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Langmuir circulation : ウィキペディア英語版
Langmuir circulation

In physical oceanography, Langmuir circulation consists of a series of shallow, slow, counter-rotating 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 windrows of seaweed in the Sargasso Sea in 1927.〔

Langmuir circulations circulate within the mixed layer; however, it is not yet so clear how strongly they can cause mixing at the base of the mixed layer.


== Theory ==

The driving force of these circulations is an interaction of the mean flow with wave averaged flows of the surface waves.
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 \nu_T.
For a flow driven by a wind \tau characterized by friction velocity u_
* the ratio of vorticity diffusion and production defines the Langmuir number

:
\mathrm
=
\sqrt}
\ \mathrm\
\sqrt}

where the first definition is for a monochromatic wave field of amplitude a, frequency \sigma, and wavenumber k and the second uses a generic inverse length scale \beta, and Stokes velocity scale S_0.
This is exemplified by the Craik-Leibovich equations〔

which are an approximation of the Lagrangian mean


.〔

In the Boussinesq approximation the governing equations can be written
:
\frac
+u_j\nabla_ju_i
=
\begin
-2\epsilon_\Omega_j\left(u^s_k+u_k\right)
-\nabla_i\left(\frac+\fracu^s_ju^s_j+u^s_ju_j\right)\\
+\epsilon_u^s_j\epsilon_\nabla_lu_m
+g_i\frac
+\nabla_j\nu\nabla_ju_i
\end

:
\nabla_iu_i=0

:
\frac
+u_j\nabla_j\rho
=
\nabla_i\kappa\nabla_i\rho

where
u_i is the fluid velocity,
\Omega is planetary rotation,
u^s_i is the stokes drift velocity of the surface wave field,
P is the pressure,
g_i is the acceleration due to gravity,
\rho is the density,
\rho_0 is the reference density,
\nu is the viscosity,
and
\kappa 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.



抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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