Vn-Vz

volumetric analysis

A technique for the analysis of water masses wherein the volume of each water type or mass is ascertained. One use of this technique is to quantitatively examine changes in the character of the water in a region in the interval between surveys, although the spatial and temporal resolution of sampling in most areas has thus far made this a promising rather than a realized technique.

The procedure for performing a volumetric T-S or $\theta$-S involves: (1) preparing a suitable data set, preferably one composed of relatively closely spaced hydrographic stations consisting of surface-to-bottom data with all coverage within a single season; (2) determining the area represented by each station; (3) partitioning the temperature and salinity fields into an array of T-S classes; (4) determining the depth interval within each T-S class; (5) multiplying the depth intervals by the area represented by each station to obtain the volumes of each class; and (6) summing these volumes over the desired region. See Swift (1986).

von Humboldt, Alexander (1769-1859)

See Peterson et al. (1996), p. 64.

von Lenz, Emil (1804-1865)

See Peterson et al. (1996), p. 64.

von Waitz, Jacob (1698-1776)

See Peterson et al. (1996), p. 47.

vortex stretching

Later.

vorticity

A fluid property defined as twice the local rate of rotation of a fluid element or the curl of the velocity field, i.e.

$$\mathbf{\omega}\,=\,\nabla\times\mathbf{u}$$

where $\mathbf{u}$ is the velocity vector. In a rotating frame of reference like the earth, there is additionally a quantity known as the planetary vorticity, i.e.

$$2\Omega\,=\,\nabla\times\mathbf{U}$$

where $\mathbf{U}\,=\,\Omega\times\mathbf{u}$ is the velocity of the rotating frame at position $x$. Together these comprise the absolute vorticity, i.e.

$${\omega^a}\,=\,2\Omega\,+\,\omega .$$

It is a three-dimensional property of the field of motion of a fluid, although in large-scale geophysical fluid dynamics the vorticity component in the horizontal plane (i.e. rotation about the vertical axis) is usually the only non-negligible component. The vorticity equation governs the evolution of vorticity in a geophysical fluid.

vorticity equation

This is an equation used in large-scale geophysical fluid dynamics that relates the rate of change of the vertical component of vorticity to the horizontal divergence. It is derived by eliminating pressure (or geopotential) from the equations of motion. It can be expressed as

$${D\over{Dt}}(\omega\,+\,2\Omega )\, = \, (\omega\,+\,2\Omega )\cdot\nabla\mathbf{u}\,-\, (\omega\,+\,2\Omega )\nabla\cdot\mathbf{u}\,$$

$$- \,\nabla\upsilon\times\nabla p$$ (17)

where $D/Dt$ is the material derivative, $\omega$ the relative vorticity, $2\Omega$ the planetary vorticity, $\omega\,+\,2\Omega$ the absolute vorticity, $\mathbf{u}$ the three-dimensional velocity vector, $\upsilon$ the specific volume, and $p$ the pressure. The terms on the right-hand side describe, respectively, vorticity changes due to:

• vortex stretching and twisting,
• volume changes, and
• the baroclinicity of the flow.

See Muller (1995).

vorticity vector

A measure of the rotational component of a velocity field. This is calculated by taking the curl of the velocity vector $\mathbf{u}$, mathematically expressed as $\nabla\times\mathbf{u}$.

VOS

Acronym for Volunteer Observing Ship.