Mean Flow Direction Research Articles

Tracking hydrothermal particles from the ridge axis to the sediment column along the Endeavour segment of the Juan de Fuca Ridge

Elemental fluxes associated with mid-ocean ridge hydrothermal systems are thought to be important in the ocean budgets of many elements but quantitative models of these fluxes, and how they vary in space and time due to different boundary conditions, are in their infancy. This is especially true for non-conservative elements that can be involved in multiple processes transforming them between the dissolved and particulate phases both in the water column and after sedimentation. To help develop a more robust database for parameterizing the processes operating, we undertook a coupled sediment trap and sediment core study of hydrothermal sediments on the west flank of the Endeavour segment of the Juan de Fuca Ridge. Sediment traps deployed in the Main Endeavour Field (MEF) and 3 and 9 km southwest of this field, along the mean flow direction of the hydrothermal plume, show that the rate of change of the concentration of sulfide-associated elements (Cu, Zn, Cd, Pb, Ag, As, Mo) in sediment settling from the plume differs between elements. We interpret this as indicating both different dissolution rates of phases containing these elements and different rates of scavenging of these elements from seawater. Scavenging is most readily tracked using elements for which the scavenged fraction is large relative to the hydrothermally derived fraction. For such elements, the relative efficiency of scavenging from seawater (REE > Cr > Ni > V > P > U) matches that previously reported from the TAG system on the Mid-Atlantic ridge despite different vent fluid and seawater chemistries that are expected to lead to both differing roles of Fe-sulfide and Fe-oxyhydroxides and different Fe oxidation rates. In the sediment trap samples collected 9 km off-axis, but not in those collected 3 km off-axis, the Mn and Ti concentrations correlate strongly despite these samples having much higher Mn concentrations than background sediment. Since Ti is sourced almost entirely from background terrigenous material such a correlation was not expected. The most reasonable explanation for this is that aggregation of hydrothermally derived particles with terrigenous material settling through the water column controls removal of hydrothermally derived particles from the water column. Changes in sediment composition with depth in the off-axis sediment core, along with differences between the composition of material from the sediment core and the off-axis sediment traps, are interpreted as indicating large post-deposition changes in sediment composition. For example, much or all of the Mn, P, As and Mo carried to the sediments with hydrothermally derived particles is released back into the water column during diagenesis. In contrast, V and REE concentrations in the sediment core are higher than those in the off-axis sediment trap samples, which may be due to continued scavenging in a benthic boundary layer post-deposition. Overall these data are interpreted as indicating that the net loss of many elements from the non-buoyant plume may not be a proxy for loss from the ocean, and a better understanding of post-depositional processes in hydrothermal settings may be important in understanding cycling of the aforementioned elements, and likely others, in seawater.

Characterizing turbulence structures in convective and neutral atmospheric boundary layers via Koopman mode decomposition and unsupervised clustering

The atmospheric boundary layer (ABL) is a highly turbulent geophysical flow, which has chaotic and often too complex dynamics to unravel from limited data. Characterizing coherent turbulence structures in complex ABL flows under various atmospheric regimes is not systematically well established yet. This study aims to bridge this gap using large eddy simulations (LESs), Koopman theory, and unsupervised classification techniques. To this end, eight LESs of different convective, neutral, and unsteady ABLs are conducted. As the ratio of buoyancy to shear production increases, the turbulence structures change from roll vortices to convective cells. The quadrant analysis indicated that as this ratio increases, the sweep and ejection events decrease, and inward/outward interactions increase. The Koopman mode decomposition (KMD) is then used to characterize their turbulence structures. Our results showed that KMD can reveal non-trivial modes of highly turbulent ABL flows (e.g., transverse to the mean flow direction) and can reconstruct the primary dynamics of ABLs even under unsteady conditions with only ∼5% of the modes. We attributed the detected modes to the imposed pressure gradient (shear), Coriolis (inertial oscillations), and buoyancy (convection) forces by conducting novel timescale and quadrant analyses. We then applied the convolutional neural network combined with the K-means clustering to group the Koopman modes. This approach is displacement and rotation invariant, which allows efficiently reducing the number of modes that describe the overall ABL dynamics. Our results provide new insights into the dynamics of ABLs and present a systematic data-driven method to characterize their complex spatiotemporal patterns.

