Complex geophysical wake flows

Idealized studies of island wakes often use a cylinder-like island to generate the wake, whereas most realistic studies use a close representation of the oceanic bathymetry immersed in a complex representation of the “ambient” geophysical flows. Here, a system of multiple islands was placed into numerical and experimental channels, in order to focus on the complexity of the archipelago wake, including (a) the influence of small neighboring islands and (b) the role of the island-shelf. The numerical geostrophic and stratified channel was built using a three-dimensional primitive equation model, considering a realistic representation of the Madeira archipelago bathymetry, with prescribed initial and boundary conditions. Results from the simulations show that the neighboring islands alter the near-field wake. Small eddies generated by the neighboring islands lead to destabilization of the shear layers of the larger island. Laboratory experiments carried out in the Coriolis rotating tank corroborated this near-field disruptive mechanism. The neighboring island perturbation effect was present whatever the direction of the incoming flow, but under different regimes. North–south wakes produced geostrophic eddies (≥ R _d), whereas west–east wakes produced (exclusively) ageostrophic submesoscale eddies (< < R _d) which traveled offshore with wave-like motion. The archipelago shelf contributed to the asymmetric vertical migration of oceanic vorticity. Cyclonic vorticity dominated the surface dynamics, whereas anticyclonic circulation prevailed at the bottom part of the linearly stratified upper layer. This study identifies several likely wake scenarios induced by the Madeira archipelago, and may serve as guide for future multiscale numerical studies and in situ campaigns.     

Influence of the turbulence closure scheme on the finite-element simulation of the upwelling in the wake of a shallow-water island

A three-dimensional finite-element model is used to investigate the tidal flow around Rattray Island, Great Barrier Reef, Australia. Field measurements and visual observations show both stable eddies developing at rising and falling tide in the wake of the island. The water turbidity suggests intense upwelling able to carry bed sediments upwards. Based on previous numerical studies, it remains unclear at this point whether the most intense upwelling occurs near the centre of the eddies or off the island's tips, closer to the island. All these studies resorted to a very simple turbulence closure, with a zero-equation model whereby the coefficient of vertical viscosity is computed via an algebraic expression. In this work, we aim at studying the influence of the turbulence closure on model results, with emphasis on the prediction of vertical motions. The Mellor and Yamada level 2.5 closure scheme is used and an increase in the intensity of vertical transport is observed. This increase is partly explained by the fact that the Mellor and Yamada model takes into account the hysteresis effect in the time variation of turbulence variables. The influence of the advection of turbulence variables is estimated to be negligible. By a better representation of transient coastal phenomena, the Mellor and Yamada level 2.5 turbulence closure improves the model to a significant degree.     

The formation of headland/island sandbanks

There are four extensive sandbanks in the vicinity of the Isle of Portland, a headland in the English Channel. The formation and maintenance of the two most prominent of these sandbanks (one on either side of the headland) can largely be explained by net bedload convergence, driven by instantaneous headland eddies generated by tidal flow past the headland. However, there are also two less prominent sandbanks (again, one on either side of the headland), which are not located in zones of bedload convergence. It is suggested here that these latter two sandbanks were formed when the Isle of Portland was isolated from the mainland by a tidal strait. Relative sea-level data and radiocarbon dates indicate that this would have occurred ca. 9–7 ka BP, prior to the closure of the strait by sedimentation. Tidal flow through this strait generated eddy systems in addition to the headland eddies, leading to the formation of associated headland/island sandbanks. At 7 ka BP, sedimentation resulted in closure of the strait, leading to the present-day headland configuration, and subsequent reworking of these now moribund sandbanks formed by the strait. A series of idealised morphological model experiments, parameterised using bedrock depths and glacial isostatic adjustment model output of relative sea level, are here used to simulate this hypothesised sequence of sandbank evolution over the Holocene. The results of the model experiments are corroborated by in situ observations of bedforms and sediment characteristics, and by acoustic Doppler current profiler (ADCP) data applied to predictions of bedload transport over the sandbanks. In addition to demonstrating the mechanism which leads to the formation of sandbanks by tidal flow through a strait, the model results show that upon subsequent closure of such a strait, these sandbanks will no longer be actively maintained, in contrast to sandbanks which are continuously maintained by headland eddies.     

