Glossary

Glossary of Terms for Fluid Dynamics

Add as you feel necessary. When needed, provide a link to a reference page or other terms.

Purpose: Many of the terms on this list have multiple definitions depending on context. The context for these definitions is geophysical and environmental fluid dynamics.

Disclaimer: this list is mostly the result of googling, and as such should not be referenced directly.

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A word

A word is a word, in a wordy way. For more details, see a page. Math sample: $\nabla b$.;

Barotropic fluid

A fluid in which density is only a function of pressure. This means that surfaces of constant pressure and constant density coincide. Note that an incompressible fluid is automatically barotropic since it has constant density.

Baroclinic motion

Motion caused by the misallignment of the surfaces of constant pressure and constant density.

$\beta$ - plane

In the f-plane approximation, the Coriolis parameter, f, is assumed constant. The $\beta$ - plane approximation assumes f varies linearly with latitude. Wikipedia's entry on this is a good one.

Chaotic advection

Chaotic advection is the advection of particles under a chaotic flow map or dynamical system. When we say a dynamical system or flow map is chaotic we, mean it is highly sensitive to initial conditions. This means that particles in the flow which may be close to each other initially (i.e. they represent similar initial conditions for the flow map) can be advected in very different ways. We care about this because chaotic mixing is efficient because particles initially close to each other separate exponentially. Note that at least 3 degrees of freedom is necessary to get a chaotic system, so 2 dimensional flows are not chaotic, but a two dimensional time dependent flow may be.

Characteristic scale

This scale is context dependent. In an engineering situation like a jet out of a small hole one scale is given by the size of the hole, and another, less easily quantifiable scale will be the length over which the jet mixes with the ambient fluid.

Correlation Time

The time it takes for the auto correlation function of a process to decrease by a given amount. In the case of Gaussian white noise, since the correlation function is a delta function, the correlation time is zero. In the case of red noise the autocorrelation function is a negative exponential $\langle X(t)X(t+\tau )\rangle =\exp({\frac {-\tau }{t_{c}}})$ , so that $\tau =t_{c}$ is the correlation time, because that’s how long it takes to drop by an order of magnitude. In some sense a longer correlation time corresponds to a longer “memory” of the previous path.

Energy cascade

when the coherent structures of the continuum move to smaller and smaller scales until viscosity causes dissipation. In a fully turbulent flow, at high Reynolds number, we have large eddies breaking up into smaller ones, and those break up as well until finally the eddies are so small that they are dissipated by viscosity. Clearly the scale at which dissipation occurs depends on the viscosity. See Kolmogorov’s 5/3 law for the energy in terms of wavenumber in the inertial subrange of wavenumbers before dissipation occurs.

A poem by Lewis Fry Richardson:

Big whirls have little whirls,

Which feed on their velocity,

And little whirls have lesser whirls,

and so on to viscosity.

• Halocline: Region with a high gradient in salinity. See also Pycnocline and Thermocline
• Pycnocline: Region with a high gradient in density. See also Halocline and Thermocline
• Thermocline: Region with a high gradient in temperature. See also Halocline and Pycnocline