Manipulation of a turbulent boundary layer using sinusoidal riblets

We investigate experimentally the effects of micro-grooves on the development of a zero pressure gradient turbulent boundary layer at two different values of the friction Reynolds number. We consider both the well-known streamwise aligned riblets as well as wavy riblets, characterized by a sinusoidal pattern in the mean flow direction. Previous investigations by the authors showed that sinusoidal riblets yield larger values of drag reduction with respect to the streamwise aligned ones. We perform new particle image velocimetry experiments on wall-parallel planes to get insights into the effect of the sinusoidal shape on the near-wall organisation of the boundary layer and the structures responsible for the friction drag reduction and the turbulence generation. Conditional averages, aimed at identifying the topology of the low-speed streaks in the turbulent boundary layer, reveal that the flow is highly susceptible to wall manipulation. This is particularly evident in the cases that are associated with greater values of drag reduction. The results suggest a fragmentation and/or weakening of the streaks in the sinusoidal cases, that is triggered by the larger values of the wall-normal vorticity found at the streaks’ edges. The results are also confirmed by applying the variable interval spatial averaging events eduction technique. The turbulent kinetic energy budget also shows that the sinusoidal geometry significantly attenuates the turbulence production, hence supporting the idea of the manipulation of the turbulence regeneration cycle.

Topography‐Based Particle Image Velocimetry of Braided Channel Initiation

AbstractRiver channels shape landscapes through gradual migration and abrupt avulsion. Measuring the motion of braided rivers, which have multiple channel threads, is particularly challenging, limiting predictions for landscape evolution and fluvial architecture. To address this challenge, we extended the capabilities of image‐based particle image velocimetry (PIV)—a technique for tracking channel threads in images of the surface—by adapting it to analyze topographic change. We applied this method in a laboratory experiment where a straight channel set in non‐cohesive sediment evolved into a braided channel under constant water and sediment fluxes. Topography‐based PIV successfully tracked the motion of channel threads if displacements between observations were less than the channel‐thread width, consistent with earlier results from image‐based PIV. We filtered spurious migration vectors with magnitudes less than the elevation grid spacing, or with high uncertainties in magnitude and/or direction. During braided channel initiation, migration rates varied with the channel planform development, showing an increase as incipient meanders developed, a decrease during the transitional braiding phase, and consistently low values during the established braiding phase. In this experimental setup, migration rates varied quasi‐periodically along stream at the half scale of initial meander bends. Lateral migration with respect to the mean flow direction was much more pronounced than streamwise migration, accounting for approximately 80% of all detected motion. Results demonstrate that topography‐based PIV has the potential to advance predictions for bank erosion and landscape evolution in natural braided rivers as well as bar preservation and stratigraphic architecture in geological records.

Surface corrugations induce helical near-surface flows and transport in microfluidic channels

We study theoretically and experimentally pressure-driven flow between a flat wall and a parallel corrugated wall, a design used widely in microfluidics for low-Reynolds-number mixing and particle separation. In contrast to previous work, which focuses on recirculating helicoidal flows along the microfluidic channel that result from its confining lateral walls, we study the three-dimensional pressure and flow fields and trajectories of tracer particles at the scale of each corrugation. Employing a perturbation approach for small surface roughness, we find that anisotropic pressure gradients generated by the surface corrugations, which are tilted with respect to the applied pressure gradient, drive transverse flows. We measure experimentally the flow fields using particle image velocimetry and quantify the effect of the ratio of the surface wavelength to the channel height on the transverse flows. Further, we track tracer particles moving near the surface structures and observe three-dimensional skewed helical trajectories. Projecting the helical motion to two dimensions reveals oscillatory near-surface motion with an overall drift along the surface corrugations, reminiscent of earlier experimental observations and independent of the secondary helical flows that are induced by confining lateral walls. Finally, we quantify the hydrodynamically induced drift transverse to the mean flow direction as a function of distance to the surface and the wavelength of the surface corrugations.

