Eddy Size Research Articles

The Heat and Carbon Characteristics of Modeled Mesoscale Eddies in the South–East Atlantic Ocean

AbstractMesoscale eddies provide critical links between the atmosphere and the ocean interior modulating the exchanges of key climatic tracers across the air‐sea and mixed‐layer interface. Mesoscale eddies, widespread in the Southern Ocean, are unresolved by Earth System Models; to what extent they modify contemporary and future heat and CO2 uptake remains unknown. The missing contribution of mesoscale eddies and their effects on properties and fluxes of heat and CO2 are investigated in the South‐East Atlantic using a mesoscale resolving (1/12°) physical biogeochemical model. Unsupervised Self‐Organizing Maps are used to separate anticyclonic and cyclonic eddies into distinct sub‐categories based on spatial characteristics in relative vorticity. Thermal drivers dominated over non‐thermal on partial pressure of ocean CO2 (pCO2sw) leading to a weaker CO2 sink in anticyclonic eddies and a stronger CO2 sink in cyclonic eddies relative to the climatological mean. Magnitudes and depth extents of tracer anomalies scale with eddy size but are also dependent on background tracer gradients. Resolving only the largest (>50 km radii) eddies leads to underestimations in total magnitude of heat storage by 52% and 77%, and underestimations of 61% and 77% in dissolved inorganic carbon (CT) storage for anticyclonic and cyclonic eddies respectively. The inclusion of smaller eddy features (<50 km) also offsets the asymmetry in heat and CT storage between anticyclonic and cyclonic eddies. Resolving eddies explicitly or improvements in existing parameterizations that fail to sufficiently include eddy effects are crucial to improving estimates of heat and CO2.

Investigation of a Near-Field Cylinder Wake in the Subsonic, Transonic, and Supersonic Regimes

The near wake of a circular cylinder in a high-Reynolds-number regime is investigated using the particle image velocimetry technique for an inflow Mach number spanning 0.3 to 2. The mean flow and turbulent kinetic energy field for different Mach number cases are presented. Furthermore, the influence of the Reynolds and Mach number effects is examined based on the mean separation point along the cylinder surface, which is extracted from complementary schlieren visualization measurements, and the literature. The wake width for the supersonic inflow case is found to be an order of magnitude smaller physically than the subsonic case with an identical cylinder diameter. Additionally, the swirl strength criterion is used to identify the eddies present within the wake, and the eddy size and convection velocity are characterized based on the spatiotemporal correlations. The result suggests that the mean wake features for the subsonic and supersonic cases are very different. Moreover, the interaction of eddies generated at the cylinder’s top and bottom shear layers leads to the large-scale features present in the wake, and the differing paths followed by the eddies between the subsonic and supersonic cases are responsible for the variation in the observed wake width.

Effect of the integral length scales of turbulent inflows on wind turbine loads

As wind turbines become larger, the fluctuations in the inflow become increasingly influential in the turbine structural loading. These fluctuations are characterized by the integral length scale, which represents the average size of the largest energy-containing turbulent eddies. Current design standards neglect the varying integral length scales that characterize inflows of wind turbines in operation. Using large-eddy simulations, we generate turbulent inflows of varying integral length scales and quantify the loads of the IEA 15-MW reference wind turbine. Results illustrate that the impact of turbulence on rotor and tower loads is up to 10 times greater than the impact of the mean shear profile. Increasing integral length scales from 0.3x to 0.5x the rotor diameter reduces blade root flapwise moments and rotor and tower loads. Increasing integral length scales from 0.5x to 1.7x the rotor diameter increases the rotor aerodynamic thrust force and the blade root flapwise shear loads and decreases the tower base torsional moment and the tilting and yawing rotor aerodynamic moments. Additionally, turbulence intensity has a greater impact on wind turbine loads than integral length scales. Findings indicate that design standards should consider varying integral length scales for accurate wind turbine loading characterization in turbulent inflow conditions.

