Eddy (fluid dynamics)

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A vortex street around a cylinder. This can occur around cylinders and spheres, for any fluid, cylinder size and fluid speed, provided that the flow has a Reynolds number in the range ~40 to ~1000. Vortex-street-animation.gif
A vortex street around a cylinder. This can occur around cylinders and spheres, for any fluid, cylinder size and fluid speed, provided that the flow has a Reynolds number in the range ~40 to ~1000.

In fluid dynamics, an eddy is the swirling of a fluid and the reverse current created when the fluid is in a turbulent flow regime. [2] The moving fluid creates a space devoid of downstream-flowing fluid on the downstream side of the object. Fluid behind the obstacle flows into the void creating a swirl of fluid on each edge of the obstacle, followed by a short reverse flow of fluid behind the obstacle flowing upstream, toward the back of the obstacle. This phenomenon is naturally observed behind large emergent rocks in swift-flowing rivers.

Contents

An eddy is a movement of fluid that deviates from the general flow of the fluid. An example for an eddy is a vortex which produces such deviation. However, there are other types of eddies that are not simple vortices. For example, a Rossby wave is an eddy [3] which is an undulation that is a deviation from mean flow, but does not have the local closed streamlines of a vortex.

Swirl and eddies in engineering

The propensity of a fluid to swirl is used to promote good fuel/air mixing in internal combustion engines.

In fluid mechanics and transport phenomena, an eddy is not a property of the fluid, but a violent swirling motion caused by the position and direction of turbulent flow. [4]

A diagram showing the velocity distribution of a fluid moving through a circular pipe, for laminar flow (left), time-averaged (center), and turbulent flow, instantaneous depiction (right) Pipe flow velocity distribution laminar turbulent.svg
A diagram showing the velocity distribution of a fluid moving through a circular pipe, for laminar flow (left), time-averaged (center), and turbulent flow, instantaneous depiction (right)

Reynolds number and turbulence

Reynolds Experiment (1883). Osborne Reynolds standing beside his apparatus. Reynolds fluid turbulence experiment 1883.jpg
Reynolds Experiment (1883). Osborne Reynolds standing beside his apparatus.

In 1883, scientist Osborne Reynolds conducted a fluid dynamics experiment involving water and dye, where he adjusted the velocities of the fluids and observed the transition from laminar to turbulent flow, characterized by the formation of eddies and vortices. [5] Turbulent flow is defined as the flow in which the system's inertial forces are dominant over the viscous forces. This phenomenon is described by Reynolds number, a unit-less number used to determine when turbulent flow will occur. Conceptually, the Reynolds number is the ratio between inertial forces and viscous forces. [6]

Schlieren photograph showing the thermal convection plume rising from an ordinary candle in still air. The plume is initially laminar, but transition to turbulence occurs in the upper third of the image. The image was made by Gary Settles using a one-meter-diameter schlieren mirror. Laminar-turbulent transition.jpg
Schlieren photograph showing the thermal convection plume rising from an ordinary candle in still air. The plume is initially laminar, but transition to turbulence occurs in the upper third of the image. The image was made by Gary Settles using a one-meter-diameter schlieren mirror.

The general form for the Reynolds number flowing through a tube of radius r (or diameter d):

where v is the velocity of the fluid, ρ is its density, r is the radius of the tube, and μ is the dynamic viscosity of the fluid. A turbulent flow in a fluid is defined by the critical Reynolds number, for a closed pipe this works out to approximately

In terms of the critical Reynolds number, the critical velocity is represented as

Research and development

Computational fluid dynamics

These are turbulence models in which the Reynolds stresses, as obtained from a Reynolds averaging of the Navier–Stokes equations, are modelled by a linear constitutive relationship with the mean flow straining field, as:

where

  •  is the coefficient termed turbulence "viscosity" (also called the eddy viscosity)
  • is the mean turbulent kinetic energy
  •  is the mean strain rate
Note that that inclusion of in the linear constitutive relation is required by tensorial algebra purposes when solving for two-equation turbulence models (or any other turbulence model that solves a transport equation for  . [7]

Hemodynamics

Hemodynamics is the study of blood flow in the circulatory system. Blood flow in straight sections of the arterial tree are typically laminar (high, directed wall stress), but branches and curvatures in the system cause turbulent flow. [2] Turbulent flow in the arterial tree can cause a number of concerning effects, including atherosclerotic lesions, postsurgical neointimal hyperplasia, in-stent restenosis, vein bypass graft failure, transplant vasculopathy, and aortic valve calcification.

