Topography Interaction Research Articles

The sandpaper theory of flow–topography interaction for multilayer shallow-water systems

The sandpaper theory of flow–topography interaction for multilayer shallow-water systems

The sandpaper theory of flow–topography interaction for homogeneous shallow-water systems

Recent studies reveal the dramatic impact of seafloor roughness on the dynamics and stability of broad oceanic flows. These findings motivate the development of parameterizations that concisely represent the effects of small-scale bathymetric patterns in theoretical and coarse-resolution numerical circulation models. The previously reported quasi-geostrophic ‘sandpaper’ theory of flow–topography interaction a priori assumes gentle topographic slopes and weak flows with low Rossby numbers. Since such conditions are often violated in the ocean, we now proceed to formulate a more general model based on shallow-water equations. The new version of the sandpaper model is validated by comparing roughness-resolving and parametric simulations of the flow over a corrugated seamount.

Emplacement of lava flows on eroded terrain, part I: The case of the Tiretaine valley (Chaîne des Puys, France)

Lava flows often erupt onto eroded landscapes, flowing across plateaus, into valleys and basins, and down escarpments. With the Tiretaine lava flow system in the Chaîne des Puys (Central France), lava flowed over the complex topography of an ancient rift margin. Erupted 41.3 ± 1.3 ka ago onto the granite plateau of the Massif Central, flow initially advanced over a surface that sloped 2°E. On reaching a fault scarp that delimits the plateau, flows descended the 6° slopes of a ravine that cuts the scarp E-W. In part 1 of this work we thus consider the case where lava is emplaced onto relatively flat terrain, then passes over a break-in-slope onto steeper slopes. To do this, we carried out mapping and facies analysis down this ∼6-km-long system, collecting 24 samples on which we completed textural and geochemical analyses. Results reveal three lava facies:(i)a 3 × 2 km proximal zone of inflated pāheohoe with a thickness of 25–50 m;(ii)a channelized medial zone with simple rubble levees nested in the ravine; and(iii)a valley-ponded distal zone with tubes and well-formed columnar jointing.Through simple mass balance calculations, and analogy with systems displaying similar facies, we find that the proximal inflated zone was fed at relatively low (1–5 m3/s) effusion rates. This built the proximal portion of the flow field over a period of 1–6 years, forming a volume of flow-field stored, degassed lava. Failure of the eastern edge of the proximal flow field at the head of the Tiretaine ravine fed high (215–315 m3/s) effusion rate flow down the ravine, to build a channelized flow system in just a few hours. However, the presence of a lava dam at the mouth of the ravine impeded further flow and resulted in ponding. This ponded volume then cooled in-place over a period of 10–11 years. Breaks-in-slope, and the resulting lava–topography interaction, thus created a system of reservoirs and transfers, with different flow rates, dynamics and emplacement time scales. For our case, where the lava flow system is mostly in a UNESCO World Heritage site, the study provides scientific support for Geoheritage efforts, outreach, and initiatives to support protection of geologically important sites.

Spin-down of a baroclinic vortex by irregular small-scale topography

This study explores the impact of small-scale variability in the bottom relief on the dynamics and evolution of broad baroclinic flows in the ocean. The analytical model presented here generalizes the previously reported barotropic ‘sandpaper’ theory of flow–topography interaction to density-stratified systems. The multiscale asymptotic analysis leads to an explicit representation of the large-scale effects of irregular bottom roughness. The utility of the multiscale model is demonstrated by applying it to the problem of topography-induced spin-down of an axisymmetric vortex. We find that bathymetry affects vortices by suppressing circulation in their deep regions. As a result, vortices located above rough topography tend to be more stable than their flat-bottom counterparts. The multiscale theory is validated by comparing corresponding topography-resolving and parametric simulations.

