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.

Note: The AMS Glossary is a good source for definitions, should the definition that you seek not be available below.

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A-D

Barotropic fluid

A fluid in which $\nabla p\times \nabla \rho =0$. This means that surfaces of constant pressure and constant density are parallel. Fluids in which $p=p(\rho )$ or the density is constant ($\rho =\rho _{0}$) are necessarily barotropic.

Baroclinic motion

Motion caused by the misallignment of the surfaces of constant pressure and constant density (i.e. $\nabla p\times \nabla \rho \neq 0$).

Boundary Layer

Region near a surface in which friction becomes important.

$\beta$ - plane

The $\beta$ - plane approximation assumes that the Coriolis frequency varies linearly with latitude i.e. $f=f_{0}+\beta y$. $f_{0}=2\Omega \sin(\theta _{0})$ and $\beta ={\frac {2\Omega }{a}}\cos(\theta _{0})$ where $\Omega$ is the period of Earth's rotation, $\theta _{0}$ is the reference latitude, and $a$ is the mean radius of the Earth. Wikipedia's entry on this is a good one. cf. $f$-plane

Capillary Wave

Waves in which the dominant restoring force is due to surface tension. Typical length scales are under 7cm.

Chaotic Advection

The advection of particles under a chaotic flow map or dynamical system.

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.

Direct Numerical Simulation (DNS)

Simulation in which you make no assumption on turbulence, and typically attempt to resolve as much as possible. cf. LES

Dispersion Relation

We can write $\omega$, the angular frequency of a wave, as a function of the wavenumber $k$. We call this function the dispersion relation for the wave. See also phase velocity, group velocity, and dispersive waves.

E-J

Energy Cascade

When the coherent structures of the continuum move to smaller and smaller scales until viscosity causes dissipation.

Enstrophy

$\int _{\Omega }\omega ^{2}dV$, the norm squared of the vorticity over a given domain.

$f$ - plane

The $f$ - plane approximation assumes that the Coriolis frequency is constant in latitude i.e. $f=f_{0}$. Where $f_{0}=2\Omega \sin(\theta _{0})$, $\Omega$ is the period of Earth's rotation, and $\theta _{0}$ is the reference latitude. cf. $\beta$-plane

Isentropic Surface

A surface of constant entropy.

Gravity Wave

A wave in which the dominant restoring force is due to gravity acting to restore displaced mass.

Group Velocity

The velocity with which the energy of a wave packet propagates. Closely related to the velocity of the wave envelope. See Wave Envelope

Gyre

A vortex, a region dominated by a coherent rotating structure.

Halocline

Region with a high gradient in salinity. See also pycnocline and thermocline

Internal Tide

Internal Waves generated at a tidal frequency. See Internal Wave.

Internal Wave

Waves in which the displaced quantity is an isopycnal. These can include gravity waves and Rossby waves.

K-Q

Large Scale Flow

In geophysical fluid dynamics this refers to the flow dominated by the Earth's rotation, so almost geostrophic flow.

Large Eddy Simulation

A simulation in which a turbulence model has been included to approximate small scale motion and thus reduce the complexity of the problem.

Normal Mode

For a linear PDE, the normal modes are the functions which describe the spatial structure of the standing waves that solve that PDE. We can then approximate any wave that solves the PDE, including non-standing waves, by using the normal modes as a basis

Pycnocline

Region with a high gradient in density. See also halocline and thermocline

R-Z

Rossby Wave

Waves in which the dominant restoring force is to due the conservation of potential vorticity.

Stratification

The way in which a fluids density varies with depth.

Surface Wave

Waves in which the displaced quantity is a water-air interface. These can include gravity waves, Rossby waves, and capillary waves.

Thermocline

Region with a high gradient in temperature. See also halocline and pycnocline

Wave Envelope

The curve which outlines the extremes of a Wave Packet. See Wave Packet

Wave Packet

Composition of waves in a localized region acting in matrimony.