Industrial processes

Lift and drag properties of golf balls are customized by the manipulation of dimples along the surface of the ball, allowing for the golf ball to travel further and faster in the air. [8] [9] The data from turbulent-flow phenomena has been used to model different transitions in fluid flow regimes, which are used to thoroughly mix fluids and increase reaction rates within industrial processes. [10]

Fluid currents and pollution control

Oceanic and atmospheric currents transfer particles, debris, and organisms all across the globe. While the transport of organisms, such as phytoplankton, are essential for the preservation of ecosystems, oil and other pollutants are also mixed in the current flow and can carry pollution far from its origin. [11] [12] Eddy formations circulate trash and other pollutants into concentrated areas which researchers are tracking to improve clean-up and pollution prevention. The distribution and motion of plastics caused by eddy formations in natural water bodies can be predicted using Lagrangian transport models. [13] Mesoscale ocean eddies play crucial roles in transferring heat poleward, as well as maintaining heat gradients at different depths. [14]

Environmental flows

Modeling eddy development, as it relates to turbulence and fate transport phenomena, is vital in grasping an understanding of environmental systems. By understanding the transport of both particulate and dissolved solids in environmental flows, scientists and engineers will be able to efficiently formulate remediation strategies for pollution events. Eddy formations play a vital role in the fate and transport of solutes and particles in environmental flows such as in rivers, lakes, oceans, and the atmosphere. Upwelling in stratified coastal estuaries warrant the formation of dynamic eddies which distribute nutrients out from beneath the boundary layer to form plumes. [15] Shallow waters, such as those along the coast, play a complex role in the transport of nutrients and pollutants due to the proximity of the upper-boundary driven by the wind and the lower-boundary near the bottom of the water body. [16]

Mesoscale ocean eddies

Downwind of obstacles, in this case, the Madeira and the Canary Islands off the west African coast, eddies create turbulent patterns called vortex streets. Canary A2002186 1155 250m.jpg
Downwind of obstacles, in this case, the Madeira and the Canary Islands off the west African coast, eddies create turbulent patterns called vortex streets.

Eddies are common in the ocean, and range in diameter from centimeters to hundreds of kilometers. The smallest scale eddies may last for a matter of seconds, while the larger features may persist for months to years.

Eddies that are between about 10 and 500 km (6 and 300 miles) in diameter and persist for periods of days to months are known in oceanography as mesoscale eddies. [17]

Mesoscale eddies can be split into two categories: static eddies, caused by flow around an obstacle (see animation)[ clarification needed ], and transient eddies, caused by baroclinic instability.

When the ocean contains a sea surface height gradient this creates a jet or current, such as the Antarctic Circumpolar Current. This current as part of a baroclinically unstable system meanders and creates eddies (in much the same way as a meandering river forms an oxbow lake). These types of mesoscale eddies have been observed in many major ocean currents, including the Gulf Stream, the Agulhas Current, the Kuroshio Current, and the Antarctic Circumpolar Current, amongst others.

Mesoscale ocean eddies are characterized by currents that flow in a roughly circular motion around the center of the eddy. The sense of rotation of these currents may either be cyclonic or anticyclonic (such as Haida Eddies). Oceanic eddies are also usually made of water masses that are different from those outside the eddy. That is, the water within an eddy usually has different temperature and salinity characteristics to the water outside the eddy. There is a direct link between the water mass properties of an eddy and its rotation. Warm eddies rotate anti-cyclonically, while cold eddies rotate cyclonically.

Because eddies may have a vigorous circulation associated with them, they are of concern to naval and commercial operations at sea. Further, because eddies transport anomalously warm or cold water as they move, they have an important influence on heat transport in certain parts of the ocean. [18]

Influences on apex predators

The sub-tropical Northern Atlantic is known to have both cyclonic and anticyclonic eddies that are associated with high surface chlorophyll and low surface chlorophyll, respectively. The presence of chlorophyll and higher levels of chlorophyll allows this region to support higher biomass of phytoplankton, as well as, supported by areas of increased vertical nutrient fluxes and transportation of biological communities. This area of the Atlantic is also thought to be an ocean desert, which creates an interesting paradox due to it hosting a variety of large pelagic fish populations and apex predators [19] [20] [21]

These mesoscale eddies have shown to be beneficial in further creating ecosystem-based management for food web models to better understand the utilization of these eddies by both the apex predators and their prey. Gaube et al. (2018), used “Smart” Position or Temperature Transmitting tags (SPOT) and Pop-Up Satellite Archival Transmitting tags (PSAT) to track the movement and diving behavior of two female white sharks (Carcharodon carcharias) within the eddies. The eddies were defined using sea surface height (SSH) and contours using the horizontal speed-based radius scale. This study found that the white sharks dove in both cyclones but favored the anticyclone which had three times more dives as the cyclonic eddies. Additionally, in the Gulf Stream eddies, the anticyclonic eddies were 57% more common and had more dives and deeper dives than the open ocean eddies and Gulf Stream cyclonic eddies. [21]