Low-cost field particle image velocimetry for quantifying environmental turbulence

To date, there is a lack of in-situ turbulence data in natural aquatic systems. Adapting particle image velocimetry (PIV) to field use is of interest to provide such data. Past field PIV systems have been successful, but suffer from high costs, lack of portability, and flow disruption. We present a new field PIV system designed to address these limitations and capture turbulence metrics significant to aquatic biota: velocity, turbulent kinetic energy (TKE), vorticity, eddy size, and eddy circulation. Velocity measurements by the novel PIV system were compared to measurements by an acoustic doppler velocimeter (ADV) and an electromagnetic flowmeter for validation, and its results agreed with these other two methods. The PIV’s TKE results were compared to those of an ADV, and they agreed as well. Vorticity, eddy size, and eddy circulation were validated in the field through repeating past measurements. Each of these data sets generated by the novel PIV fell within the range of the validation measurements. The novel system thus provides accurate turbulence and velocity measurements; further, its design is low-cost, uses widely available materials, is minimally disruptive to the flow, and is highly portable and adjustable, offering an accessible method for acquiring meaningful field turbulence data.

The investigation of a likely scenario for natural tornado genesis and evolution from an initial instability profile

A likely mechanism for the little-understood tornado genesis is proposed and its numerical implementation is presented. The Burgers-Rott vortex with its axis in the vertical direction is introduced as an instability mechanism, and the flow field then evolves under the influence of the atmospheric pressure, temperature and density variations with altitude. Buoyancy effects are implemented using the Boussinesq model. Results are presented and discussed for a set of conditions including mesh type and size, different turbulence models, and a few different boundary conditions. Post-processed results of the transient simulations including animations contain a wealth of information to help analyze tornado behavior. Velocity contours, pressure contours, vorticity contours, streamlines, and iso-surfaces show the evolution of a complex flow field possessing many characteristics of a tornado. At longer times from the start, the flow field becomes more asymmetric with the vortex core becoming more twisted, and the eye of the vortex drifting away from the axis of the computational domain. The single initial vortex then transitions into multiple vortices of varying size and orientation. These high Reynolds number (ReΓ ∼109) simulation results show flow fields that resemble highly unsteady, turbulent flows with large regions of flow separation, and large eddy size range.

Scale-Dependent Eddy Diffusivities at the Kuroshio Extension: A Particle-Based Estimate and Comparison to Theory

Abstract For eddy-permitting climate models, only eddies smaller than the smallest resolvable scale need to be parameterized. Therefore, it is important to study the diffusivities induced by eddies smaller than a specific separation scale L*, that is, the scale-dependent eddy diffusivities. Using a submesoscale-permitting model solution (MITgcm llc4320), we estimate the scale-dependent eddy diffusivity in the Kuroshio Extension. We find that, as the separation scale L* increases, the diffusivity increases, and the spatial structure approaches that of the total eddy diffusivity. We quantify this scale dependence through fitting the diffusivity to L*n. Our derivation shows that n is approximately (a + 1)/2, where a is the eddy kinetic energy spectral slope. For domain-averaged diffusivity, n is 1.33. We then extend four existing mixing theories by including scale dependence. Our results show that both of the theories designed for intense-jet regions, the suppressed mixing length theory and the multiwavenumber theory, closely match the magnitude of the scale-dependent diffusivity but fail to capture well the diffusivity’s spatial structure. However, the other two theories based on eddy size and Rhines scale can reasonably represent the spatial structure. Based on this finding, we propose an empirical formula for scale-dependent eddy diffusivity that well represents both the magnitude and the spatial structure of the eddy diffusivity. Our work demonstrates that climate models should use scale-dependent diffusivity, and designing appropriate empirical formulas may be a reasonable approach to represent these scale-dependent diffusivities. Also, our diagnostic framework and theories for scale-dependent eddy diffusivity may be applicable to the global ocean.