Impact of Gulf Stream Warm-Core Rings on Slope Water Intrusion into the Gulf of Maine

Abstract Intruding slope water is a major source of nutrients to sustain the high biological productivity in the Gulf of Maine (GoM). Slope water intrusion into the GoM is affected by Gulf Stream warm-core rings (WCRs) impinging onto the nearby shelf edge. This study combines long-term mooring measurements, satellite remote sensing data, an idealized numerical ocean model, and a linear coastal-trapped wave (CTW) model to examine the impact of WCRs on slope water intrusion into the GoM through the Northeast Channel. Analysis of satellite sea surface height and temperature data shows that the slope sea region off the GoM is a hotspot of ring activities. A significant linear relationship is found between interannual variations of ring activities in the slope sea region off the GoM and bottom salinity at the Northeast Channel, suggesting the importance of WCRs in modulating variability of intruding slope water. Analysis of the mooring data reveals enhanced slope water intrusion through bottom-intensified along-channel flow following impingements of WCRs on the nearby shelf edge. Numerical simulations qualitatively reproduce the observed WCR impingement processes and associated episodic enhancement of slope water intrusion in the Northeast Channel. Diagnosis of the model result indicates that baroclinic CTWs excited by the ring–topography interaction are responsible for the episodically intensified subsurface along-channel inflow, which carries more slope water into the GoM. A WCR that impinges onto the shelf edge to the northeast of the Northeast Channel tends to generate stronger CTWs and cause stronger enhancement of the slope water intrusion into the GoM.

Lagrangian Vertical Spreading and Its Relation to Diapycnal Diffusivity

Abstract The present study provides a theoretical linkage between the Lagrangian dispersion diffusivity and the diapycnal diffusivity in the context of vertical mixing, although previous studies have demonstrated their equivalence under the assumptions of stationary, homogeneous, and stratified turbulence. This is achieved in a new coordinate in which the fluid density is adiabatically sorted in the vertical direction. In the density-sorted coordinate, 1) the vertical motion of Lagrangian particles is solely subjected to irreversible diffusion process; 2) relations between Lagrangian dispersion diffusivity, diapycnal diffusivity, and the generalized Osborn diffusivity are exact; and 3) a generalization of the classical Munk balance between vertical advection and diffusion is also illustrated in an exact sense. Since the adiabatic sorting of the fluid does not require the turbulence to be statistically stationary, homogeneous, and stably stratified, the present solution eliminated these requirements and is thus more general than previous studies. Upon this, a new Lagrangian diagnostic is proposed to quantify the local, instantaneous, and irreversible mixing. Applications are demonstrated in a turbulent scenario of internal wave breaking induced by current–topography interaction, in which the turbulence is intermittent, nonstationary, and inhomogeneous.

The Impact of Fortnightly Stratification Variability on the Generation of Baroclinic Tides in the Luzon Strait

The impact of fortnightly stratification variability induced by tide–topography interaction on the generation of baroclinic tides in the Luzon Strait is numerically investigated using the MIT general circulation model. The simulation shows that advection of buoyancy by baroclinic flows results in daily oscillations and a fortnightly variability in the stratification at the main generation site of internal tides. As the stratification for the whole Luzon Strait is periodically redistributed by these flows, the energy analysis indicates that the fortnightly stratification variability can significantly affect the energy transfer between barotropic and baroclinic tides. Due to this effect on stratification variability by the baroclinic flows, the phases of baroclinic potential energy variability do not match the phase of barotropic forcing in the fortnight time scale. This phenomenon leads to the fact that the maximum baroclinic tides may not be generated during the maximum barotropic forcing. Therefore, a significant impact of stratification variability on the generation of baroclinic tides is demonstrated by our modeling study, which suggests a lead–lag relation between barotropic tidal forcing and maximum baroclinic response in the Luzon Strait within the fortnightly tidal cycle.

Experiments on the influence of spot fire and topography interaction on fire rate of spread.

