Stable and unstable stratification

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Stable stratification of fluids occurs when each layer is less dense than the one below it. Unstable stratification is when each layer is denser than the one below it.

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Buoyancy forces tend to preserve stable stratification; the higher layers float on the lower ones. In unstable stratification, on the other hand, buoyancy forces cause convection. The less-dense layers rise though the denser layers above, and the denser layers sink though the less-dense layers below. Stratifications can become more or less stable if layers change density. The processes involved are important in many science and engineering fields.

Destablization and mixing

Model of the initiation of termination of a Rayleigh-Taylor instability in 2D.gif
A simple model of an unstable stratification converting to a stable one (in immiscible fluids, like oil and water, or the wax and water of a lava lamp). Note Rayleigh–Taylor instability plumes (with "mushroom" heads) in both colours/directions.
Latte macchiato.jpg
A stably-stratified beverage of cold milk, warm coffee, and cream. The least dense layer is on top. The milk and coffee are slowly mixing to form new diffusive layers, visible in intermediate shades of brown, as the milk warms and the coffee cools at the interface.
Schematic of staircase structure due to salt fingering.pdf
Diffusive layers may internally be homogeneously-mixed, but with each layer different from the next. This leads to stair-step profiles in physical properties (here, temperature and salinity; in the previous photo, colour).
Thermal-plume-from-human-hand.jpg
A human hand heating air. The heated air is underneath unheated air, an unstable stratification, so the hand-heated air rises and the cool air sinks, causing convection.
Typical mixing pattern for many lakes, caused by the fact that water is less dense at the freezing point than at 4 Celsius. Lake stratification is stable in summer and winter, becoming unstable in spring and fall when the surface waters cross the 4 Celsius mark. LSE Stratification.png
Typical mixing pattern for many lakes, caused by the fact that water is less dense at the freezing point than at 4 Celsius. Lake stratification is stable in summer and winter, becoming unstable in spring and fall when the surface waters cross the 4 Celsius mark.

Stable stratifications can become unstable if layers change density. This can happen due to outside influences (for instance, if water evaporates from a freshwater lens, making it saltier and denser, or if a pot or layered beverage is heated from below, making the bottom layer less dense). However, it can also happen due to internal diffusion of heat (the warmer layer slowly heats the adjacent cooler one) or other physical properties. This often causes mixing at the interface, creating new diffusive layers (see photo of coffee and milk).

Sometimes, two physical properties diffuse between layers simultaneously; salt and temperature, for instance. This may form diffusive layers or even salt fingering, when the surfaces of the diffusive layers become so wavy that there are "fingers" of layers reaching up and down.

Not all mixing is driven by density changes. Other physical forces may also mix stably-stratified layers. Sea spray and whitecaps (foaming whitewater on waves) are examples of water mixed into air, and air into water, respectively. In a fierce storm the air/water boundary may grow indistinct. Some of these wind waves are Kelvin-Helmholtz waves. [1]

Depending on the size of the velocity difference and the size of the density contrast between the layers, Kelvin-Helmholtz waves can look different. For instance, between two layers of air or two layers of water, the density difference is much smaller and the layers are miscible; see black-and-white model video.

Applications

Planetary science

When two stably-stratified layers are moving relative to one another, Kelvin-Helmholtz waves may form at the interface. These patterns are also seen on other planets. [1]
Kelvin-Helmholtz instability clouds.jpg
These clouds trace the Kelvin-Helmholtz waves between two thermally-stratified layers of the atmosphere.
Earth's lithosphere includes upwards heat flow, partial convection, and a metal-layer core. Models of mantle dynamics.jpg
Earth's lithosphere includes upwards heat flow, partial convection, and a metal-layer core.

Stratification is commonly seen in the planetary sciences.

Solar energy passes as visible radiation through the air, and is absorbed by the ground, to be re-emitted as heat radiation. The lower atmosphere is therefore heated from below (UV absorption in the ozone layer heats that layer from within). Outdoor air is thus usually unstably stratified and convecting, giving us wind. Temperature inversions are a weather event which happens whenever an area of the lower atmosphere becomes stably-stratified and thus stops moving. [2] [3]

Oceans, on the other hand, are heated from above, and are usually stably stratified. Only near the poles does the coldest and saltiest water sink. The deep ocean waters slowly warm and freshen through internal mixing (a form of double diffusion [4] ), and then rise back to the surface.