Estimating the turbulent kinetic energy dissipation rate from one-dimensional velocity measurements in time

Abstract. The turbulent kinetic energy dissipation rate is one of the most important quantities characterizing turbulence. Experimental studies of a turbulent flow in terms of the energy dissipation rate often rely on one-dimensional measurements of the flow velocity fluctuations in time. In this work, we first use direct numerical simulation of stationary homogeneous isotropic turbulence at Taylor-scale Reynolds numbers 74≤Rλ≤321 to evaluate different methods for inferring the energy dissipation rate from one-dimensional velocity time records. We systematically investigate the influence of the finite turbulence intensity and the misalignment between the mean flow direction and the measurement probe, and we derive analytical expressions for the errors associated with these parameters. We further investigate how statistical averaging for different time windows affects the results as a function of Rλ. The results are then combined with Max Planck Variable Density Turbulence Tunnel hot-wire measurements at 147≤Rλ≤5864 to investigate flow conditions similar to those in the atmospheric boundary layer. Finally, practical guidelines for estimating the energy dissipation rate from one-dimensional atmospheric velocity records are given.

Long-term evolution of meandering channel planforms in response to the mean annual flow and width–depth ratio

A depth-averaged linearized meander evolution model was used to numerically evaluate the spatiotemporal evolution of the meandering channel centerline in the plane at various mean annual flows and width–depth ratios for capturing the overall average trend of the meandering channel planform. This analysis was done to better understand the consistent responses of the river morphology to possible future tectonic and climatic changes. The computational cases included an idealized sine-generated meandering channel with a moderate maximum deflection angle and a typical natural meander for the Jiyun River in China. The study results showed phased development and response characteristics of the meandering channel centerline (to the mean annual flow), along with increases in the specified mean annual width (B)–depth (H) ratio (represented by B/H). First, the spatial meander straightening trend over time weakened during Phase 1 (B/H ≤ 16.5) and gradually changed to a meander developing trend during Phase 2 (16.5 < B/H ≤ 27) with an overall insensitivity to the flow magnitude. Second, starting from the downstream tail during Phase 3 (27 < B/H ≤ 28.9), the symmetric development form along the transverse direction (perpendicular to the mean flow direction) was disrupted, while flow effects were highlighted when the mean annual B/H exceeded 28. Finally, an obvious onset and jump process of the channel sensitivity in response to flow occurred during Phase 4 (28.9 < B/H ≤ 29.5). These event characteristics are very similar to the transition from laminar to turbulent flow in fluid mechanics. This study provides insights for more in-depth exploration of meandering mechanisms and technical support for effective river management.

Dynamics and proliferation of turbulent stripes in plane-Poiseuille and plane-Couette flows

The first long-lived turbulent structures observable in planar shear flows take the form of localized stripes, inclined with respect to the mean flow direction. The dynamics of these stripes is central to transition, and recent studies proposed an analogy to directed percolation where the stripes’ proliferation is ultimately responsible for the turbulence becoming sustained. In the present study we focus on the internal stripe dynamics as well as on the eventual stripe expansion, and we compare the underlying mechanisms in pressure- and shear-driven planar flows, respectively, plane-Poiseuille and plane-Couette flow. Despite the similarities of the overall laminar–turbulence patterns, the stripe proliferation processes in the two cases are fundamentally different. Starting from the growth and sustenance of individual stripes, we find that in plane-Couette flow new streaks are created stochastically throughout the stripe whereas in plane-Poiseuille flow streak creation is deterministic and occurs locally at the downstream tip. Because of the up/downstream symmetry, Couette stripes, in contrast to Poiseuille stripes, have two weak and two strong laminar turbulent interfaces. These differences in symmetry as well as in internal growth give rise to two fundamentally different stripe splitting mechanisms. In plane-Poiseuille flow splitting is connected to the elongational growth of the original stripe, and it results from a break-off/shedding of the stripe's tail. In plane-Couette flow splitting follows from a broadening of the original stripe and a division along the stripe into two slimmer stripes.

