Eddy Diffusion

Turbulence with inverse energy cascade and its transport properties are investigated experimentally in a flow associated with a westward propagating jet. Turbulence and the jet were produced by an electromagnetic force in a rotating tank filled with an electrolytic saline solution. The parabolic free surface emulated the topographic β effect which evoked the zonation. The spectral and transport flow characteristics were highly anisotropic. Turbulence is diagnosed by exploring the analogy between vertical and horizontal turbulent overturns in, respectively, stably stratified and quasigeostrophic flows which gives rise to a method of potential vorticity (PV) monotonizing. The anisotropization of transport properties of the flow is investigated using the finite scale Lyapunov exponent technique. After initial exponential particle separation, radial (meridional in geophysical and planetary applications) diffusion attains a short-ranged Richardson regime which transitions to the Taylor (...

The presence of dense submerged vegetation alters mixing characteristics in open channel flows as they cause differential velocities inside and above canopies. The prediction models for longitudinal mixing in the presence of submerged canopies often use the drag coefficient to represent the canopy, which limits the usability of the models when the canopy properties are not fully understood. Here, attempts were made to present a methodology which can be used for deriving the coefficient of longitudinal dispersion in the presence of submerged vegetation based on velocity measurements, using a mixing length approach to model turbulence. An experimental study was conducted in a large-scale laboratory facility to investigate the longitudinal dispersion characteristics in open channel flow with submerged aquatic vegetation canopies. Detailed velocity and solute tracer measurements were undertaken for a representative range of flow velocities. The velocity measurements were used for derivi...

We used a two-year dataset (1998-1999) of monthly temperature profiles from Lake Alchichica, Mexico to estimate values of the vertical coefficient of eddy diffusivity. This lake is located in a tropical region at high altitude and shows considerable seasonal variations (i.e., rainy and dry seasons). It has an area of 2.3 km2 and a mean depth of 40.9 m. Alchichica is a warm monomictic lake, which annually becomes isothermal near the end of December or early January at the onset of the dry season and remains stratified for the rest of the year (from late March or early April to early December) during the warm-rainy season. Mathematical models of the spatial and temporal variation of passive substances in lakes and oceans require a quantitative formulation of the vertical transport. Vertical mixing is generally a function of the density profile, which, in lakes, can be directly related to the temperature profile. A widely used method to estimate the vertical diffusion coefficients in l...

During night time, when the air close to the surface cools-down and the atmosphere becomes stable, katabatic down-slope ows may occur in mountainous regions. Contrary, during day time, when the sun heats-up the air close to the surface, and the atmosphere becomes unstable, anabatic upslope ows are prevalent. Up to date, slope winds in the WKB Prandtl model are determined solely by means of specifying the height zj of the maximum turbulent jet above ground. Furthermore, depending on zj parameters K0 and h for a height-dependent eddy thermal diffusivity function KH(z) and a parameter C determining the amplitude for the Prandtl wind speeds must be specified. They are most often estimated from height-dependent wind speeds u, including slope angle α and fixed Prandtl number Pr = KM/KH with KH = KH(z) and KM the eddy viscosity. Having estimated those parameters, friction velocity u*, friction temperature θ* and sensible heat ux QH may be calculated. This article takes the reverse approach...

R. H. Kraichnan (1966) and T. S. Lundgren (1981) derived a formula for the eddy-diffusivity in Richardson's theory of turbulent 2-particle dispersion: ηij(r, t)=^t0ds <(ui(x + r, t) - ui(x, t)) (ui(x + r, t|s) - uj(x, t |s)>. This formula involves the Lagrangian velocity field u(x, t |s) experienced at time s < t by the fluid particle which is at point x at time t. Evaluating this formula requires tracking fluid particles backward in time, a difficult task with standard DNS. We compute the formula using the JHU Turbulence Database,ootnotetexthttp://turbulence.pha.jhu.edu/ which stores the entire spacetime history of a 1024^3 DNS of homogeneous, isotropic turbulence at Reλ=433. We average over particle pairs started at many different initial positions x with initial separations r. We obtain a time-dependent eddy-diffusivity ηij(r, t) which has Batchelor scaling (ɛr)^2/3t for short time and Richardson scaling &1/3 circ;r^4/3 for long time. Our resulting diffusion model de...