Stability Dependence of the Turbulent Dissipation Rate in the Convective Atmospheric Boundary Layer

AbstractTurbulent dissipation rate (ɛ) is a crucial parameter in turbulence theory, and an essential component of higher‐order planetary boundary layer schemes for numerical weather prediction and climate models. It is most often modeled diagnostically based on the dissipation scaling ɛ ∝ e3/2/L, where e and L are the turbulence kinetic energy (TKE) and the size of the largest turbulent eddies, respectively. Utilizing three‐month‐long vertically‐extended observations accompanied by high resolution large‐eddy simulations, scaling‐based ɛ‐models are evaluated, focusing on their stability dependence under daytime convective conditions. The analysis uncovers biases in the parameterized ɛ profiles that cannot be corrected through tuning of model constants. The biases are attributed to the limited and even opposing stability dependence of the modeled dissipation length. Close examination reveals violation of the dissipation scaling by the inclusion of TKE associated with organized convection. A self‐similar dissipation length is obtained when only the isotropic component of TKE is considered.

Observations of two-dimensional turbulence in the surfzone

Low-frequency, many-minute-period horizontal surfzone eddies are an important mechanism for the dispersion of material, transporting larvae, pollutants, sediment, and swimmers both across and along the nearshore. Previous numerical, laboratory, and field observations on alongshore uniform bathymetry with no or roughly uniform mean background flows suggest that the low-frequency eddies may be the result of a two-dimensional inverse energy cascade that transfers energy from relatively small spatial-scale vorticity injected by depth limited breaking waves to larger and larger spatial scales. Here, using remotely sensed high-spatial resolution estimates of currents, those results are extended to surfzones with strong complex mean circulation patterns [flows O(1 m/s)] owing to nonuniform bathymetry. Similar to previous results, wavenumber spectra and second-order structure functions calculated from the observations are consistent with a two-dimensional inverse energy cascade. The size of the largest eddies is shown to depend on the surfzone width and the spatial scales of the mean currents. Third-order structure functions also are consistent with an inverse cascade for spatial scales greater than ∼50 m. At smaller scales, the third-order structure functions suggest a mixture of inverse and forward cascades.

Separate and joint clustering characteristics of large-Stokes-number sprays subjected to turbulent co-flows

Separate and joint droplets, clusters, and voids characteristics of sprays injected in a turbulent co-flow are investigated experimentally. Simultaneous Mie scattering and interferometric laser imaging for droplet sizing along with separate hotwire anemometry are performed. The turbulent co-flow characteristics are adjusted using zero, one or two perforated plates. The Taylor-length-scale-based Reynolds number varies from 10 to 38, and the Stokes number estimated based on the Kolmogorov time scale varies from 3 to 25. The results show that the mean length scale of the clusters normalized by the Kolmogorov length scale varies linearly with the Stokes number. However, the mean void length scale is of the order of the integral length scale. It is shown that the number density of the droplets inside the clusters is approximately 7 times larger than that in the voids. The ratios of the droplets number densities in the clusters and voids to the total number density are independent of the test conditions and equal 5.5 and 0.8, respectively. The joint probability density function of the droplets diameter and clusters area shows that the droplets with the most probable diameter are found in the majority of the clusters. It is argued that intensifying the turbulence broadens the range of turbulent eddy size in the co-flow which allows for accommodating droplets with a broad range of diameters in the clusters. The results are of significance for engineering applications that aim to modify the clustering characteristics of large-Stokes-number droplets sprayed into turbulent co-flows.

Global trends in surface eddy mixing from satellite altimetry

Mixing induced by oceanic mesoscale eddies can affect tracer distributions in the ocean and thus modulate the evolution of the physical and biochemical marine system. In the context of global warming, regionally different trends in eddy mixing could exist. Motivated by this hypothesis, we quantified the trend in surface eddy diffusivity, a metric widely used to quantify the eddy mixing rate, in the global ocean using satellite altimetry data. The global average of the particle-based eddy diffusivity increases by 284.1 m2s−1 per decade during the period of 1994-2017, or 3.7% per decade relative to its climatological mean value. In 54% of the global ocean, eddy diffusivity shows an increasing trend. The diffusivity trend can be decomposed into two components: one related to changes in eddy mixing length and the other related to eddy velocity magnitude. In 73% of the global ocean, changes in eddy mixing length account for more than 50% of the diffusivity trend. The suppressed mixing length theory (SMLT) is employed to interpret the trend in eddy mixing length. SMLT well captures the sign of the trend in two of the representative regions. Among all the parameters (e.g., eddy size, phase speed) inherent in SMLT, the eddy velocity magnitude plays a dominant role in determining the trend in the SMLT-based eddy mixing length. Diagnosing the geostrophic eddy kinetic energy budget reveals that the dominant mechanism for the trend in eddy velocity magnitude is the pressure work induced by ageostrophic flows. Our results suggest that a time-dependent eddy parameterization scheme should be employed in non-eddy-resolving models to account for the trend in eddy mixing.

