## Properties of Fluid Flow that Relate to Motion and Shape of Cloud Patterns and Ocean Features on Satellite Imagery

Kinematics—The branch of dynamics that describes the properties of pure motion without regard to force, momentum, or energy. Translation (advection), divergence (lateral spreading), vorticity (rotation), and deformation are examples of kinematic variables.

Translation (advection) -- the transport of some property of the atmosphere or ocean from place to place. In common usage in meteorology and oceanography, advection is considered to be horzontal, but strictly speaking advection can occur on any of the coordinate axes. Cloud masses will appear to translate with the wind and not change shape or evolve if advection was the only process that accounted for evolution of patterns.

Translation (advection) can be used to understand the motion and evolution of clouds to a lesser extent the longer the time interval. For time frames of 1 h or less, translation can explain most of the evolution of cloud masses seen on satellite imagery. For synoptic scale systems (time scale ~1 day) translation (advection) is a minor, but still significant factor in understanding such cloud pattern evolution. Divergence, vorticity and deformation are the dominant kinematic "players" for this larger time scale, but advection is still of importance.

Detail:

(Please note, meteorologists* learn (in Metr 430) that the vector definition of advection is the dot product of the wind vector with the gradient of some atmospheric or oceanographic variable. Mathematically, the advection is a PRODUCT operation of the wind or current speed and the gradient of something else, such as temperature. Operationally and descriptively, the advection gives the local change of a variable, such as temperature, in a unit amount of time due the the inflow or outflow of air or ocean with a different value of that variable. Conceptually, an example would be the temperature change that would occur, say, at San Francisco because air of a different temperature replaced the air there.) (Metr 201 Link to Advection Discussion.)

Chart showing condtions at the 200 mb level in the atmosphere. Wind is nearly in geostrophic balance, and so appears to be flowing parallel to the height contours. In the ocean, a similar chart would show contours of ocean altimetry. Currents in geostrophic balance flow parallel to the altimetry contours.

(Metr 201 Link on Geostrophic Flow in the Atmosphere and Ocean and exercise on calculating wind or current speed)

Divergence -- the expansion or spreading out of a velocity field as measured by the fractional rate of change of the horizontal surface area of a portion of that field. A fluid element such as a cloud pattern or a phytoplankton bloom in a purely divergent wind field would not change its basic shape, but would experience a change in area. An example of this would be the lateral growth of the anvil of a thunderstorm.

Divergence (lateral spreading) occurs most markedly at the smaller time scales. For example, in meteorology the divergence at the top of thunderstorms is one order of magnitude larger than the divergence observed with synoptic scale circulation systems, which in turn is one order of magnitude larger than that associated with the macroscale (for example, the equtorial low pressure area). Thus, divergence explains much of one sees in terms of cloud evolution in the middle latitudes at the time scales of interest to weather forecasters.

An example of divergence in the ocean would be the lateral spreading that occurs at surface surmounting an area of upwelling.

Vorticity (Rotation) -- a measure of the tendency fluid parcels have to rotate around an axis through their center of mass. Integrated mathematically and conceptually over a large area, this is known as circulation. A cloud pattern in a purely rotational wind field would not change its basic chape, but would appear to turn either clockwise or counterclockwise relative to the earth.

Rotational effects on cloud elements are evident at all time scales, but tend to have greater magnitudes the smaller the time and space scales. The effects of vorticity and circulation (rotation) explain about 35% or so of the cloud evolution we see at the synoptic scale.

Rotational effects are very evident in the ocean, accounting at the meso and synoptic-scale for the evolution of warm-core and cold-core eddies and, at the largest scales, the general circulation gyres.

Deformation -- the change in shape of a fluid mass by spatial variations in the velocity field, specifically by stretching or shearing. A cloud pattern in a wind field of pure deformation would not experience area changes, nor would it rotate, but it would change shape (be deformed).

Deformational effects on cloud elements, particularly those elements of a large scale, such as cloud shields, play a very important role in the evolution of cloud patterns. Although we will be discussing this a bit and helping you find such patterns on satellite imagery, the theoretical background must await Metr 500 and 520.