A novel analytical solution has been developed for the three-dimensional dispersion of atmospheric pollutants, providing a new approach to understanding and addressing this important environmental issue. The central concept of the study is to divide the planetary boundary layer into multiple vertical sub-layers, each characterized by its own average wind speed and eddy diffusivity. This allows for a more comprehensive and nuanced examination of atmospheric processes within the boundary layer. The validity of the model is thoroughly evaluated through a comparison of its predictions with data collected from the Copenhagen Diffusion and Prairie Grass experiments. This approach ensures that the model accurately reflects the complexities of atmospheric dispersion in real-world scenarios. The results of the study demonstrate a strong correlation between the predicted and measured crosswind-integrated concentrations. Furthermore, the statistical indices computed for the model fall within a...

Eddy diffusion coefficients used in eddy parameterization schemes have been diagnosed with various methods in the Southern Ocean. These studies have produced conflicting results, although they are consistent with different hypotheses for eddy diffusivity distributions. Even though eddy mixing can be diagnosed with different methods, the fundamental issue remains whether these eddy diffusion coefficients actually have sufficient skill to parameterize eddy transports in a downgradient parameterization. Lagrangian floats provide a way to test the applicability of the eddy diffusion model. Here, we will assess how well Lagrangian diffusivities, deduced from numerical float trajectories in the Southern Ocean of the 1/10 degree Parallel Ocean Program, parameterize zonally integrated as well as local eddy transports. With the 50,000 numerical floats we achieve stable Lagrangian statistics and unprecedented horizontal and vertical resolution of Lagrangian diffusivities. We then calculate Eu...

High spatial resolution isopycnal diffusivities are estimated in the Kuroshio Extension (KE) region (28°–40°N, 120°–190°E) from a global ° Parallel Ocean Program (POP) simulation. The numerical float tracks are binned using a clustering approach. The number of tracks in each bin is thus roughly the same leading to diffusivity estimates that converge better than those in bins defined by a regular geographic grid. Cross-stream diffusivities are elevated in the southern recirculation gyre region, near topographic obstacles and downstream in the KE jet, where the flow has weakened. Along-stream diffusivities, which are much larger than cross-stream diffusivities, correlate well with the magnitudes of eddy velocity. The KE jet suppresses cross-stream mixing only in some longitude ranges. This study estimates the critical layer depth both from linear local baroclinic instability analysis and from eddy phase speeds in the POP model using the Radon transform. The latter is a better predicto...

A multiwavenumber theory is formulated to represent eddy diffusivities. It expands on earlier single-wavenumber theories and includes the wide range of wavenumbers encompassed in eddy motions. In the limiting case in which ocean eddies are only composed of a single wavenumber, the multiwavenumber theory is equivalent to the single-wavenumber theory and both show mixing suppression by the eddy propagation relative to the mean flow. The multiwavenumber theory was tested in a region of the Southern Ocean (70°–45°S, 110°–20°W) that covers the Drake Passage and includes the tracer/float release locations during the Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean (DIMES). Cross-stream eddy diffusivities and mixing lengths were estimated in this region from the single-wavenumber theory, from the multiwavenumber theory, and from floats deployed in a global ° Parallel Ocean Program (POP) simulation. Compared to the single-wavenumber theory, the horizontal structures of cross-...

Lagrangian subsurface isopycnal eddy diffusivities are calculated from numerical floats released in several regions of the Antarctic Circumpolar Current (ACC) of the 0.1° Parallel Ocean Program. Lagrangian diffusivities are horizontally highly variable with no consistent latitudinal dependence. Elevated values are found in some areas in the core of the ACC, near topographic features, and close to the Brazil‐Malvinas Confluence Zone and Agulhas Retroflection. Cross‐stream eddy diffusivities are depth invariant in the model ACC. An increase of Lagrangian eddy length scales with depth is masked by the strong decrease with depth of eddy velocities. The cross‐stream diffusivities average 750 ± 250 m2 s−1 around the Polar Frontal Zone. The results imply that parameterizations that (only) use eddy kinetic energy to parameterize the diffusivities are incomplete. We suggest that dominant correlations of Lagrangian eddy diffusivities with eddy kinetic energy found in previous studies may have...