Moist available potential energy of the mean state of the atmosphere and the thermodynamic potential for warm conveyor belts and convection

Abstract. Much of our understanding of atmospheric circulation comes from relationships between aspects of the circulation and the mean state of the atmosphere. In particular, the concept of mean available potential energy (MAPE) has been used previously to relate the strength of the extratropical storm tracks to the zonal-mean temperature and humidity distributions. Here, we calculate for the first time the MAPE of the zonally varying (i.e., three-dimensional) time-mean state of the atmosphere including the effects of latent heating. We further calculate a local MAPE by restricting the domain to an assumed eddy size, and we partition this local MAPE into convective and nonconvective components. Local convective MAPE maximizes in the subtropics and midlatitudes, in many cases in regions of the world that are known to have intense convection. Local nonconvective MAPE has a spatial pattern similar to the Eady growth rate, although local nonconvective MAPE has the advantage that it takes into account latent heating. Furthermore, the maximum potential ascent associated with local nonconvective MAPE is related to the frequency of warm conveyor belts (WCBs), which are ascending airstreams in extratropical cyclones with large impacts on weather. This maximum potential ascent can be calculated based only on mean temperature and humidity, and WCBs tend to start in regions of high maximum potential ascent on a given day. These advances in the use of MAPE are expected to be helpful to connect changes in the mean state of the atmosphere, such as under global warming, to changes in important aspects of extratropical circulation.

The Log-Law of the Wall in the Overlap from a Functional Equation

The log-law of the wall in the overlap for wall-bounded turbulent flows is rederived from a pure dimensional analysis and functional equation based on three experimental facts: (1) in the inner flow region, the mean velocity distribution is dominated by the viscous length scale; (2) in the outer flow region, the mean velocity distribution is dominated by the largest eddy size or the boundary layer thickness; and (3) there is an overlap between the inner and outer regions. These facts lead to a functional equation that yields a universal log-law in the overlap. Hence, the log-law is independent of any turbulence model, and it is an axiom accepted widely in fluid mechanics.

Characteristics of constrained turbulent transport in flux-driven toroidal plasmas.

We study the dynamics of turbulence transport subject to a constraint on the profile formation and relaxation, dominated by the ion temperature gradient modes, within the framework of adiabatic electron response using a flux-driven global gyro-kinetic toroidal code, GKNET. We observe exponentially constrained profiles, with two different scale lengths, that are spatially constant in each region in higher input power regimes. The profiles are smoothly connected in the knee region located at [Formula: see text] of the minor radius, outside which the gradient is steepened and shows a weak confinement improvement. Based on the probability density function analysis of heat flux eddies, the power law demonstrates a dependence on the eddy size S, as [Formula: see text], which distinguishes events into diffusive and non-diffusive parts including the validation of quasi-linear hypotheses. Radially localized avalanches and global bursts, which exhibit different spatial scales, play central roles in giving rise to constrained profiles on an equal footing. It is also found that the [Formula: see text] shear layers are initiated by the global bursts, which evolve downward on a slow time scale across the knee region and play a role in adjusting the profile by increasing the gradient. This article is part of a discussion meeting issue 'H-mode transition and pedestal studies in fusion plasmas'.

