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# Hydrostatic stability

The distribution of is useful for, among other things, ascertaining the degree of gravitational stability of sea water.

Sea water which has an increasing potential density with depth as is usually the case in the upper layers at mid-latitudes possesses a stable density stratification. If a parcel of water is displaced upwards instantaneously, then it will be of greater density than its new surroundings and will tend to return to its own level; if displaced downwards it will be of less density than its surroundings and will likewise tend to return to its own level.

If the potential density decreases with depth then the water is unstable, and the slightest disturbance will tend to create vertical convection currents.

A state of neutral stability exists if the potential density is constant with depth. A parcel which is displaced will tend to remain at the position to which it has been displaced since its density will the same as in the new environment.

As a quantitative measure of the stability E it is logical to use

where z is measured upwards as before. In the light of the discussion in Art. 3.13 this may be approximated by

As Sverdrup et al. (1942) point out, the exact expression is necessary only at great depths in the ocean.

In terms of the vertial gradient of the stability of the upper layers is

The actual degree of stability is important in connectino with studies of vertical mixing by external agents.

Instability can be divided into two types: conditional instability and absolute instability (with the latter sometimes called auto-convective instability. If the actual in situ density decreases with depth, then no initial displacement is required to set the water in vertical motion. The sea water in this case is said to possess an auto-convective lapse rate of density with depth. For the condition the sea water is conditionally unstable since a vertical displacement is required to initiate convection.

The condition of constant density versus depth can be expressed approximately by

Thus the upper limit of conditional instability under quasi-static conditions is given by

. The magnitude of this gradient is about 0.45 mg/cm per 100 meters. Thus, the sea water is

A set of computations of E for a typical oceanographic station in the North Atlantic off the African coast is given in Table 62 of The Oceans (p. 417). The minimum value of E is which occurs in the upper 10 meters of the water column. This value is very close to the condition of absolute instability, and is probably associated with and maintained by vertical convection caused by evaporative cooling of the surface layers in that region. At depths below 50 meters E is positive and a maximum stability condition (600/100 m) is reached in the layer from 50 to 75 meters deep. Below this the stability decreases and approaches zero at the bottom.

Next: The Fundamental Equations of Up: Fluid Density and Hydrostatic Previous: Potential density and sigma-t

Steve Baum
Mon Dec 1 08:50:29 CST 1997