Experimental and numerical modelling of sedimentation in a rectangular shallow basin

Numerical simulation of flows in shallow reservoirs has to be checked for its consistency in predicting real flow conditions and sedimentation patterns. Typical flow patterns may exhibit flow separation at the inlet, accompanied by several recirculation and stagnation areas all over the reservoir surface. The aim of the present research project is to study the influence of the geometry of a reservoir on sediment transport and deposition numerically and experimentally, focusing on a prototype reservoir depth between 5 and 15 m as well as suspended sediment transport.
A series of numerical simulations is presented and compared with scaled laboratory experiments, with the objective of testing the sensitivity to different flow and sediment parameters and different turbulence closure schemes. Different scenarios are analyzed and a detailed comparison of preliminary laboratory tests and some selected simulations are presented.
The laboratory experiments show that suspended sediment transport and deposition are determined by the initial flow pattern and by the upstream and downstream boundary conditions. In the experiments, deposition in the rectangular basin systematically developed along the left bank, although inflow and outflow were positioned symmetrically along the centre of the basin. Three major horizontal eddies developed influencing the sediment deposition pattern. Although asymmetric flow patterns are privileged, a symmetric pattern can appear from time to time. This particular behaviour could also be reproduced by a two-dimensional depth-averaged flow and sediment transport model （CCHE2D）. The paper presents numerical simulations using different turbulence closure schemes （k-ε and eddy viscosity models）. In spite of the symmetric setup, these generally produced an asymmetric flow pattern that can easily switch sides depending on the assumptions made for the initial and boundary conditions. When using the laboratory experiment as a reference, the most reliable numerical results have been obtai     

Simulation of airflow around rain gauges: Comparison of LES with RANS models

Wind is responsible for systematic errors that affect rain gauge measurements. The authors investigate the use of computational fluid dynamics (CFD) to calculate airflow around rain gauges by applying a high-resolution large eddy simulation (LES) model to determine the flow fields around a measuring system of two rain gauges. The simulated air flow field is characterized by the presence of massive separation which induces the formation and shedding of highly unsteady eddies in the detached shear layers and wakes. Parts of these detached structures occur over the orifice of the rain gauges and may substantially affect the dynamics of the raindrops in this critical region. Non-dissipative LES methods used with fine enough meshes can successfully predict these eddies and their associated fluctuations. The authors compare statistics from LES with steady-state Reynolds averaged Navier–Stokes (RANS) simulations using the k–ε and shear stress transport k–ω turbulence models. They find that both RANS and LES models predict similar mean velocity distributions around the rain gauges. However, they determine the distribution of the resolved turbulent kinetic energy (TKE) to be strongly dependent on the RANS model used. Neither RANS model predictions of TKE are close to those of LES. The authors conclude that the failure of RANS to predict TKE is an important limitation, as TKE is needed to scale the local velocity fluctuations in stochastic models used to calculate the motion of raindrops in the flow field.     

Seasonal characteristics of the Tsushima Current in the Tsushima/Korea Strait obtained by a fine-resolution numerical model

The horizontal distribution of the Tsushima Current in the Tsushima/Korea Strait is assessed by a fine-resolution numerical experiment. The comparison of the model results with the observations along a section crossing the strait shows that the model represents relatively well, the general tendency of what was observed, such as the separation of the Tsushima Current into the western and eastern streams by the Tsushima Island. In summer, strong and relatively uniformly distributed surface currents enhance the formation of the wake downstream of the Tsushima Island. The axis of the countercurrent, embedded in the wake, is closer to the western stream. Anti-cyclonic eddies are shed near the downstream tip of the Tsushima Island and propagate along the boundary between the western stream and the wake. The exchange of water between the western stream and the wake takes place through the intermediation of these eddies. There is a net water supply from the western stream to the wake, which is then carried to the eastern stream by the countercurrent via the eastern coast of the Tsushima Island. In winter, currents, strongly barotropic, tend to have banded structures, especially in the region downstream of the western channel where isobaths converge in the downstream direction. The eddies found in this region in winter appear to be fundamentally different from those associated with the Tsushima Island wake. The necessary condition for barotropic instability is satisfied for the monthly mean currents in this region, suggesting that the currents are barotropically unstable in this region in winter.     