Turbulence Organization and Mean Profile Shapes in the Stably Stratified Boundary Layer: Zones of Uniform Momentum and Air Temperature

A persistent spatial organization of eddies is identified in the lowest portion of the stably stratified planetary boundary layer. The analysis uses flow realizations from published large-eddy simulations (Sullivan et al. in J Atmos Sci 73(4):1815–1840, 2016) ranging in stability from near-neutral to almost z-less stratification. The coherent turbulent structure is well approximated as a series of uniform momentum zones (UMZs) and uniform temperature zones (UTZs) separated by thin layers of intense gradients that are significantly greater than the mean. This pattern yields stairstep-like instantaneous flow profiles whose shape is distinct from the mean profiles that emerge from long-term averaging. However, the scaling of the stairstep organization is closely related to the resulting mean profiles. The differences in velocity and temperature across the thin gradient layers remain proportional to the surface momentum and heat flux conditions regardless of stratification. The vertical thickness of UMZs and UTZs is proportional to height above the surface for near-neutral and weak stratification, but becomes thinner and less dependent on height as the stability increases. Deviations from the logarithmic mean profiles for velocity and temperature observed under neutral conditions are therefore predominately due to the reduction in eddy size with increasing stratification, which is empirically captured by existing Monin–Obukhov similarity relations for momentum and heat. The zone properties are additionally used to explain trends in the turbulent Prandtl number, thus providing a connection between the eddy organization, mean profiles, and turbulent diffusivity in stably stratified conditions.

Spatial variation of mean flow and turbulence characteristics within channel contraction – an experimental approach

ABSTRACT The influence of three different channel contractions on the mean flow and turbulent characteristics has been measured experimentally in a recirculating flume. The velocity deficit, turbulence intensity, Reynolds stress, and turbulence scales data within the channel contractions were obtained from three-dimensional velocity fluctuations measurements using Acoustic Doppler Velocimeter. The mean flow profile shows undulation towards the free surface for all the contraction ratios, indicating the presence of the velocity-dip phenomenon due to the secondary currents. These currents changed the pattern of turbulence intensities and Reynolds shear stresses significantly within the channel contraction compared to the without contraction case. The results reveal that with the increase of channel contraction ratio, the strength of the secondary current increased considerably and resulted in a significant change in flow patterns close to the free surface compared to the bottom. The length scales of turbulent flow indicate eddy sizes in different ranges to be smaller at near-bed region within the contraction zone due to the breakdown of larger eddies.

Moffatt eddies in electrohydrodynamics flows: numerical simulations and analyses

We study numerically a sequence of eddies in two-dimensional electrohydrodynamics (EHD) flows of a dielectric liquid, driven by an electric potential difference between a hyperbolic blade electrode and a flat plate electrode (or the blade–plate configuration). The electrically driven flow impinges on the plate to generate vortices, which resemble Moffatt eddies (Moffatt, J. Fluid Mech., vol. 18, 1964, pp. 1–18). Such a phenomenon in EHD was first reported in the experimental work of Perri et al. (J. Fluid Mech., vol. 900, 2020, A12). We conduct direct numerical simulations of the EHD flow with three Moffatt-type eddies in a large computational domain at moderate electric Rayleigh numbers ( $T$ , quantifying the strength of the electric field). The ratios of size and intensity of the adjacent eddies are examined, and they can be compared favourably to the theoretical prediction of Moffatt; interestingly, the quantitative comparison is remarkably accurate for the two eddies in the far field. Our investigation also shows that a larger $T$ strengthens the vortex intensity, and a stronger charge diffusion effect enlarges the vortex size. A sufficiently large $T$ can further result in an oscillating flow, consistent with the experimental observation. In addition, a global stability analysis of the steady blade–plate EHD flow is conducted. The global mode is characterised in detail at different values of $T$ . When $T$ is large, the confinement effect of the geometry in the centre region may lead to an increased oscillation frequency. This work contributes to the quantitative characterisation of the Moffatt-type eddies in EHD flows.

