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	~~Andrew Berryhill~~ is ~~what his spouse enjoys to call him~~ and ~~he totally digs that name~~. ~~The favorite hobby~~ for ~~him~~ and ~~his children~~ is ~~fashion~~ and ~~he'll~~ be ~~starting something else alongside with it~~. For ~~years she~~'~~s been operating as a travel agent~~. ~~North Carolina~~ is the ~~location he loves most but now he~~ is ~~considering other choices~~.<br><br>~~My weblog ..~~. [~~http~~://~~www~~.~~chk~~.~~woobi~~.co.kr/xe/~~?document_srl~~=~~346069 best psychic readings~~]		{{Unreferenced\|date=December 2009}}

			In [[atmospheric dynamics]], [[oceanography]], [[asteroseismology]] and [[geophysics]], the '''Brunt–Väisälä frequency''', or [[buoyancy]] frequency, is the angular frequency at which a vertically displaced parcel will oscillate within a statically stable environment. It is named after [[David Brunt]] and [[Vilho Väisälä]].

			==Derivation for a general fluid==
			Consider a parcel of (water or gas) that has density of <math>\rho_0</math> and the environment with a density that is a function of height: <math>\rho = \rho (z)</math>. If the parcel is displaced by a small vertical increment <math>z'</math>, it will subject to an extra gravitational force against its surroundings of:

			:<math>\rho_0 \frac{\partial^2 z'}{\partial t^2} = - g (\rho (z)-\rho (z+z'))</math>

			g is the gravitational acceleration, and is defined to be positive. We make a [[Newton's method]] approximation to <math>\rho (z+z') - \rho (z) = \frac{\partial \rho (z)}{\partial z} z'</math>, and move <math>\rho_0</math> to the RHS:

			:<math>\frac{\partial^2 z'}{\partial t^2} = \frac{g}{\rho_0} \frac{\partial \rho (z)}{\partial z} z' </math>

			The above 2nd order [[differential equation]] has straightforward solutions of:

			:<math>z' = z'_0 e^{\sqrt{-N^2} t}\!</math>

			where the Brunt–Väisälä frequency ''N'' is:

			:<math>N = \sqrt{- \frac{g}{\rho_0} \frac{\partial \rho (z)}{\partial z}}</math>

			For negative <math>\frac{\partial \rho (z)}{\partial z}</math>, z' has oscillating solutions (and N gives our angular frequency). If it is positive, then there is run away growth – i.e. the fluid is statically unstable.

			==In meteorology and oceanography==
			In the atmosphere,

			: <math>N \equiv \sqrt{\frac{g}{\theta}\frac{d\theta}{dz}}</math>, where <math>\theta</math> is [[potential temperature]], <math>g</math> is the local acceleration of [[gravity]], and <math>z</math> is [[geometric height]].

			In the ocean where [[salinity]] is important, or in fresh water lakes near freezing, where density is not a linear function of temperature,

			: <math>N \equiv \sqrt{-\frac{g}{\rho}\frac{d\rho}{dz}}</math>, where <math>\rho</math>, the [[potential density]], depends on both temperature and salinity.

			==Context==
			The concept derives from Newton's Second Law when applied to a fluid parcel in the presence of a background stratification (in which the density changes in the vertical). The parcel, perturbed vertically from its starting position, experiences a vertical acceleration. If the acceleration is back towards the initial position, the stratification is said to be stable and the parcel oscillates vertically. In this case, {{math\|<var>N</var><sup>2</sup> > 0}} and the [[angular frequency]] of oscillation is given {{math\|<var>N</var>}}. If the acceleration is away from the initial position ({{math\|<var>N</var><sup>2</sup> < 0}}), the stratification is unstable. In this case, overturning or convection generally ensues.

			The Brunt–Väisälä frequency relates to internal gravity waves and provides a useful description of atmospheric and oceanic stability.

			==See also==
			*[[Buoyancy]]
			*[[Bénard cell]]

			{{DEFAULTSORT:Brunt-Vaisala Frequency}}
			[[Category:Atmospheric thermodynamics]]
			[[Category:Atmospheric dynamics]]
			[[Category:Fluid dynamics]]
			[[Category:Oceanography]]
			[[Category:Buoyancy]]

en>777sms at 03:22, 14 April 2012

2012-04-14T03:22:29Z

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Andrew Berryhill is what his spouse enjoys to call him and he totally digs that name. The favorite hobby for him and his children is fashion and he'll be starting something else alongside with it. For years she's been operating as a travel agent. North Carolina is the location he loves most but now he is considering other choices.<br><br>My weblog ... [http://www.chk.woobi.co.kr/xe/?document_srl=346069 best psychic readings]

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