Examples:

Engineering

Vertical temperature gradient cause by stable stratification of air inside a room. Note hot air rising convectively from the person; bodyheat temporarily disrupts the stable stratification. UFAD Air Stratification Example Diagram.jpg
Vertical temperature gradient cause by stable stratification of air inside a room. Note hot air rising convectively from the person; bodyheat temporarily disrupts the stable stratification.

In engineering applications, stable stratification or convection may or may not be desirable. In either case it may be deliberately manipulated. Stratification can strongly affect the mixing of fluids, [5] which is important in many manufacturing processes.

Related Research Articles

<span class="mw-page-title-main">Convection</span> Fluid flow that occurs due to heterogeneous fluid properties and body forces

Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity. When the cause of the convection is unspecified, convection due to the effects of thermal expansion and buoyancy can be assumed. Convection may also take place in soft solids or mixtures where particles can flow.

<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.

<span class="mw-page-title-main">Convection cell</span> Cyclic flow of convection currents in a fluid

In fluid dynamics, a convection cell is the phenomenon that occurs when density differences exist within a body of liquid or gas. These density differences result in rising and/or falling convection currents, which are the key characteristics of a convection cell. When a volume of fluid is heated, it expands and becomes less dense and thus more buoyant than the surrounding fluid. The colder, denser part of the fluid descends to settle below the warmer, less-dense fluid, and this causes the warmer fluid to rise. Such movement is called convection, and the moving body of liquid is referred to as a convection cell. This particular type of convection, where a horizontal layer of fluid is heated from below, is known as Rayleigh–Bénard convection. Convection usually requires a gravitational field, but in microgravity experiments, thermal convection has been observed without gravitational effects.

Equivalent potential temperature, commonly referred to as theta-e, is a quantity that is conserved during changes to an air parcel's pressure, even if water vapor condenses during that pressure change. It is therefore more conserved than the ordinary potential temperature, which remains constant only for unsaturated vertical motions.

<span class="mw-page-title-main">Thermocline</span> Distinct layer of temperature change in a body of water

A thermocline is a distinct layer based on temperature within a large body of fluid with a high gradient of distinct temperature differences associated with depth. In the ocean, the thermocline divides the upper mixed layer from the calm deep water below.

<span class="mw-page-title-main">Pycnocline</span> Layer where the density gradient is greatest within a body of water

A pycnocline is the cline or layer where the density gradient is greatest within a body of water. An ocean current is generated by the forces such as breaking waves, temperature and salinity differences, wind, Coriolis effect, and tides caused by the gravitational pull of celestial bodies. In addition, the physical properties in a pycnocline driven by density gradients also affect the flows and vertical profiles in the ocean. These changes can be connected to the transport of heat, salt, and nutrients through the ocean, and the pycnocline diffusion controls upwelling.

The potential temperature of a parcel of fluid at pressure is the temperature that the parcel would attain if adiabatically brought to a standard reference pressure , usually 1,000 hPa (1,000 mb). The potential temperature is denoted and, for a gas well-approximated as ideal, is given by

In atmospheric dynamics, oceanography, asteroseismology and geophysics, the Brunt–Väisälä frequency, or buoyancy frequency, is a measure of the stability of a fluid to vertical displacements such as those caused by convection. More precisely it is the frequency at which a vertically displaced parcel will oscillate within a statically stable environment. It is named after David Brunt and Vilho Väisälä. It can be used as a measure of atmospheric stratification.

Isopycnals are layers within the ocean that are stratified based on their densities and can be shown as a line connecting points of a specific density or potential density on a graph. Isopycnals are often displayed graphically to help visualize "layers" of the water in the ocean or gases in the atmosphere in a similar manner to how contour lines are used in topographic maps to help visualize topography.

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<span class="mw-page-title-main">Mixed layer</span> Layer in which active turbulence has homogenized some range of depths

The oceanic or limnological mixed layer is a layer in which active turbulence has homogenized some range of depths. The surface mixed layer is a layer where this turbulence is generated by winds, surface heat fluxes, or processes such as evaporation or sea ice formation which result in an increase in salinity. The atmospheric mixed layer is a zone having nearly constant potential temperature and specific humidity with height. The depth of the atmospheric mixed layer is known as the mixing height. Turbulence typically plays a role in the formation of fluid mixed layers.