A numerical study of island wakes in the Southern California Bight

With the existence of eight substantial islands in the Southern California Bight, the oceanic circulation is significantly affected by island wakes. In this paper a high-resolution numerical model (on a 1 km grid), forced by a high-resolution wind (2 km), is used to study the wakes. Island wakes arise due both to currents moving past islands and to wind wakes that force lee currents in response. A comparison between simulations with and without islands shows the surface enstrophy (i.e., area-integrated square of the vertical component of vorticity at the surface) decreases substantially when the islands in the oceanic model are removed, and the enstrophy decrease mainly takes place in the areas around the islands. Three cases of wake formation and evolution are analyzed for the Channel Islands, San Nicolas Island, and Santa Catalina Island. When flows squeeze through gaps between the Channel Islands, current shears arise, and the bottom drag makes a significant contribution to the vorticity generation. Downstream the vorticity rolls up into submesoscale eddies. When the California Current passes San Nicolas Island from the northwest, a relatively strong flow forms over the shelf break on the northeastern coast and gives rise to a locally large bottom stress that generates anticyclonic vorticity, while on the southwestern side, with an adverse flow pushing the main wake current away from the island, positive vorticity has been generated and a cyclonic eddy detaches into the wake. When the northward Southern California Countercurrent passes the irregular shape of Santa Catalina Island, cyclonic eddies form on the southeastern coast of the island, due primarily to lateral stress rather than bottom stress; they remain coherent as they detach and propagate downstream, and thus they are plausible candidates for the submesoscale “spirals on the sea” seen in many satellite images. Finally, the oceanic response to wind wakes is analyzed in a spin-up experiment with a time-invariant wind that exhibits strips of both positive and negative curl in the island lee. Corresponding vorticity strips in the ocean develop through the mechanism of Ekman pumping.     

Observations and simulations of an unsteady island wake in the Firth of Forth, Scotland

Beamer Rock, a 50-m-wide island in the Firth of Forth, produces a distinctive von Kármán vortex street wake, the characteristics of which depend on the speed and direction of the tidal flow. ADCP (acoustic Doppler current profiler), CTD (conductivity–temperature–depth) and aerial photograph data were collected from the region during flood and ebb tidal flow under neap and spring conditions. Good agreement was found between the observations and the results from a fixed-grid depth-averaged numerical tidal model. The island wake parameter correctly predicted the unsteady nature of the wake, and the Strouhal number (defined in terms of flow past a circular cylinder) was found to give excellent predictions of the wake wavelength when scaled on the island width. Contrary to published results, the study shows that it is possible to accurately simulate an unsteady island wake using a relatively coarse fixed-grid numerical model.Responsible Editor: Jens Kappenberg     

A three‐dimensional numerical investigation of the idealized planetary boundary layer

Abstract

The nonlinear equations of motion are integrated numerically in time for a region of x‐y‐z space of volume 3h × h × h, where h turns out to be a height slightly above the level where the wind first attains the geostrophic flow direction. Only the ideal case is treated of a horizontal lower boundary, neutral stability, horizontal homogeneity of all dependent mean variables except the mean pressure, and statistically steady state. The resulting flow patterns are turbulent and the eddies transport required amounts of momentum vertically.

Topics which are investigated include the relative directions of stress, wind shear and wind; differences in Ekman wind spirals for the neutral numerical case and a stable atmospheric case; profiles of dimensionless turbulence statistics; effect of allowing the mean density to be either constant or to decrease with height; effect of the wind direction or latitude upon the turbulence intensities; and characteristic structure of the eddies in the planetary boundary layer.     

Sand settling through bedform-generated turbulence in rivers

Fluvial bedforms generate a turbulent wake that can impact suspended-sediment settling in the passing flow. This impact has implications for local suspended-sediment transport, bedform stability, and channel evolution; however, it is typically not well-considered in geomorphologic models. Our study uses a three-dimensional OpenFOAM hydrodynamic and particle-tracking model to investigate how turbulence generated from bedforms and the channel bed influences medium sand-sized particle settling, in terms of the distribution of suspended particles within the flow field and particle-settling velocities. The model resolved the effect of an engineered bedform, which altered the flow field in a manner similar to a natural dune. The modelling scenarios alternated bed morphology and the simulation of turbulence, using detached eddy simulation (DES), to differentiate the influence of bedform-generated turbulence relative to that of turbulence generated from the channel bed. The bedform generated a turbulent wake that was composed of eddies with significant anisotropic properties. The eddies and, to a lesser degree, turbulence arising from velocity shear at the bed substantially reduced settling velocities relative to the settling velocities predicted in the absence of turbulence. The eddies tended to advect sediment particles in their primary direction, diffuse particles throughout the flow column, and reduced settling likely due to production of a positively skewed vertical-velocity fluctuation distribution. Study results suggest that the bedform wake has a significant impact on particle-settling behaviour (up to a 50% reduction in settling velocity) at a scale capable of modulating local suspended transport rates and bedform dynamics. © 2020 John Wiley & Sons, Ltd.     