Variability of travel time of solute particles in single fractures with spatially variable aperture

The arrival time of solutes from the source to a prescribed compliance boundary is a global transport quantity that is of practical interest in many applications, such as risk assessment for environmentally sensitive sites in regulatory analyses. Estimates of uncertainty are necessary and can play an important role in the decision-making process. The objective of this work is therefore to quantify the variability of solute travel time in individual fractures with spatially variable apertures. The variability of solute transport in fractures is largely determined by the heterogeneity of the apertures of naturally occurring rock fractures. To model solute transport, the fracture apertures and flow fields are considered as spatial random functions. Using the relationship between the two-dimensional depth-averaged solute conservation equation and the Fokker-Planck equation, it is possible to formulate the solute convection velocity in such a way that a general expression for the solute travel time variance can be developed by taking into account the effects of the variation in fracture aperture. A closed-form expression for the variance of travel time in the mean flow direction is derived for the case of advection-dominated solute transport. This derived expression allows the analysis of the effects of the variation of the fracture aperture on the variability of the solute travel time.

Displacement Patterns of a Newtonian Fluid by a Shear‐Thinning Fluid in a Rough Fracture

AbstractTwo‐phase flow involving non‐Newtonian fluids in fractured media is of vital importance in many natural processes and subsurface engineering applications, such as rock grouting, groundwater remediation, and enhanced oil recovery. Yet, how the displacement dynamics is impacted by the non‐Newtonian rheology remains an open question. Here, we conduct primary drainage experiments in which a shear‐thinning Xanthan gum solution displaces a silicone oil in a transparent rough fracture for a wide range of shear‐thinning property (controlled by polymer concentration) and flow rates. We first evaluate the effects of shear‐thinning property on displacement efficiency. Based on qualitative and quantitative analyses of the observed fluid morphologies, we present an experimental phase diagram of the obtained displacement patterns. We characterize a novel displacement pattern where the fluid‐fluid interface changes from stable (plug flow) to unstable (fingering) as the fracture aperture, averaged over the transverse direction, varies along the mean flow direction. We demonstrate that the existence of this mixed displacement pattern can be explained by local viscosity heterogeneity induced by the coupling of the shear‐thinning behavior and the spatial variability of apertures. Finally, we propose a theoretical model elucidating the mechanisms behind the flow regime transitions. The interface stability criterion predicted by this model exhibits good agreement with the experimental measurements, and stresses the potentially important role of fluid rheology, coupled to aperture variability, in immiscible displacements in rough fractures. These findings provide new insights into the dynamics of immiscible two‐phase flows with non‐Newtonian effects, and has potential implications for the aforementioned engineering applications.

Effects of the direction of rotation axis on turbulent flows in rectangular ducts

The effects of the direction of rotation axis on flows in rectangular ducts are studied using direct numerical simulation. The rotation axis lies in the cross section of the duct. The angle of the rotation axis relative to the bottom edge of the cross section is altered from 0° to 90°. A series of cases are considered, including three Reynolds numbers Reτ = 300, 454, and 900, three rotation numbers Roτ = 2, 4, and 8, and two cross-sectional aspect ratios ar = 1.0 and 2.0. The results show that as the angle increases, the bulk velocity remains almost constant in the square duct while it decreases monotonically in the duct with ar = 2.0. When the angle increases from 0° to 45°, turbulence is significantly or even completely suppressed, while the secondary flow is gradually enhanced. Furthermore, with the same rotation number, turbulence is more strongly suppressed at a lower Reynolds number. As the angle further increases from 45° to 90° in the cases with ar = 2.0, the intensity of turbulence is recovered to some extent and the secondary flow gradually weakens. With the angle increasing from 0°, the Ekman layer is formed above the pressure wall and gradually strengthens, resulting in a drastic wall-normal variation of the mean flow direction and a tilting of the low-speed streaks near the wall, which may cause the weakening of the turbulence. In addition, in the flow fields where turbulence is severely suppressed, periodic structures are observed in the corner of the duct, which needs further study.

