. This paper discusses some of the open questions associated with the formulation of an EKE budget and mixing length, and proposes an improved energy budget-based parameterization for the mesoscale eddy diffusivity. A series of numerical simulations is performed, using an idealized flat-bottomed β-plane channel configuration with quadratic bottom drag. The results stress the importance of the mixing length formulation, as well as the formulation for the bottom signature of the mesoscale EKE, which is important in determining the rate of EKE dissipation. In the limit of vanishing planetary vorticity gradient, the mixing length is ultimately controlled by bottom drag, though the frictional arrest scale predicted by barotropic turbulence theory needs to be modified to account for the effects of baroclinicity. Any significant planetary vorticity gradient, β, is shown to suppress mixing, and limit the effective mixing length to the Rhines scale. While the EKE remains moderated by bottom friction, the bottom signature of EKE is shown to decrease as the appropriately non-dimensionalized friction increases, which considerably weakens the impact of changes in the bottom friction compared to barotropic turbulence. For moderate changes in the bottom-friction, eddy fluxes are thus reasonably well approximated by the scaling relation proposed by Held and Larichev (1996), which ignores the effect of bottom friction.

Topographic vorticity generation, submesoscale instability and vortex street formation in the Gulf Stream

AbstractMeanders and eddies are routinely observed in the Gulf Stream along the South Atlantic Bight. We analyze here the instability processes that lead to the formation of submesoscale eddies on the cyclonic side of the Gulf Stream at the exit of the Florida Straits using very high resolution realistic simulations. The positive relative vorticity and potential vorticity on the cyclonic side of the Gulf Stream are strongly intensified in the Straits due to topographic drag along the continental slope. The bottom drag amplifies the cyclonic shear by generating large positive vertical vorticity values within the sloped turbulent bottom boundary layer. Downstream from the Straits the current becomes unstable to horizontal shear instability, rolls up, and forms a street of submesoscale vortices. The vortices expand as they propagate northward along the shelf, where they can generate large vertical displacements and enhance cross‐shelf exchanges.

The assessment of extactable tidal energy and the effect of tidal energy turbine deployment on the hydrodynamics in Zhoushan

In this study, we construct one 2-dimensional tidal simulation, using an unstructured Finite Volume Coastal Ocean Model (FVCOM). In the 2-D model, we simulated the tidal turbines through adding additional bottom drag in the element where the tidal turbines reside. The additional bottom drag was calculated from the relationship of the bottom friction dissipation and the rated rotor efficiency of the tidal energy turbine. This study analyzed the effect of the tidal energy turbine to the hydrodynamic environment, and calculated the amount of the extractable tidal energy resource at the Guishan Hangmen Channel, considering the rotor wake effect.

Comparing three conventional penaeid-trawl otter boards and the new batwing design

Three experiments were conducted to compare the engineering and catching performances of a hydrodynamic otter board termed the ‘batwing’ (comprising a sled-and-sail assembly, configured to operate at 20° angle of attack – AOA and with minimal bottom contact) against three conventional designs (termed the ‘flat-rectangular’, ‘kilfoil’ and ‘cambered’ otter boards) with AOAs between ∼30 and 40°. Experiments involved paired penaeid trawls (7.35-m headlines). The first experiment compared the batwing otter boards against all other designs (using 41-mm mesh trawls). In experiment 2, the batwing was tested against the flat-rectangular design (with 32-mm mesh trawls). In experiment 3, the batwing and flat-rectangular otter boards were towed without trawls to facilitate estimates of their partitioned drag. Overall, compared to the conventional otter boards, the batwings had up to ∼86 and ∼18% less bottom contact and drag, respectively. Among the conventional otter boards, the trawls spread by the cambered design caught up to 13% more school prawns Metapenaeus macleayi attributed to their greater solid profile. No significant differences were detected among catches of fish in the trawls spread by the various otter boards. The results reaffirm that because otter boards contribute towards a large proportion of total system drag (estimated here at up to ∼56%), their appropriate configuration is essential to maximise the fuel efficiency of penaeid-trawl systems.