Tidally generated island wakes and surface water cooling over Izu Ridge

The Kuroshio current is well known for generating cold wakes behind islands over Izu Ridge in Northwestern Pacific. Observational data from the geostationary Himawari-8 satellite for 2015–2017 revealed the occurrence of cold waters during the period when the Kuroshio current flows away from the islands. With a focus on tidal currents, this study presents an investigation of dynamical processes responsible for the formation of areas with low sea surface temperature (SST) through the adoption of a high-resolution numerical ocean model for an event that happened in July 2017. Areas with cold water emerged only when tidal currents are included in the numerical model. The model results indicate the cold surface waters are formed in the vicinity of the islands because of upwelling and vertical mixing. Qualitative features of the cold water formation for each island are found to depend on its size, topography, and ambient currents. Near Kozu Island, the tidal excursion is large enough to cause eddy shedding. These shed eddies are stirred by tidal currents to extend the surface cooling effect to wider areas. Near Hachijo Island, a persistent wake is formed by the ambient northward current. Inclusion of tidal currents destabilizes the wake, and consequently leads to the formation of a low SST area, although no clear eddy shedding is detected. The flow patterns around the islands are classified using an additional non-dimensional parameter, defined as the ratio between tidal excursion and island diameter.

     

A note on the geostrophic flow past a crater in a rotating fluid

Abstract

Laboratory experiments are described on the flow past a solid obstacle in a rotating, homogeneous fluid. Specifically, the obstacle has the form of a walled crater specially constructed so that the volume of the depression is identically equal to the volume of the walls. The results show that closed streamlines occur rather more easily above such topography than above other obstacle types of the same scale but that the conditions for closure are determined essentially by the detailed geometry of the crater, the value of the Rossby number, and the depth of the fluid. The observed flow patterns are analysed and classified and attempts to quantify the most common flow type are made.     

An experimental study of Stewartson layer separation

Abstract

The separation of sidewall boundary layers in a rotating annulus of homogeneous fluid is studied experimentally. The flow is driven by a differentially rotating lid, and a very small uniform slope of the bottom causes a weak mountain vortex pair to form in the interior, away from the sidewalls. A necessary condition for aerodynamic separation of the sidewall boundary layers is derived and compared with the experimental results. The laboratory flow separates for parameters that are just slightly more inviscid than those required by the necessary condition for the existence of adverse pressure gradients at the wall. As the bottom friction is decreased further, the flow becomes unsteady and chaotic. The most interesting aspect of this problem is that chaotic interior behavior, associated with the separated boundary layer, is observed for parameter values for which the interior topographically forced flow is, by itself, essentially linear.     

Stochastic Models of Quasigeostrophic Turbulence

Atmospheric and oceanic eddies are believed to be manifestations of quasigeostrophic turbulence — turbulence that occurs in rapidly rotating, vertically stratified fluid systems. The heat, momentum, and water transport by these eddies constitute a significant component of the climate balance, without which climate change cannot be understood. A major, unsolved problem is whether the turbulent eddy fluxes can be parameterized in terms of the large-scale, background flow. In the past, stochastic models have been used quite extensively to investigate quasigeostrophic turbulence in the case in which the eddy statistics are isotropic and homogeneous. Unfortunately, these models ignore the background shear which is absolutely essential to maintaining the eddies in the presence of dissipation. Recent attempts to extend stochastic models to shear flows have shown significant skill in predicting the structure of the eddy fluxes in arbitrary, three-dimensionally varying flows. This paper provides an accessible introduction to these models. The topics reviewed include quasigeostrophic turbulence and two-dimensional turbulence, non-modal andoptimal perturbations, mathematical theory of stochastic models, stochastic model simulations with realistic background states, and recent closure theories. A list of unsolved problems concludes this review.     

Laboratory and numerical investigation of flow and transport near a seepage-face boundary

Laboratory and numerical modeling investigations were completed to study the unconfined ground water flow and transport processes near a seepage-face boundary. The laboratory observations were made in a radial sand tank and included measurements of the height of the seepage face, flow velocity near the seepage face, travel time distribution of multiple tracer slugs, and streamlines. All the observations were reliably reproduced with a three-dimensional, axi-symmetric, variably saturated ground water flow model. Physical data presented in this work demonstrate and quantify the importance of three-dimensional transport patterns within a seepage-face zone. The results imply that vertically averaged flow models that employ Dupuit approximations might introduce error in the analysis of localized solute transport near a seepage-face boundary. The experimental dataset reported in this work will also be of interest for those who are attempting to validate a numerical algorithm for solving ground water and contaminant discharge patterns near a surface-water boundary.     