Solute transport in highly heterogeneous media: The asymptotic signature of connectivity

The connectivity of the more conductive hydrofacies strongly determines flow and transport in heterogeneous media. Here we study solute transport in 3D binary isotropic samples with a proportion p of a high hydraulic conductivity facies (k+), and (1−p) of a low (k−) one. The k+ facies is characterized by two connectivity parameters: a connectivity structure type (no, low, intermediate and high), that controls how well the k+ facies is connected, and an integral scale Ib, that controls the heterogeneity characteristic lengthscale. Under ergodic conditions, and in the asymptotic Fickian regime that arises only very far from the injection plane, we analyze two transport quantities: the normalized mean solute arrival time 〈ta∗〉, and the longitudinal dispersivity αL. As p reaches the percolation threshold pc (pc depends on the connectivity parameters), k+ channels spanning the sample along the mean flow direction appear, giving rise to fast flow pathways . A sharp decrease of 〈ta∗〉, and a sharp increase of αL, occur when p→pc. As p exceeds pc, a subsequent minimum of 〈ta∗〉 and a maximum of αL are observed. This result is in contrast with previous ones by other authors that found a maximum of αL at p=pc. On the other hand, p kept fixed, αL decreases as the connectivity of the k+ facies increases. We conclude that the connectivity features sampled by the solute particles during their trajectories are retained in the transport quantities even after the asymptotic regime is attained. Also, that connectivity mainly affects αL through a shift or displacement of pc. Finally, the existence of a spatial connectivity structure may imply early, but also late, arrival times, compared with the absence of structure.

An open-source anisotropic k−ε−v2−f model for turbulent viscoelastic duct flows

A novel open-source anisotropic k−ε−v2−f model is presented for turbulent viscoelastic duct flow with dilute polymeric solutions described by the finitely extensible nonlinear elastic-Peterlin constitutive model. The turbulence model for channel and square duct flow of Newtonian fluids is adapted to incorporate the polymeric terms within the governing equations. All the required non-linear terms are validated with simple closure models and are assessed a priori against independent direct numerical simulation data in fully developed channel flow. The NLTij term, which accounts for the interaction between fluctuating components of the conformation tensor and the velocity gradient tensor, is modeled with the mean flow direction, ti, and wall-normal, ni, present in the Newtonian model, based on the streamwise alignment of mean polymer stretch. The implicit polymer effects on pressure–strain are assessed with a simple ad hoc closure accounting for the reduced near-wall production of turbulent kinetic energy. The same closure is also adapted for the spanwise Reynolds stress predictions of polymer-enhanced secondary flow. The model performs well in channel flow and captures low, intermediate, and high drag reduction features for a wide range of rheological parameters. The capabilities are extended for square ducts (or any regular polygon) due to the symmetric modeling of the closure models, which can predict the mean streamwise and secondary flow features associated with second normal Reynolds stress differences. Accessible codes and models are crucial for the advancement and improvement of turbulent viscoelastic models, and an OpenFOAM C++ code package is developed and freely available on GitHub (https://github.com/MikeMcDermott-Code/v2f).