Spotting is thought to increase wildfire rate of spread (ROS) and in some cases become the main mechanism for spread. The role of spotting in wildfire spread is controlled by many factors including fire intensity, number of and distance between spot fires, weather, fuel characteristics and topography. Through a set of 30 laboratory fire experiments on a 3 m x 4 m fuel bed, subject to air flow, we explored the influence of manually ignited spot fires (0, 1 or 2), the presence or absence of a model hill and their interaction on combined fire ROS (i.e. ROS incorporating main fire and merged spot fires). During experiments conducted on a flat fuel bed, spot fires (whether 1 or 2) had only a small influence on combined ROS. Slowest combined ROS was recorded when a hill was present and no spot fires were ignited, because the fires crept very slowly downslope and downwind of the hill. This was up to, depending on measurement interval, 5 times slower than ROS in the flat fuel bed experiments. However, ignition of 1 or 2 spot fires (with hill present) greatly increased combined ROS to similar levels as those recorded in the flat fuel bed experiments (depending on spread interval). The effect was strongest on the head fire, where spot fires merged directly with the main fire, but significant increases in off-centre ROS were also detected. Our findings suggest that under certain topographic conditions, spot fires can allow a fire to overcome the low spread potential of downslopes. Current models may underestimate wildfire ROS and fire arrival time in hilly terrain if the influence of spot fires on ROS is not incorporated into predictions.

Nutrient transport and dynamics in the South China Sea: A modeling study

The South China Sea (SCS) is one of the largest marginal seas in the world, yet the processes that drive its nutrient distribution are not well understood. Using the three-dimensional China Sea Multiscale Ocean Modeling System (CMOMS) embedded with a nitrogen-phosphorus-phytoplankton-zooplankton-detritus ecosystem model, we investigated nutrient transport and dynamics in the SCS. The model was well validated with field and remotely sensed observations. We found that the unique layered distribution of nutrients that increases from north to south in the upper layer and increases in the opposite direction in the middle and deep layers. We found that the lateral and vertical fluxes associated with three-dimensional ocean circulation and biogeochemical processes shape the distribution. The lateral fluxes are provided extrinsically by the sandwich-like transport through Luzon Strait (LS) and the exchanges through other straits, and intrinsically by the interior vertical motion due to flow-slope topography interaction. The nutrient deficiency in the upper layer due to dilution by inflow from the Western Pacific Ocean is mainly compensated by the upward nutrient-rich deep water. The nutrient transport is jointly regulated by volume transport and the uneven spatiotemporal distribution of nutrients. We demonstrated that labile organic matter plays an important role in total nutrient budgets. In euphotic layer, biological production is the major sink, but remineralization contributions to PO4 are more important than to NO3 due to the higher recycling rate of PO4. In the shelf water, coastal upwelling serves as major source for both NO3 and PO4, vertical diffusion is another important source of PO4 due to the strong downward increasing gradient.

Dissolved inorganic nitrogen and particulate organic nitrogen budget in the Yucatán shelf: driving mechanisms through a physical–biogeochemical coupled model

Abstract. Continental shelves are the most productive areas in the seas with the strongest implications for global nitrogen cycling. The Yucatán shelf (YS) is the largest shelf in the Gulf of Mexico (GoM); however, its nitrogen budget has not been quantified. This is largely due to the lack of significant spatio-temporal in situ measurements and the complexity of the shelf dynamics, including coastal upwelling, coastal-trapped waves (CTWs), and influence of the Yucatán Current (YC) via bottom Ekman transport and dynamic uplift. In this paper, we investigate and quantify the nitrogen budget of dissolved inorganic nitrogen (DIN) and particulate organic nitrogen (PON) in the YS using a 9-year output from a coupled physical–biogeochemical model of the GoM. The sum of DIN and PON is here referred to as total nitrogen (TN). Results indicate that the main entrance of DIN is through its southern (continental) and eastern margins. The TN is then advected to the deep oligotrophic Bay of Campeche and central GoM. It is also shown that the inner shelf (bounded by the 50 m isobath) is “efficient” in terms of TN, since all DIN imported into this shelf is consumed by the phytoplankton. Submarine groundwater discharges (SGDs) contribute 20 % of the TN, while denitrification removes up to 53 % of TN that enters into the inner shelf. The high-frequency variability of the TN fluxes in the southern margin is modulated by fluxes from the YC due to enhanced bottom Ekman transport when the YC leans against the shelf break (250 m isobath) on the eastern margin. This current–topography interaction can help to maintain the upwelling of Cape Catoche, uplifting nutrient-rich water into the euphotic layer. The export of TN at both western and northwestern margins is modulated by CTWs with a mean period of about 10 d in agreement with recent observational and modelling studies.