Dynamics of intrathermocline vortices in a gyre flow over a seamount chain

The interaction of meddies with a complex distribution of seamounts is studied in a three-layer quasi-geostrophic model on the f-plane. This study aims at understanding if and how this seamount chain can represent a barrier to the propagation of these eddies and how it can be involved in their decay. The eddies are idealized as vortex patches in the middle layer, interacting with a regional cyclonic current and with ten idealized seamounts. The numerical code is based on the contour surgery technique. The initial position, radius, shape, number and polarity of the eddies are varied. The main results are the following: (1) Though they do not describe the unsteady flow, the streamlines of the regional and topographic flow provide a useful estimate of the vortex trajectories, in particular towards the major seamounts, where stronger velocity shears are expected. (2) The tallest and widest seamounts which have the largest vorticity reservoir are able to considerably erode the vortices, but also to draw anticyclones towards the seamount top. The ability of narrower seamounts to erode vortices is related to their multiplicity. (3) Only 1/3 of the anticyclones with about 30-km radius reach the southern boundary of the seamount chain, and their erosion is larger than 50 %. The other anticyclones are either completely eroded or trapped over a wide seamount top. Cyclones are less affected by seamounts because they oppose the topographic draft towards the seamount top and they drift along the side of the seamount. (4) Large vortices resist topographic erosion more efficiently. The rate of erosion grows from a few percent to about 35–50 % as the vortex radius decreases from about 60 to 30 km. Small cyclones are not eroded, contrary to small anticyclones (which completely decay), in relation with the different trajectories of these eddies in the vicinity of the seamounts. (5) The detailed vortex shape does not appear critical for their evolution, if they are close enough to the seamount chain initially. The interaction between a group of vortices initially north of the seamount chain can modify their trajectory to such an extent that they finally avoid collision with seamounts. (6) Finally, meddy trajectories across the Horseshoe Seamounts (data from the AMUSE experiment) show qualitative similarity with the vortex paths in the model. Several events of vortex decay also occur at comparable locations (in particular over the wide and tall seamounts) in the model and observations.     

Topographic eddies in temporally varying oceanic flows

Abstract

In this paper we examine the behaviour of oceanic unsteady flow impinging on isolated topography by means of numerical simulation. The ocean model is quasigeostrophic and forced by an oscillatory mean flow. The fluid domain is of the channel type and open-boundary numerical conditions are used to represent downstream and upstream flow.

In certain cases, vortex shedding, either cyclonic or anticyclonic, is observed in the lee of obstacles. Such shedding can be explained as the consequence of both an enhanced process of vorticity dissipation over the topography which locally affects the balance of potential vorticity on the advective timescale, and a periodic dominance of advective effects which sweep the fluid particles trapped on the seamount. For refined resolution and smallest viscosity the model will predict flows in which the shed eddies are coherent structures with closed streamlines.

The model suggests a mechanism by which topographically generated eddies may be swept away from a seamount in the ocean.     

A simulation of the Chilean Coastal Current and associated topographic upwelling near Valparaíso, Chile

A 4-year simulation of the surface circulation driven by the local wind on a section of the central Chilean coast is presented. The model is shown to reproduce the major observed features of the circulation. Comparison to observations of sea-surface temperature (SST) taken within the study area suggests that the model captures well coastal upwelling processes in the region. The circulation is shown to have two distinct modes corresponding to spring/summer and autumn/winter. During spring/summer sustained strong south-westerly wind forcing drives an equatorward coastal jet consistent with the Chile Coastal Current (CCC) and coastal upwelling at previously identified locations of intense upwelling at Topocalma Point and Curaumilla Point. Weaker winds during autumn/winter produce a slower CCC and a more homogenous SST field. Upwelling/relaxation and topographic eddies provide the main sources of variability on sub-seasonal time-scales in the model. The mechanisms responsible for each of these are discussed. Upwelling at Topocalma and Curaumilla Points is shown to be produced through generation of an upwelling Ekman bottom boundary layer following acceleration of the CCC close to the coast, reinforced by secondary circulation due to flow curvature around the headlands. Additional upwelling occurs north of Curaumilla Point due to development of shallow wind-driven overturning flow. Wind-sheltering is shown to be an important factor for explaining the fact that Valparaíso Bay is typically an upwelling shadow. Flow separation and eddy formation within Valparaíso Bay is seen to occur on the order of 10 times per year during relaxation after strong wind events and may persist for a number of weeks. Shorter lived topographic eddies are also seen to occur commonly at Topocalma and Toro Points. These eddies are shown to form in response to the surface elevation minima produced at each of these locations during upwelling.