A dimictic lake is a body of freshwater whose difference in temperature between surface and bottom layers becomes negligible twice per year, allowing all strata of the lake's water to circulate vertically. All dimictic lakes are also considered holomictic, a category which includes all lakes which mix one or more times per year. During winter, dimictic lakes are covered by a layer of ice, creating a cold layer at the surface, a slightly warmer layer beneath the ice, and a still-warmer unfrozen bottom layer, while during summer, the same temperature-derived density differences separate the warm surface waters, from the colder bottom waters. In the spring and fall, these temperature differences briefly disappear, and the body of water overturns and circulates from top to bottom. Such lakes are common in mid-latitude regions with temperate climates.

<span class="mw-page-title-main">Atmospheric instability</span> Condition where the Earths atmosphere is generally considered to be unstable

Atmospheric instability is a condition where the Earth's atmosphere is considered to be unstable and as a result local weather is highly variable through distance and time. Atmospheric instability encourages vertical motion, which is directly correlated to different types of weather systems and their severity. For example, under unstable conditions, a lifted parcel of air will find cooler and denser surrounding air, making the parcel prone to further ascent, in a positive feedback loop.

<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">Double diffusive convection</span> Convection with two density gradients

Double diffusive convection is a fluid dynamics phenomenon that describes a form of convection driven by two different density gradients, which have different rates of diffusion.

<span class="mw-page-title-main">Geophysical fluid dynamics</span> Dynamics of naturally occurring flows

Geophysical fluid dynamics, in its broadest meaning, refers to the fluid dynamics of naturally occurring flows, such as lava flows, oceans, and planetary atmospheres, on Earth and other planets.

The flow in many fluids varies with density and depends upon gravity. The fluid with lower density is always above the fluid with higher density. Stratified flows are very common such as the Earth's ocean and its atmosphere.

<span class="mw-page-title-main">Stratification (water)</span> Layering of a body of water due to density variations

Stratification in water is the formation in a body of water of relatively distinct and stable layers by density. It occurs in all water bodies where there is stable density variation with depth. Stratification is a barrier to the vertical mixing of water, which affects the exchange of heat, carbon, oxygen and nutrients. Wind-driven upwelling and downwelling of open water can induce mixing of different layers through the stratification, and force the rise of denser cold, nutrient-rich, or saline water and the sinking of lighter warm or fresher water, respectively. Layers are based on water density: denser water remains below less dense water in stable stratification in the absence of forced mixing.

<span class="mw-page-title-main">Turner angle</span>

The Turner angleTu, introduced by Ruddick(1983) and named after J. Stewart Turner, is a parameter used to describe the local stability of an inviscid water column as it undergoes double-diffusive convection. The temperature and salinity attributes, which generally determine the water density, both respond to the water vertical structure. By putting these two variables in orthogonal coordinates, the angle with the axis can indicate the importance of the two in stability. Turner angle is defined as:

Open ocean convection is a process in which the mesoscale ocean circulation and large, strong winds mix layers of water at different depths. Fresher water lying over the saltier or warmer over the colder leads to the stratification of water, or its separation into layers. Strong winds cause evaporation, so the ocean surface cools, weakening the stratification. As a result, the surface waters are overturned and sink while the "warmer" waters rise to the surface, starting the process of convection. This process has a crucial role in the formation of both bottom and intermediate water and in the large-scale thermohaline circulation, which largely determines global climate. It is also an important phenomena that controls the intensity of the Atlantic Meridional Overturning Circulation (AMOC).

References

  1. 1 2 Zell, Holly; Fox, Karen C. (30 December 2014). "NASA's Solar Dynamics Observatory Catches "Surfer" Waves on the Sun". NASA.
  2. Mahrt, L. (3 January 2014). "Stably Stratified Atmospheric Boundary Layers" (PDF). Annual Review of Fluid Mechanics. 46 (1): 23–45. Bibcode:2014AnRFM..46...23M. doi:10.1146/annurev-fluid-010313-141354.
  3. "Stable and unstable atmospheric stratification in simple words". WINDY.APP.
  4. Maiti, D. K.; Gupta, A. S.; Bhattacharyya, S. (1 December 2008). "Stable/Unstable Stratification in Thermosolutal Convection in a Square Cavity". Journal of Heat Transfer. 130 (12): 122001. doi:10.1115/1.2969757.
  5. Xu, Duo; Chen, Jun (December 2016). "On the mixing models for stratified flows subjected to concomitant stable and unstable stratifications". Journal of Turbulence. 17 (12): 1087–1111. Bibcode:2016JTurb..17.1087X. doi:10.1080/14685248.2016.1223846.