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[[File:Langmuir Circulation.jpg|right|thumb|Langmuir circulation]]
[[File:Rodeo Lagoon From Trail.JPG|thumb|right|White streaks in this lagoon are due to the Langmuir circulation.]]
[[File:Lines of sargassum Sargasso Sea.jpg|thumb|right|These lines of [[sargassum]] can stretch for miles along the surface. The clumps of floating [[algae]] are often concentrated by the strong winds and wave action associated with the [[Gulf Stream]].]]


In [[physical oceanography]], '''Langmuir circulation''' consists of a series of shallow, slow, counter-rotating [[vortex|vortices]] at the ocean's surface aligned with the wind.
These circulations are developed when wind blows steadily over the sea surface.
[[Irving Langmuir]] discovered this phenomenon after observing [[windrow]]s of seaweed in the [[Sargasso Sea]] in 1927.<ref>
{{Citation | publisher = Butterworth-Heinemann | isbn = 9780750652780 | author = Open University | edition = 2nd | title = Ocean Circulation | year = 2001 }}
</ref>
Langmuir circulations circulate within the [[mixed layer]], there is some uncertainty as to how strongly they can case mixing at the base of the mixed layer.
<ref>
{{citation | last1=Thorpe | first1=S.A. | year=2004 | title=Langmuir circulation| journal=Annual Reviews Fluid Mechanics | volume=36  | pages=55–79 | doi= 10.1146/annurev.fluid.36.052203.071431 }}
</ref>


== Theory ==
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The driving force of these circulations is an interaction of the mean flow with wave averaged flows of the surface waves.
[[Stokes drift|Stokes drift velocity]] of the waves stretches and tilts the vorticity of the flow near the surface.
The production of vorticity in the upper ocean is balanced by downward (often turbulent) diffusion <math>\nu_T</math>.
For a flow driven by a wind <math>\tau</math> characterized by [[friction velocity]] <math>u_*</math> the ratio of vorticity diffusion and production defines the Langmuir number
<ref>
{{citation | last1=Thorpe | first1=S.A. | year=2004 | title=Langmuir circulation| journal=Annual Reviews Fluid Mechanics | volume=36  | pages=55–79 | doi= 10.1146/annurev.fluid.36.052203.071431 }}
</ref>
: <math>
\mathrm{La}
=
\sqrt{\frac{\nu^3_Tk^6}{\sigma a^2u^2_*k^4}}
\ \mathrm{or}\
\sqrt{\frac{\nu_T^3\beta^6}{u^2_*S_0\beta^3}}
</math>
where the first definition is for a monochromatic wave field of amplitude <math>a</math>, frequency <math>\sigma</math>, and wavenumber <math>k</math> and the second uses a generic inverse length scale <math>\beta</math>, and Stokes velocity scale <math>S_0</math>.
This is exemplified by the Craik-Leibovich equations<ref>
{{citation | last1=Craik | first1=A.D.D. | last2=Leibovich |first2=S. | year=1976 | title=A Rational model for Langmuir circulations| journal=Journal of Fluid Mechanics | volume=73  | pages=401–426 | doi= 10.1017/S0022112076001420 }}
</ref>
which are an approximation of the Lagrangian mean
<ref>
{{citation | last1=Andrews | first1=D.G. | last2=McIntyre |first2=M.E. | year=1978 | title=An exact theory of nonlinear waves on a Lagrangian-mean flow| journal=Journal of Fluid Mechanics | volume=89 | pages=609–646 | doi= 10.1017/S0022112078002773 }}
</ref>
.<ref>
{{citation | last1=Leibovich |first1=S. | year=1980 | title=On wave-current interactions theories of Langmuir circulations| journal=Journal of Fluid Mechanics | volume=99  | pages=715–724 | doi= 10.1017/S0022112080000857 }}
</ref>
In the [[Boussinesq approximation (buoyancy)|Boussinesq approximation]] the governing equations can be written
: <math>
\frac{\partial u_i}{\partial t}
+u_j\nabla_ju_i
=
\begin{array}{l}
-2\epsilon_{ijk}\Omega_j\left(u^s_k+u_k\right)
-\nabla_i\left(\frac{P}{\rho_0}+\frac{1}{2}u^s_ju^s_j+u^s_ju_j\right)\\
+\epsilon_{ijk}u^s_j\epsilon_{klm}\nabla_lu_m
+g_i\frac{\rho}{\rho_0}
+\nabla_j\nu\nabla_ju_i
\end{array}
</math>
: <math>
\nabla_iu_i=0
</math>
: <math>
\frac{\partial \rho}{\partial t}
+u_j\nabla_j\rho
=
\nabla_i\kappa\nabla_i\rho
</math>
where
<math>u_i</math> is the fluid velocity,  
<math>\Omega</math> is planetary rotation,  
<math>u^s_i</math> is the stokes drift velocity of the surface wave field,  
<math>P</math> is the pressure,
<math>g_i</math> is the acceleration due to gravity,  
<math>\rho</math> is the density,
<math>\rho_0</math> is the reference density,  
<math>\nu</math> is the viscosity,
and
<math>\kappa</math> is the diffusivity.
 