Time-dependent Kelvin cat-eye structure due to current–topography interaction

Non-stationary, rotational, linear surface waves are considered where the underlying sheared current has constant vorticity. A time-dependent study is presented on the formation and persistence of a Kelvin cat-eye structure in the presence of bottom topography. The flow domain is two-dimensional, which allows for the use of a conformal mapping and working in a computational flat-bottom domain. In some cases an initial disturbance is prescribed, while in others the waves are generated from rest. Submarine particle dynamics numerically captures the horizontal critical layer, defined by closed orbits separating the fluid domain into two disjoint regions. In the wave’s moving frame, these recirculation regions are structured in the form of Kelvin cat-eyes. Owing to the interaction with topography, the usual travelling-wave formulation is abandoned and the critical layer is identified through a non-stationary set of equations. The respective time-dependent Kelvin cat-eye structure dynamically adjusts itself at the onset of wave–topography interaction, without losing its integrity. The formation of a Kelvin cat-eye structure is also studied in the case where the surface is initially undisturbed. Surface waves are generated from either the current–topography interaction or by a pressure distribution suddenly imposed along the free surface. Under the pressure forcing, an isolated cat-eye forms with a single recirculation region beneath the wave.

Multicore structures and the splitting and merging of eddies in global oceans from satellite altimeter data

Abstract. This study investigated the statistics of eddy splitting and merging in the global oceans based on 23 years of altimetry data. Multicore structures were identified using an improved geometric closed-contour algorithm of sea surface height. Splitting and merging events were discerned from continuous time series maps of sea level anomalies. Multicore structures represent an intermediate stage in the process of eddy evolution, similar to the generation of multiple nuclei in a cell as a preparatory phase for cell division. Generally, splitting or merging events can substantially change (by a factor of 2 or more) the eddy scale, amplitude, and eddy kinetic energy. Specifically, merging (splitting) generally causes an increase (decrease) of eddy properties. Multicore eddies were found to tend to split into two eddies with different intensities. Similarly, eddy merging is not an interaction of two equal-intensity eddies, and it tends to manifest as a strong eddy merging with a weaker one. A hybrid tracking strategy based on the eddy overlap ratio, considering both multicore and single-core eddies, was used to confirm splitting and merging events globally. The census revealed that eddy splitting and merging do not always occur most frequently in eddy-rich regions; e.g., their frequencies of occurrence in the Antarctic Circumpolar Current and western boundary currents were found to be greater than in midlatitude regions (20–35∘) to the north and south. Eddy splitting and merging are caused primarily by an unstable configuration of multicore structures due to obvious current– or eddy–topography interaction, strong current variation, and eddy–mean flow interaction.

Energy Conversion Routes in the Western Mediterranean Sea Estimated from Eddy–Mean Flow Interactions

AbstractEnergy conversion routes are investigated in the western Mediterranean Sea from the eddy–mean flow interactions. The sources of eddy kinetic energy are analyzed by applying a regional formulation of the Lorenz energy cycle to 18 years of numerical simulation at eddy-resolving resolution (3.5 km), which allows for identifying whether the energy exchange between the mean and eddy flow is local or nonlocal. The patterns of energy conversion between the mean and eddy kinetic and potential energy are estimated in three subregions of the domain: the Alboran Sea, the Algerian Basin, and the northern basin. The spatial characterization of the energy routes hints at the physical mechanisms involved in maintaining the balance, suggesting that flow–topography interaction is strongly linked to eddy growth in most of the domain.