Analyses of Spatial Correlation and Coherence in ABL Flow with a Fleet of UAS

The spatial structures of turbulent flow in the atmospheric boundary layer (ABL) are complex and diverse. Multi-point spatial correlation measurements can help improve our understanding of these structures and their statistics. In this context, we investigate Taylor’s hypothesis and the statistics of spatial structures on the microscale. For the first time, simultaneous horizontally distributed wind measurements with a fleet of 20 quadrotor UAS (unmanned aerial systems) are realized. The measurements were taken at different heights and under different atmospheric conditions at the boundary layer field site in Falkenberg of the German Meteorological Service (DWD). A horizontal flight pattern has been specifically developed, consisting of measurements distributed along and lateral to the mean flow direction with separation distances of 5ldots 205 m. The validity of Taylor’s hypothesis is studied by examining the cross-correlations of longitudinally distributed UAS and comparing them with the autocorrelations of single UAS. To assess the similarity of flow structures on different scales, the lateral and longitudinal coherence of the streamwise velocity component is examined. Two modeling approaches for the decay of coherence are compared. The experimental results are in good agreement with the model approaches for neutral atmospheric conditions, whereas in stable and convective ABL, the exponential approaches are not unconditionally valid. The validation results and the agreement with the literature on coherence in the ABL underline the potential of the UAS fleet for the purpose of spatial turbulence measurements.

Stress and stretching regulate dispersion in viscoelastic porous media flows.

In this work, we study the role of viscoelastic instability in the mechanical dispersion of fluid flow through porous media at high Péclet numbers. Using microfluidic experiments and numerical simulations, we show that viscoelastic instability in flow through a hexagonally ordered (staggered) medium strongly enhances dispersion transverse to the mean flow direction with increasing Weissenberg number (Wi). In contrast, preferential flow paths can quench the elastic instability in disordered media, which has two important consequences for transport: first, the lack of chaotic velocity fluctuations reduces transverse dispersion relative to unstable flows. Second, the amplification of flow along preferential paths with increasing Wi causes strongly-correlated stream-wise flow that enhances longitudinal dispersion. Finally, we illustrate how the observed dispersion phenomena can be understood through the lens of Lagrangian stretching manifolds, which act as advective transport barriers and coincide with high stress regions in these viscoelastic porous media flows.

Numerical Analysis of Flow and Heat Transfer Characteristics of Lattice-Based Compact Heat Sinks

Abstract Single unit cell thick lattice frame materials have applications in efficient heat exchangers. This study is focused on strut-based sandwich-type configurations obtained through reticulation of unit cell topologies of tetrakaidecahedron (TKD), octet, and rhombic dodecahedron (DDC) shapes at a porosity of 0.9 with water as the working fluid. Interfacial heat transfer coefficient values on struts and endwalls were determined by imposing constant temperature boundary condition. Averaged heat transfer coefficient on the endwall was the highest for tetrakaidecahedron lattice whereas rhombic dodecahedron lattice exhibited the highest average interfacial heat transfer coefficients on the struts. Flow analysis showed the presence of strong secondary flow features on planes normal to the mean flow direction that demonstrated the unique flow mixing capabilities of these lattices. Reported interfacial heat transfer coefficient at struts and endwall can be used in volume-averaged computations of metal foams (representative of lattices' flow and thermal properties) under local thermal nonequilibrium.

Assessment of flow characteristics over complex terrain covered by the heterogeneous forest at slightly varying mean flow directions: (A case study of a Swedish wind farm)

The impact of heterogeneous forest canopies and complex terrain on the horizontal distortion of the inflow is studied. Large-Eddy Simulation (LES) of the neutral Atmospheric Boundary Layer (ABL) flow is performed for a wind farm in Sweden for three cases associated with three different wind directions at the range of the static yaw misalignment (≃±6∘) where the yaw control system is not activated. The ground topography and forest properties for the numerical modeling are extracted from the Airborne Laser Scanning (ALS) 3D data. The wind turbines within the wind farm are introduced using the actuator disk model. To focus on the airflow deflection only by the complex terrain and vegetation, the study is limited to upstream wind turbines without any wake interaction. The predicted mean wind speed and turbulence intensity for the upstream wind turbines are compared against the nacelle-mounted anemometers taken from the wind farm’s turbine SCADA data. To quantify the additional load and moments induced at the rotor blades by the horizontal misalignment of the incoming flow, aero-structural simulation of the upstream wind turbines in the wind farm for all three cases is performed. The results show that the horizontal distortion of the inflow over the rotor swept area is usually kept below the range of static yaw misalignment (≃6∘) for the majority of the upstream wind turbines for all three cases. However, the impact of a large vertical shear exponent leading to misinterpretation of the results must be taken into consideration. Furthermore, the load imbalance of the rotor due to the vertical wind shear has the least direct contribution to the yaw moment. However, for a mean vertical shear exponent larger than α=0.25, contrary to expectation, a positive mean yaw moment under the positive-yawed inflow may be observed.

