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.

See also Dimensionless Numbers.

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A-B

Available Potential Energy

The potential energy available for conversion into other forms of energy. For intuitive purposes one may think of this as Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle APE = \int_\Omega \left(\rho-\rho^*\right)dV } where $\rho$ is the density field, and $\rho ^{*}$ is the redistributed density field such that the potential energy is minimized.

Azimuth

The horizontal angle. In polar coordinates, the angular direction.

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

Boundary Layer

Region near a boundary in which viscosity becomes important.

Buoyancy Frequency

The frequency at which an infinitesimally perturbed fluid parcel oscillates around its rest state in the absence of friction. Formally given as $N^{2}(z)=-{\frac {g}{\rho _{0}}}{\frac {d{\overline {\rho }}(z)}{dz}}$, where ${\overline {\rho }}(z)$ is the background stratification.

$\beta$ - 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

C-D

Capillary Wave

Waves in which the dominant restoring force is due to surface tension. Typical length scales are under 7cm (Kundu, 4th ed.).

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.

Circulation

The circulation of a flow is the integral of the vorticity over a surface, $\Gamma =\int _{\Omega }{\vec {\omega }}dA$, and represents the vorticity flux through the surface $\Omega$. By Stokes' theorem, $\Gamma =\int _{\partial \Omega }{\vec {u}}\cdot ds$.

Coriolis Frequency

$f=2\Omega \sin \theta$, where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Omega } is the rate of earth's rotation, and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \theta } is the latitude (with the northern hemisphere to be positive). See also Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f} -plane, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \beta} -plane.

Correlation Time

The time it takes for the auto correlation function of a process to decrease by a given amount.

Diffusivity

Rate of diffusion (unit: mFailed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ^2} /s). Mass diffusivity: the rate at which mass (molecular) of the substance diffuses through a unit surface in a unit time. Thermal diffusivity: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \kappa = \frac{k}{\rho C_p} } , where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k } is the thermal conductivity, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho } is the density, and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C_p } is the specific heat. Momentum diffusivity: see kinematic viscosity.

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

For a given wave, the dispersion relation is the relationship between wavenumber, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k } , and (angular) wave frequency, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \omega } ; typically written as Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \omega = \omega(k) } . See also Phase Velocity, Group Velocity, and Dispersive Waves.

Dispersive Wave

A wave for which the group velocity is dependent on wavenumber, so energy in different wavelengths propagates at different velocities.

E-G

Energy Cascade

When energy is supplied at large scales and then passed to smaller and smaller scales until viscosity causes dissipation.

Enstrophy

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}\omega^2 } , the norm squared of the vorticity.

Fluid Parcel

A volume of fluid which (see chapter 1 of Kundu.):

• deforms under outside forces
• is non-diffusive, such that molecules do not cross the boundary
• is large enough to be well defined by thermodynamic quantities
• is small enough to reach internal equilibrium much faster than the background flow

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f} - plane

The Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f } - plane approximation assumes that the Coriolis frequency is constant in latitude i.e. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f=f_0} . Where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f_0=2\Omega\sin(\theta_0)} , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Omega} is the period of Earth's rotation, and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \theta_0} is the reference latitude. cf. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \beta} -plane

Geostrophic Balance

Geostrophic balance occurs when the Coriolis pseudo-force balances the pressure forces. Under geostrophic balance, flow is along lines of constant pressure.

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. Mathematically, the group velocity Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{c_g}= \nabla_{\vec{k}} \omega =\left(\frac{\partial \omega}{\partial k},\frac{\partial \omega}{\partial l},\frac{\partial \omega}{\partial m} \right)} , where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{k}=(k,l,m)} is the wavenumber. The group velocity is closely related to the velocity of a wave envelope .

Gyre

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

H-J

Halocline

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

Internal Solitary Wave

A single, internal, travelling wave, often located at a pycnocline.

Internal Tide

Internal waves generated at a tidal frequency.

Internal Wave

A wave whose displaced quantity is interior to the fluid. These can include gravity waves and Rossby waves.

Isentropic

Of or having constant entropy. An isentropic surface is a surface of constant entropy.

Isobaric

Of or having constant pressure. An isobaric surface is a surface of constant pressure.

Isohaline

Of or having constant salinity. An isohaline surface is a surface of constant salinity.

Isopycnal

Of or having constant density. An isopycnal surface is a surface of constant density.

Isothermal

Of or having constant temperature. An isothermal surface is a surface of constant temperature.

K-Q

Kelvin Wave

Gravity waves that are boundary trapped and are in geostrophic balance in the direction orthogonal to the boundary. Kelvin waves require the presence of a boundary such as a coastline, channel wall, or the equator. Like Poincaré waves, Kelvin waves are rotating gravity waves. In the Northern (Southern) hemisphere, Kelvin waves propagate with the boundary on the right (left) with respect to the direction of propagation.

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.

Meridional

Along a north-south direction; or along a meridian.

Mixing

This has the standard English language meaning, but there are many more connotations in fluid mechanics.

Nepheloid Layer

A layer of water with a high concentration of suspended sediment.

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.

Particle Image Velocimetry (PIV)

A non-invasive method used to measure whole velocity fields by taking two images shortly after each other, and calculating the distance individual tracer particles have travelled within the time interval. From the known time interval and the measured displacement, the velocity is calculated.

Phase Velocity

The velocity at which a wave crest or trough propagates. Mathematically, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{c_p}=\frac{\omega}{|k|}\hat{k}} where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c} is the phase velocity, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle |k|} is the magnitude of the wavenumber, and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \hat{k}} is the unit vector corresponding to Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{k}} . cf. group velocity. The magnitude of the phase velocity, the phase speed, is sometimes called the celerity of the wave.

Poincaré Wave

Gravity waves that are slow/large enough to feel the effects of rotation, but for which gravity remains the dominant restoring force. Under the linear shallow-water equations with an f-plane, the dispersion relation for Poincaré waves is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \omega^2 = f_0^2 + c_0^2K^2} , where $f_{0}$ is the Coriolis frequency, $c_{0}^{2}=gH$ is the shallow-water gravity-wave speed, and $K={\frac {2\pi }{\lambda }}$ is the horizontal wavenumber.

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. These waves are a result of gradient in potential vorticity imparted by the latitudinal variation of the Coriolis frequency. Waves for which the gradient in potential vorticity is provided by topography are termed topographic Rossby waves.

Soliton

A single wave crest or trough that propagates at a constant speed, without changing its shape, even after interacting with other waves.

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

Thermohaline Flow

Flow in the ocean due to density gradients which are caused by surface heat (thermal fluxes) and freshwater or saline fluxes.

Tracer

A quantity transported by the flow.

Viscosity

A quantity measuring the magnitude of internal friction. Dynamic viscosity: $\mu$ (unit: ${\text{kg}}\cdot {\text{m}}^{-1}{\text{s}}^{-1}$). Kinematic viscosity: $\nu =\mu /\rho$ (unit: ${\text{m}}^{2}/{\text{s}}$), also called momentum diffusivity.

Wave Envelope

The curve which outlines the extremes of a wave packet.

Wave Packet

A group of waves which travel together, often as the result of a burst of energy. This leads to the concept of a wave envelope. Also called a wave train.

Zonal

Along an east-west direction; or along a latitude circle.