Within these anticyclonic eddies, the isotherm was displaced 50 meters downward allowing for the warmer water to penetrate deeper in the water column. This warmer water displacement may allow for the white sharks to make longer dives without the added energetic cost from thermal regulation in the cooler cyclones. Even though these anticyclonic eddies resulted in lower levels of chlorophyll in comparison to the cyclonic eddies, the warmer waters at deeper depths may allow for a deeper mixed layer and higher concentration of diatoms which in turn result in higher rates of primary productivity. [21] [22] Furthermore, the prey populations could be distributed more within these eddies attracting these larger female sharks to forage in this mesopelagic zone. This diving pattern may follow a diel vertical migration but without more evidence on the biomass of their prey within this zone, these conclusions cannot be made only using this circumstantial evidence. [21]

The biomass in the mesopelagic zone is still understudied leading to the biomass of fish within this layer to potentially be underestimated. A more accurate measurement on this biomass may serve to benefit the commercial fishing industry providing them with additional fishing grounds within this region. Moreover, further understanding this region in the open ocean and how the removal of fish in this region may impact this pelagic food web is crucial for the fish populations and apex predators that may rely on this food source in addition to making better ecosystem-based management plans. [21]

See also

Related Research Articles

<span class="mw-page-title-main">Fluid dynamics</span> Aspects of fluid mechanics involving flow

In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics and hydrodynamics. Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation.

<span class="mw-page-title-main">Laminar flow</span> Flow where fluid particles follow smooth paths in layers

In fluid dynamics, laminar flow is characterized by fluid particles following smooth paths in layers, with each layer moving smoothly past the adjacent layers with little or no mixing. At low velocities, the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards. There are no cross-currents perpendicular to the direction of flow, nor eddies or swirls of fluids. In laminar flow, the motion of the particles of the fluid is very orderly with particles close to a solid surface moving in straight lines parallel to that surface. Laminar flow is a flow regime characterized by high momentum diffusion and low momentum convection.

In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between those layers.

<span class="mw-page-title-main">Baroclinity</span> Measure of misalignment between the gradients of pressure and density in a fluid

In fluid dynamics, the baroclinity of a stratified fluid is a measure of how misaligned the gradient of pressure is from the gradient of density in a fluid. In meteorology a baroclinic flow is one in which the density depends on both temperature and pressure. A simpler case, barotropic flow, allows for density dependence only on pressure, so that the curl of the pressure-gradient force vanishes.

The Richardson number (Ri) is named after Lewis Fry Richardson (1881–1953). It is the dimensionless number that expresses the ratio of the buoyancy term to the flow shear term:

<span class="mw-page-title-main">Large eddy simulation</span> Mathematical model for turbulence

Large eddy simulation (LES) is a mathematical model for turbulence used in computational fluid dynamics. It was initially proposed in 1963 by Joseph Smagorinsky to simulate atmospheric air currents, and first explored by Deardorff (1970). LES is currently applied in a wide variety of engineering applications, including combustion, acoustics, and simulations of the atmospheric boundary layer.

In fluid dynamics, the Reynolds stress is the component of the total stress tensor in a fluid obtained from the averaging operation over the Navier–Stokes equations to account for turbulent fluctuations in fluid momentum.

In fluid dynamics, the Schmidt number of a fluid is a dimensionless number defined as the ratio of momentum diffusivity and mass diffusivity, and it is used to characterize fluid flows in which there are simultaneous momentum and mass diffusion convection processes. It was named after German engineer Ernst Heinrich Wilhelm Schmidt (1892–1975).

In fluid dynamics, turbulence kinetic energy (TKE) is the mean kinetic energy per unit mass associated with eddies in turbulent flow. Physically, the turbulence kinetic energy is characterised by measured root-mean-square (RMS) velocity fluctuations. In the Reynolds-averaged Navier Stokes equations, the turbulence kinetic energy can be calculated based on the closure method, i.e. a turbulence model.

<span class="mw-page-title-main">Eddy diffusion</span> Mixing of fluids due to eddy currents

In fluid dynamics, eddy diffusion, eddy dispersion, or turbulent diffusion is a process by which fluid substances mix together due to eddy motion. These eddies can vary widely in size, from subtropical ocean gyres down to the small Kolmogorov microscales, and occur as a result of turbulence. The theory of eddy diffusion was first developed by Sir Geoffrey Ingram Taylor.