Numerical studies of the tilting of mesoscale eddies: The effects of rotation and stratification

This study aims to better understand the tilting of mesoscale eddies that has been frequently observed in oceans. To systematically study the features and factors controlling eddy tilt, a series of ideal numerical experiments are conducted. The simulated eddies in most cases are nonlinear near the surface and gradually become Rossby waves with depth, consistent with previous eddy observations in the open oceans. The tilt of eddies with depth appears in nearly every experiment. The characteristics of eddy tilting are generally consistent with in situ eddy observations as well as composite eddies derived from satellite observations and Argo profiles in the simulation area. A set of sensitivity experiments indicates that the eddy tilt is increased with a decrease (increase) in the planetary rotation (ocean stratification). The eddy tilt is positively correlated with the Burger number (the ratio of vertical stratification to the planetary rotation and eddy size). Furthermore, it is noticed that the eddy tilt gradually grows with time in the experiments, implying different translation speeds of the eddy (Rossby waves) at different depths. Therefore, we propose that the eddy tilt is attributed to the depth-dependent propagation speed of the eddy (Rossby waves), and worth further investigation.

Hollow bluff body-stabilized natural gas-air premixed flames

The effects of hollow bluff body geometry, surface curvature, blockage ratio, mixture residence time, impingement strength, heat recirculation eddy size, Reynolds and Froude numbers were all investigated via 10 bluff body shapes. It was found that duplicating the wake flow zone and increasing the mixture flow velocity inside the bluff body cavity via a disc configuration provide a maximum blow-off velocity of 49 m/s. Enlarging the bluff body exterior surface area and the flow wake width in addition to elongating the mixture residence time inside the bluff body cavity via a trapezoidal configuration yield a minimum lean limit of 0.42. Having grooves on the bluff body exterior surface or providing a concave surface part at the wake region favorably develops flow turbulence and intensive heat recirculation. The bluff body cavity height should be adjusted at an optimum value which keeps a high impingement velocity onto the combustor hot surface via a large vortex and simultaneously allows enough mixture preheating length. The stability limits were thus correlated to the geometrical and thermal effective parameters in addition to Reynolds and Froude numbers.

Global Mapping of Mesoscale Eddy Vertical Tilt

AbstractVertical motion induced by oceanic mesoscale eddies can strengthen ocean ventilation, and regulate vertical distribution of heat, dissolved CO2 and other tracers on a global scale. Eddy‐induced vertical motion is closely related to eddy vertical structure. Here, based on available satellite observations and Argo profiles, we find that mesoscale eddies in global oceans are prevalently vertical tilted. Anticyclonic eddies are frequently tilted westward and poleward from 300 dbar up to sea surface, while cyclonic eddies are frequently tilted westward and equatorward. The horizontal tilting distance of eddies is significantly correlated (r ≥ 0.84) with the Burger number (the ratio of vertical stratification to planetary rotation and eddy size), indicating a strong constraint of Earth's rotation and ocean stratification on eddy vertical tilt. On average, the maximum vertical velocity in tilted circular eddies is at least one order of magnitude larger than that in non‐tilted circular eddies. This finding would improve estimates of eddy‐induced vertical motion, ventilation, so as to heat/salt and biogeochemical responses.

Instability of a Surface Jet over Rough Topography

Abstract The instability of a surface-trapped jet over rough bottom topography is examined using a linearized quasigeostrophic model. The jet is laterally sheared and thus susceptible to both barotropic and baroclinic instability. The relative magnitude of the two depends on the jet width and on the spectral characteristics and amplitude of the bathymetry. The most unstable eddies in the upper layer are typically smaller over bathymetry than with a flat bottom. Topography also alters momentum flux convergence in the upper layer and causes the perturbations to resemble eddies in a 1.5-layer flow. But as long as the jet is wider than the deformation radius, baroclinic instability is present, yielding deep eddies that are phase-locked to those at the surface. In addition, topography facilitates scattering of energy at depth to other scales. So, instability over rough topography could be an efficient, and largely overlooked, means of transferring mesoscale energy to the dissipative scales. Significance Statement This study investigates the effects of bottom roughness on large-scale ocean currents and their associated eddies. Roughness affects the eddy size and speed and how they exchange energy with the mean flow. Roughness also facilitates energy transfer to smaller scales where it can be dissipated. Thus, instability over rough topography could be an important part of the oceanic energy balance.