Glossary

Glossary of Terms for Fluid Dynamics

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• A word: A word is a word, in a wordy way. For more details, see a page.
• 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: Baroclinicity is proportional to the cross product of the gradients of pressure and density. Both gradients are perpendicular to their respective level sets, meaning surfaces of constant density and pressure. In a baroclinic fluid these are parallel, so the cross product vanishes. A baroclinic motion is a motion caused by the misallignment of these two surfaces, so this term is nonzero and effects the dynamics of the vorticity equation. An example from the baroclinity entry of Wikipedia: "Divers may be familiar with the very slow waves that can be excited at a thermocline or a halocline; these are internal waves. Similar waves can be generated between a layer of water and a layer of oil. When the interface between these two surfaces is not horizontal and the system is close to hydrostatic equilibrium, the gradient of the pressure is vertical but the gradient of the density is not. Therefore the baroclinic vector is nonzero, and the sense of the baroclinic vector is to create vorticity to make the interface level out. In the process, the interface overshoots, and the result is an oscillation which is an internal gravity wave. Unlike surface gravity waves, internal gravity waves do not require a sharp interface. For example, in bodies of water, a gradual gradient in temperature or salinity is sufficient to support internal gravity waves driven by the baroclinic vector."
• Chaotic advection: When we say a dynamical system, or flow map, is chaotic we mean it his highly sensitive to initial conditions. This means that particles in the flow which may be close to each other initially (ie they represent similar initial conditions for the flow map) can be advected in very different ways. Chaotic advection is the advection of particles under a chaotic flow map or dynamical system. 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 some cases it’s zero, in the case of red noise the autocorrelation function is negative exponential, so the exponent gives the auto 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 Re, 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. #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. See Kolmogorov’s 5/3 law for the energy in terms of wavenumber in the inertial subrange of wavenumbers before dissipation occurs.
• 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