Stable and unstable stratification

Last updated

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.

Contents

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

KHI.gif
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.

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">Thermohaline circulation</span> Part of large-scale ocean circulation

Thermohaline circulation (THC) is a part of the large-scale ocean circulation that is driven by global density gradients created by surface heat and freshwater fluxes. The adjective thermohaline derives from thermo- referring to temperature and -haline referring to salt content, factors which together determine the density of sea water. Wind-driven surface currents travel polewards from the equatorial Atlantic Ocean, cooling en route, and eventually sinking at high latitudes. This dense water then flows into the ocean basins. While the bulk of it upwells in the Southern Ocean, the oldest waters upwell in the North Pacific. Extensive mixing therefore takes place between the ocean basins, reducing differences between them and making the Earth's oceans a global system. The water in these circuits transport both energy and mass around the globe. As such, the state of the circulation has a large impact on the climate of the Earth.

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">Thermocline</span> Thermal layer in a body of water

A thermocline is a distinct layer based on temperature within a large body of fluid A gradiant 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">Surface layer</span> Layer of a turbulent fluid affected by interaction with a surface

The surface layer is the layer of a turbulent fluid most affected by interaction with a solid surface or the surface separating a gas and a liquid where the characteristics of the turbulence depend on distance from the interface. Surface layers are characterized by large normal gradients of tangential velocity and large concentration gradients of any substances transported to or from the interface.

<span class="mw-page-title-main">Convective available potential energy</span>

In meteorology, convective available potential energy, is the integrated amount of work that the upward (positive) buoyancy force would perform on a given mass of air if it rose vertically through the entire atmosphere. Positive CAPE will cause the air parcel to rise, while negative CAPE will cause the air parcel to sink. Nonzero CAPE is an indicator of atmospheric instability in any given atmospheric sounding, a necessary condition for the development of cumulus and cumulonimbus clouds with attendant severe weather hazards.

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.

Ocean stratification is the separation of an ocean's water in layers. Stratification occurs in all ocean basins and also in other water bodies. Stratified layers act as a barrier to the mixing of water, which impacts the exchange of heat, carbon, oxygen and other nutrients. Due to upwelling and downwelling, which are both wind-driven, mixing of different layers can occur through the rise of cold nutrient-rich and warm water, respectively. Generally, layers are based on water density: heavier, and hence denser, water is below the lighter water, representing a stable stratification.

<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 stability is a measure of the atmosphere's tendency to discourage vertical motion, and vertical motion is directly correlated to different types of weather systems and their severity. In unstable conditions, a lifted thing, such as a parcel of air will be warmer than the surrounding air. Because it is warmer, it is less dense and is prone to further ascent.

<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.

<span class="mw-page-title-main">Barrier layer (oceanography)</span> Layer of water separating the well-mixed surface layer from the thermocline

The Barrier layer in the ocean is a layer of water separating the well-mixed surface layer from the thermocline.

The flow in many fluids varies with density and depends upon the gravity. Due to which 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.

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.