An analysis of atmospheric energy transport in 22 years (1980–2001) of the 40-yr ECMWF Re-Analysis (ERA-40) is presented. In the analyzed budgets, there is a large cancellation between divergences of dry static and latent energy such that the total energy divergence is positive over all tropical oceanic regions except for the east Pacific cold tongue, consistent with previous studies. The west Pacific and Indian Oceans are characterized by a balance between diabatic sources and mean advective energy export, with a small eddy contribution. However, in the central and eastern Pacific convergence zone, total energy convergence by the mean circulation is balanced by submonthly eddies, with a small diabatic source. Decomposing the mean advective tendency into terms due to horizontal and vertical advection shows that the spatial variation in the mean advection is due largely to variations in vertical advection; these variations are further attributed to variations in the vertical profile ...

Meromictic lakes are unique aquatic ecosystems that occur extremely rarely. The phenomenon of meromixis can result from both natural and anthropogenic factors. The aim of this study was to analyse thermal and chemical stratification in a small, deep (6 ha, H max = 24.5 m) lake. The evaluated lake had a typical summer thermal profile with a shallow epilimnion, a sharp thermocline, and a distinct monimolimnion layer in the hypolimnion, which was also maintained during circulation. The lake had a clinograde oxygen profile, with an oxygen deficit in the metalimnion and permanent anoxic conditions in the deeper layers, including during circulation. A redox zone was identified during summer stagnation. The monimolimnion formed a thermally isolated layer at a depth of around 15 m, and the chemocline was situated above the monimolimnion. In the chemocline, the EC gradient ranged from 61 to 77 μS·cm−1 per meter of depth in the summer and from 90 to 130 μS·cm−1 per meter of depth during circu...

Lagrangian isopycnal diffusivities quantify the along-isopycnal mixing of any tracer with mean gradients along isopycnal surfaces. They are studied in the Southern Ocean of the 1/10° Parallel Ocean Program (POP) model using more than 50 000 float trajectories. Concurrent Eulerian isopycnal diffusivities are estimated directly from the eddy fluxes and mean tracer gradients. Consistency, spatial variation, and relation to mean jets are evaluated. The diffusivities are calculated in bins large enough to reduce contributions from the rotational components that do not lead to net tracer mixing. Because the mean jets are nonzonal and nonparallel, meridional dispersion includes standing eddies and is significantly different from cross-stream dispersion. With the subtraction of the local Eulerian mean, the full Lagrangian diffusivity tensor can be estimated. Along-stream diffusivities are about 6 times larger than cross-stream diffusivities. Along-streamline averages of Eulerian and Lagrang...

The effect of mesoscale eddies on the vertical heat transport of the ocean is examined using two eddy‐resolving numerical models. The global heat transport by the mean flow and diffusion are both downwards and are balanced by an upward eddy heat flux. Mean and eddy advective heat fluxes dominate the subpolar regions, while diffusive flux is important primarily in the subtropics. In the subtropical abyss, the mean advective heat flux is balanced by a combination of eddy and diffusive fluxes and the classical Munk‐type advective‐diffusive heat balance must be modified. The Munk and Wunsch (1998) expression for the vertical turbulent diffusivity over‐estimates the diffusivity by as much as a factor of four near the base of the main thermocline. This implies that the mixing required to close the meridional overturning circulation determined by Munk and Wunsch (1998) may be an over‐estimate due to the neglect of mesoscale eddies.

This study examines the relative importance of the mean advection and mesoscale currents in the property exchange between the Southern Ocean mixed layer and downstream in the upper 2000 m; this exchange is referred to as ventilation. A new, highly efficient off‐line tracer model employed here uses precalculated velocities to advect dynamically passive tracers. Two idealized tracers are considered: the Boundary Impulse Response (BIR) tracer, which helps to determine the ventilation pathways and time scales, and the Transient Surface Tracer (TST), which is relevant to transient atmospheric tracers. The importance of eddies is isolated by contrasting the control simulation with a simulation without mesoscale currents. The analysis reveals complex three‐dimensional ventilation pathways, controlled by the interplay between the mean advection and eddy‐induced spreading. The mean currents carry the tracers eastward within ACC and contribute to the formation of the Antarctic Intermediate Wa...