Dominant Circulation Patterns of the Deep Gulf of Mexico

AbstractThe large-scale circulation of the bottom layer of the Gulf of Mexico is analyzed, with special attention to the historically least studied western basin. The analysis is based on 4 years of data collected by 158 subsurface floats parked at 1500 and 2500 m and is complemented with data collected by current meter moorings in the western basin during the same period. Three main circulation patterns stand out: a cyclonic boundary current, a cyclonic gyre in the abyssal plain, and the very high eddy kinetic energy observed in the eastern Gulf. The boundary current and the cyclonic gyre appear as distinct features, which interact in the western tip of the Yucatan shelf. The persistence and continuity of the boundary current is addressed. Although high variability is observed, the boundary flow serves as a pathway for water to travel around the western basin in approximately 2 years. An interesting discovery is the separation of the boundary current over the northwestern slope of the Yucatan shelf. The separation and retroflection of the along-slope current appears to be a persistent feature and is associated with anticyclonic eddies whose genesis mechanism remains to be understood. As the boundary flow separates, it feeds into the westward flow of the deep cyclonic gyre. The location of this gyre—named the Sigsbee Abyssal Gyre—coincides with closed geostrophic contours, so eddy–topography interaction via bottom form stresses may drive this mean flow. The contribution to the cyclonic vorticity of the gyre by modons traveling under Loop Current eddies is discussed.

TopoWellPlate: A Well-Plate-Based Screening Platform to Study Cell-Surface Topography Interactions.

The field of biomaterial engineering is increasingly using high-throughput approaches to investigate cell-material interactions. Because most material libraries are prepared as chips, immunofluorescence-based read-outs are used to uniquely image individual materials. This paper proposes to produce libraries of materials using a well-based strategy in which each material is physically separated, and thus compatible with standard biochemical assays. In this work, the TopoWellPlate, a novel system to study cell-surface topography interaction in high-throughput is presented. From a larger library of topographies, 87 uniquely defined bioactive surface topographies are identified, which induce a wide variety of cellular morphologies. Topographically enhanced polystyrene films are fabricated in a multistep cleanroom process and served as base for the TopoWellPlate. Thermal bonding of the films to bottomless 96-well plates results in a cell culture ready, topographically enhanced, 96-well plate. The overall metabolic activity of bone marrow-derived human mesenchymal stem cells is measured to show the functionality of the TopoWellPlate as a screening tool, which showed a 2.5-fold difference range in metabolic activity per cell. TopoWellPlates of this and other topographical designs can be used to analyze cells using the wealth of standardized molecular assays available and thus disclose the mechanisms of biomaterials-induced mechanotransduction.

Analysis of current–topography interaction in remote sensing imaging procedures for shallow water topography

Underwater topography can be imaged using remote sensing methods. Numerous studies have been conducted to understand the imaging mechanism of shallow water topography. However, current–topography interaction constitutes the weakest link in the remote sensing imaging mechanism of underwater topography. In addition, few studies focused on different topography patterns. Current velocity is highly correlated with bathymetry, and velocity gradient is used as an indicator of sea surface roughness. In this research, we analyzed the distribution characteristics of current velocity and velocity gradient in different cases using a 3-dimensional (3-D) hydrodynamic model to discuss the current–topography interaction part of the remote sensing imaging mechanism, especially the modulation by current parallel or normal to the underwater topography, both positive and negative. Results showed remarkable agreement between 3-D current analysis and surface velocity analysis. Parallel and normal currents had different responses to different topography types. The distribution of surface current gradient showed opposite features over negative and positive topography in parallel and normal current fields. This can be used to distinguish negative topography from positive topography with different current directions to a certain extent.

A model for Faraday pilot waves over variable topography

Couder et al. (Nature, vol. 437 (7056), 2005, p. 208) discovered that droplets walking on a vibrating bath possess certain features previously thought to be exclusive to quantum systems. These millimetric droplets synchronize with their Faraday wavefield, creating a macroscopic pilot-wave system. In this paper we exploit the fact that the waves generated are nearly monochromatic and propose a hydrodynamic model capable of quantitatively capturing the interaction between bouncing drops and a variable topography. We show that our reduced model is able to reproduce some important experiments involving the drop–topography interaction, such as non-specular reflection and single-slit diffraction.