<span class="mw-page-title-main">Hydrodynamic stability</span> Subfield of fluid dynamics

In fluid dynamics, hydrodynamic stability is the field which analyses the stability and the onset of instability of fluid flows. The study of hydrodynamic stability aims to find out if a given flow is stable or unstable, and if so, how these instabilities will cause the development of turbulence. The foundations of hydrodynamic stability, both theoretical and experimental, were laid most notably by Helmholtz, Kelvin, Rayleigh and Reynolds during the nineteenth century. These foundations have given many useful tools to study hydrodynamic stability. These include Reynolds number, the Euler equations, and the Navier–Stokes equations. When studying flow stability it is useful to understand more simplistic systems, e.g. incompressible and inviscid fluids which can then be developed further onto more complex flows. Since the 1980s, more computational methods are being used to model and analyse the more complex flows.

<span class="mw-page-title-main">Reynolds number</span> Ratio of inertial to viscous forces acting on a liquid

In fluid mechanics, the Reynolds number is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers, flows tend to be turbulent. The turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow. These eddy currents begin to churn the flow, using up energy in the process, which for liquids increases the chances of cavitation.

Particle-laden flows refers to a class of two-phase fluid flow, in which one of the phases is continuously connected and the other phase is made up of small, immiscible, and typically dilute particles. Fine aerosol particles in air is an example of a particle-laden flow; the aerosols are the dispersed phase, and the air is the carrier phase.

K-epsilon (k-ε) turbulence model is one of the most common models used in computational fluid dynamics (CFD) to simulate mean flow characteristics for turbulent flow conditions. It is a two equation model that gives a general description of turbulence by means of two transport equations. The original impetus for the K-epsilon model was to improve the mixing-length model, as well as to find an alternative to algebraically prescribing turbulent length scales in moderate to high complexity flows.

Reynolds stress equation model (RSM), also referred to as second moment closures are the most complete classical turbulence model. In these models, the eddy-viscosity hypothesis is avoided and the individual components of the Reynolds stress tensor are directly computed. These models use the exact Reynolds stress transport equation for their formulation. They account for the directional effects of the Reynolds stresses and the complex interactions in turbulent flows. Reynolds stress models offer significantly better accuracy than eddy-viscosity based turbulence models, while being computationally cheaper than Direct Numerical Simulations (DNS) and Large Eddy Simulations.

Menter's Shear Stress Transport turbulence model, or SST, is a widely used and robust two-equation eddy-viscosity turbulence model used in Computational Fluid Dynamics. The model combines the k-omega turbulence model and K-epsilon turbulence model such that the k-omega is used in the inner region of the boundary layer and switches to the k-epsilon in the free shear flow.

<span class="mw-page-title-main">Gamma-Re Transition Model</span>

Gamma-Re (γ-Re) transition model is a two equation model used in Computational Fluid Dynamics (CFD) to modify turbulent transport equations to simulate laminar, laminar-to-turbulent and turbulence states in a fluid flow. The Gamma-Re model does not intend to model the physics of the problem but attempts to fit a wide range of experiments and transition methods into its formulation. The transition model calculated an intermittency factor that creates turbulence by slowly introducing turbulent production at the laminar-to-turbulent transition location.

Skin friction drag is a type of aerodynamic or hydrodynamic drag, which is resistant force exerted on an object moving in a fluid. Skin friction drag is caused by the viscosity of fluids and is developed from laminar drag to turbulent drag as a fluid moves on the surface of an object. Skin friction drag is generally expressed in terms of the Reynolds number, which is the ratio between inertial force and viscous force.

A baroclinic instability is a fluid dynamical instability of fundamental importance in the atmosphere and ocean. It can lead to the formation of transient mesoscale eddies, with a horizontal scale of 10-100 km. In contrast, flows on the largest scale in the ocean are described as ocean currents, the largest scale eddies are mostly created by shearing of two ocean currents and static mesoscale eddies are formed by the flow around an obstacle (as seen in the animation on eddy. Mesoscale eddies are circular currents with swirling motion and account for approximately 90% of the ocean's total kinetic energy. Therefore, they are key in mixing and transport of for example heat, salt and nutrients.

Eddy pumping is a component of mesoscale eddy-induced vertical motion in the ocean. It is a physical mechanism through which vertical motion is created from variations in an eddy's rotational strength. Cyclonic (Anticyclonic) eddies lead primarily to upwelling (downwelling) in the Northern Hemisphere and vice versa in the Southern hemisphere. It is a key mechanism driving biological and biogeochemical processes in the ocean such as algal blooms and the carbon cycle.

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