4 Flux and Transport

There are two more important quantities in Oceanography – flux and transport – that are used to describe the rate at which a substance (or just the water itself) moves through space.

The Definition of “Flux” (a vector field)

 The flux vector field is a very important concept in oceanography.

  • The flux of a substance is the rate at which that substance passes through an infinitesimimal surface perpendicular to the flux vector, per unit surface area.

Advection is the process by which a substance is moved around by ocean currents. It is one of two key physical processes that result in the movement of “stuff”, the other being diffusion (considered later on).

The Definition of “Advective Flux” (a vector field)

The advective flux of a substance is the fluid velocity multiplied by the concentration, C:

    \[  \underline{\textbf{F}}_{Advective}  = \underline{\textbf{u}}C = \left( uC,vC,wC \right) \]

Advective flux is a vector with the same direction as the ocean current.

The velocity is really just is the advective flux of water itself – the rate at which the water itself moves through space. It can also be called the volume flux. Its units are m/s. In this case, C = 1.

If you know the flux, you can find a related quantity called the transport. Transport is not a vector field that is defined at every point in space, but assumes you have in mind a particular finite-sized surface and you want to know the rate at which “stuff” passes through it. An example would be the transport of nitrate out of the mouth of the Columbia River.

The Definition of “Transport”

In general, the transport through a given surface is defined as:

    \[ Transport = Flux \times Area. \]

The Definition of “Volume Transport”

The volume transport through a given cross-section is the volume of flow passing through that section every second. Oceanographers like to use Sverdrups (Sv) for the units of volume transport where

1 Sverdrup (Sv) = 106  m3 / s.

To determine the volume transport through a section, you would find the average component of the velocity vector perpendicular (“through”) the section (units: m/s), and multiply that average velocity by the section’s area (units: m2).  The name “volume” transport comes from the units in the numerator – that volume of water passes through the section every second.

Note: If the flux varies in space, first divide up your larger area into smaller elements over which the flux could be considered effectively constant. To get the transport, add up all the individual products of flux \times area for each element. If you know advanced calculus, this is equivalent to a surface integral (but you don’t need to know that for this class!)