A Three-Layer Alternating Spinning Circulation in the South China Sea

AbstractUnderstanding of the three-dimensional circulation in the South China Sea (SCS) is crucial for determining the transports of water masses, energy, and biogeochemical substances in the regional and adjacent larger oceans. The circulation’s kinematic and dynamic natures, however, are largely unclear. Results from a three-dimensional numerical ocean circulation model and geostrophic currents, derived from hydrographic data, reveal the existence of a unique, three-layer, cyclonic–anticyclonic–cyclonic (CAC) circulation in the upper (<750 m), middle (750–1500 m), and deep (>1500 m) layers in the SCS with differing seasonality. An inflow–outflow–inflow structure in Luzon Strait largely induces the CAC circulation, which leads to vortex stretching in the SCS basin because of a lateral planetary vorticity flux in each of the respective layers. The formation of joint effects of baroclinicity and relief (JEBAR) is an intrinsic dynamic response to the CAC circulation. The JEBAR arises from the CAC flow–topography interaction in the SCS.

Interpreting layer thickness advection in terms of eddy–topography interaction

A parameterization for the spatial pattern of the eddy induced thickness advection parameter estimated from a dynamically consistent data assimilation procedure is presented. Values of the thickness advection parameter are predominantly negative (positive) over seamounts, and positive (negative) over the deep ocean in the southern (northern) hemisphere along strong currents; its magnitude is large at high latitudes but low in the tropical regions. Those characteristics motivate a parameterization based on the Coriolis parameter, the bottom depth and an eddy length scale. As a parameterization for an eddy streamfunction, the associated bolus velocities advect density anti-cyclonically (cyclonically) around seamounts (troughs). Although the parameterization has the same form as Holloway’s streamfunction for the Neptune effect, and is also related to eddy–topography interactions, Holloway’s streamfunction is in contrast applied to the momentum equation. The parameterization is independently confirmed by the flux-mean gradient relation from the output of a high resolution model. The effect of the proposed scheme is investigated using a channel model with idealized bottom topographies and a global ocean circulation model with realistic bottom topography. In agreement with the high resolution model, our scheme generates cold (warm) domes and cyclonic circulations over seamounts (troughs), which is consistent with the eddy movement in presence of the topographic β effect. This provides a different mechanism for eddy–topography interaction than the Neptune effect, which generates circulations of opposing sign.

Pyroclastic density currents and local topography as seen with the conveyer model

Pyroclastic density currents (PDCs) are multiphase flows generated during explosive volcanic eruptions, and they move down the volcano, and over the surrounding topography. The flow–topography interaction can play a fundamental role in the sedimentary processes, and in the resulting deposit facies architecture, as well as can play a dramatic role in the flow behavior, and in the associated volcanic hazard. This paper aims at discussing the PDC–topography interaction theme from the viewpoint of both deposits and flow structure, by accounting for appropriate literature, and revising the concepts in light of the theoretical conveyer model of Doronzo and Dellino (2013) on sedimentation and deposition in particulate density currents. First the effects, then the causes of the flow–topography interaction are discussed, in order to follow the historical development of theme concepts. The discussion is relative in terms of inertial and forced currents, which are defined on the basis of a dimensionless quantity (SD) representing the conservation of mass. Momentum equation relating depositional unit thickness, flow shear velocity, and density contrast shows that the flow is the cause of PDC motion, whereas the density contrast sustains the momentum, and the deposits are the process effect. In particular, the flow structure is described into three parts, flow–substrate boundary zone, boundary layer (lower part), and wake region (upper part) of the current. The facies architecture of PDC deposits, and the volcanic hazard depend on fluid dynamic and hydraulic behavior represented, in light of the conveyer model, by the balance of sedimentation and deposition rates through transport and erosion (“sedimentation–deposition” ratio, SD). This balance acts between flow–substrate boundary zone and boundary layer. The paper discussion mainly applies to small-to-intermediate volume eruptions. Field and modeling examples of Vulcano tuff cone and Colli Albani maar (Italy) constrain the conveyer model, whereas the literature of very large, ignimbrite-forming eruptions, and stratovolcanism is accounted for theme completeness. The main findings are some relative guidelines on PDC–topography interaction that can be used when modeling the flow, and interpreting the pyroclastic deposits: low SD is typical of inertial currents, whereas high SD is typical of forced currents, which can vary depending on topography.