Directly Generating Spatially Periodic, Heterogeneous Groundwater Flow Fields: A Finite Volume Approach

AbstractWe present a finite volume approach for generating doubly‐periodic, 2D heterogeneous groundwater velocity fields, given an arbitrary hydraulic conductivity field discretized on a rectangular lattice. The method conserves mass, allows direct specification of any desired mean flow direction and computes the corresponding field with a single solve operation, and solves for inter‐cell fluxes that may be used directly for particle tracking with the Pollock method without further interpolation. We demonstrate an open‐source Python implementation of the approach that we created.

Mechanics of drag reduction of an axisymmetric body of revolution with shallow dimples

In this article, the mechanics of drag reduction on an axisymmetric body of revolution by shallow dimples is presented by using the high-fidelity Reynolds Stress Modeling based simulations. Experimental results of drag evolution from published literature at different Reynolds numbers are used to validate the model predictions. The numerical predictions show good agreement with the experimental results. It is observed that the drag of the body is reduced by a maximum of [Formula: see text] with such shape modification (for the depth to diameter ratio of [Formula: see text] and coverage ratio of [Formula: see text]). This arises due to the reduced level of turbulence, flow stabilization and suppression of flow separation in the boundary layer of the body. From the analysis of turbulence states in the anisotopic invariant map (AIM) for the case of the dimpled body, we show that the turbulence reaches an axisymmetric limit in the layers close to the surface of the body. There is also a reduced misalignment between the mean flow direction and principal axis of the Reynolds stress tensor, which results in such drag reduction. The dimple depth to diameter(s/d) and coverage ratio (a/A) are also varied to evaluate its effect on drag evolution. An empirical correlation for the drag coefficient is also developed by using polynomial regression in terms of the different shape and flow parameters, for example, s/d ratio, a/A ratio, and Reynolds shear stress.

On the Vertical Structure of Oceanic Mesoscale Tracer Diffusivities

AbstractIsopycnal mixing of tracers is important for ocean dynamics and biogeochemistry. Previous studies have primarily focused on the horizontal structure of mixing, but what controls its vertical structure is still unclear. This study investigates the vertical structure of the isopycnal tracer diffusivity diagnosed by a multiple‐tracer inversion method in an idealized basin circulation model. The first two eigenvalues of the symmetric part of the 3D diffusivity tensor are approximately tangent to isopycnal surfaces. The isopycnal mixing is anisotropic, with principal directions of the large and small diffusivities generally oriented along and across the mean flow direction. The cross‐stream diffusivity can be reconstructed from the along‐stream diffusivity after accounting for suppression of mixing by the mean flow. In the circumpolar channel and the upper ocean in the gyres, the vertical structure of the along‐stream diffusivity follows that of the rms eddy velocity times a depth‐independent local energy‐containing scale estimated from the sea surface height. The diffusivity in the deep ocean in the gyres instead follows the profile of the eddy kinetic energy times a depth‐independent mixing time scale. The transition between the two mixing regimes is attributed to the dominance of nonlinear interactions and linear waves in the upper and deep ocean, respectively, distinguished by a nonlinearity parameter. A formula is proposed that accounts for both regimes and captures the vertical variation of diffusivities better than extant theories. These results inform efforts to parameterize the vertical structure of isopycnal mixing in coarse‐resolution ocean models.