In the open ocean conditions where there may not be a dominant length scale controlling the scale of the Langmuir cells the concept of [[Langmuir Turbulence]] is advanced.
<ref>
{{citation | last1=McWilliams | first1=J. | last2=Sullivan |first2=P. | last3=Moeng | first3=C. | year=1997 | title=Langmuir turbulence in the ocean| journal=Journal of Fluid Mechanics | volume=334  | pages=1–30 | doi= 10.1017/S0022112096004375 }}
</ref>
 
== Observations ==
The circulation has been observed to be between 0°-20° to the right of the wind in the [[northern hemisphere]]
<ref>
{{citation |last=Stewart |first=Robert H. |title=Introduction To Physical Oceanography |year=2002 |edition=Fall 2002 }}
</ref>
and the [[helix]] forming bands of [[divergence]] and [[Convergence zone|convergence]] at the surface.
At the convergence zones, there are commonly concentrations of floating seaweed, foam and debris along these bands.
Along these divergent zones, the ocean surface is typically clear of debris since diverging currents force material out of this zone and into adjacent converging zones.
At the surface the circulation will set a current from the divergence zone to the convergence zone and the spacing between these zones are of the order of {{convert|1|–|300|m|ft|abbr=on|sigfig=1}}.
Below convergence zones narrow jets of downward flow form and the magnitude of the current will be comparable to the horizontal flow.
The downward propagation will typically be in the order of meters or tenths of meters and will not penetrate the [[pycnocline]].
The [[upwelling]] is less intense and takes place over a wider band under the divergence zone.
In wind speeds ranging from {{convert|2|-|12|m/s|abbr=on}}  the maximum vertical velocity ranged from {{convert|2|-|10|cm/s|abbr=on}} with a ratio of down-welling to wind velocities ranging from -0.0025 to -0.0085.
<ref>
{{citation | last1=Leibovich | first1=S. | year=1983 | title=The form and dynamics of Langmuir circulations| journal=Annual Reviews of Fluid Mechanis | volume=15  | pages=391–427 | doi= 10.1146/annurev.fl.15.010183.002135 }}
</ref>
 
==References==
{{Reflist}}
 
==External links==
*{{Commons category inline|Langmuir circulation}}
 
{{physical oceanography}}
 
[[Category:Oceanography]]
[[Category:Physical oceanography]]
 
 
{{Marine-current-stub}}

Latest revision as of 06:17, 20 September 2014


Lots of people are fearful of using the services of legal counsel initially. They may be worried that they will come up with a error and hire an unacceptable one particular or which they won't find one at all. The subsequent article usually takes the pain sensation out from trying to find a legal professional. Adhere to the tips below to obtain the legitimate assist you to need to have.

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Don't imagine that an expert attorney is a lot more high-priced than a common practitioner. Whilst a specialist might in fact use a better per hour rate, they will often charge you cheaper general hrs. A professional will not likely have to commit as much time discovering and researching regulations about a case that the basic practitioner would.

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If you are looking for a lawyer, make sure you discover those that specialize in your form of issue. Lawyers their very own areas of expertise, and all are diverse. You'll help save sufficient time once you collect this info in the beginning.

Come up with a notice of methods lengthy it takes an attorney to schedule your first meeting. If this requires several weeks to even start to see the legal representative initially, the legal professional may be too active to provide appropriate support. You desire a lawyer who sets you on top of his listing of main concerns.

When conference a legal representative the first time, be really ready. They make money hourly. You'll be billed for time on the telephone, once they look for documents, and many others. When you are well prepared when you visit the meeting, you are going to turn out paying out much less and possess your problems solved in a single sitting.

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