In Art. 4.04 the discussion was restricted to constituents whose concentration is altered by advection and diffusion only, except perhaps at the boundaries of the fluid. The resulting equations are applicable to salinity or any of the major constituents such as chloride, sodium, sulfate, magnesium, etc. In fact, the equations of Art. 4.04 are applicable to any inert or conservative constituents. Dissolved nitrogen gas in another example.
Constituents such as phosphate, nitrate, and other nutrients, and dissolved oxygen, carbon dioxide, etc. are non-conservative from the physical standpoint, since the concentrations of these quantities are altered locally by chemical action associated with the life processes within the sea. Strictly speaking, these processes- consumption, photosynthesis, respiration, and reduction by the plant, animal and bacteria populations of the sea-represent localized boundary processes. However, the boundaries are neither fixed, permanent, nor predictable, except in a statistical sense. The marine life, particularly the planktonic forms and micro-organisms which comprise the bulk of the productive mass of the sea, must be considered just as much a part of the fluid which we will call sea water as the salinity, phosphate, etc. In other words, the living phytoplankton, zooplankton, micro-organisms and the detrital matter are further examples of non-conservative constituents.
The total concentration of any of these non-conservative constituents in a given mass of fluid which moves with the fluid velocity can be altered by one or more of the abovementioned processes in addition to diffusion. If we let represent the concentration of any one of the non-conservative constituents, then for a moving volume of constant mass
where it is assumed that the function can be defined such that its volume integral for any arbitrary volume represents the most probable net rate of production of the constituent N per unit time by the statistical ensemble of discrete sources contained within the volume at the instant t. The quantity represents the diffusive flux of N, and the outward unit normal to the boundary as before. The value of can of course be either positive or negative depending upon the constituent and the process; is production, is consumption.
By making use of Eq. (I-3) and the divergence theorem, and considering that the volume is arbitrary in size, it can be shown that Eq. (24) reduces to
If we introduce the diffusion velocity of N defined by
and add Eq. (I-1) multiplied by N to Eq. (IIA-1) we get the analouge to Eq. (II-4)
In the case of the non-living constituents such as phosphate, it is observed that the is controlled principally by the gradient of the concentration, the diffusion current being directed towards the regions of low concentration. The value of is positive below the euphotic zone of the sea where bacterial action on detrital matter produces this nutrient; in the surface layers it is generally negative and the magnitude must be dependent upon the concentration of plant life, radiation, temperature, etc. A detailed discussion of the production and consumption for the various non-conservative constituents is well beyond the scope of these notes. It may be remarked, however, that through relations of the type (IIA-2) much can be learned with regard to the nature of as a supplement to the more direct measurements.
The important thing to note is that a measure of N alone, representing the so-called standing crop of the constituent, is inadequate by itself in respect to ascertaining the rate of production or consumptionof N. In a region where the constituent N is virtually uniform then the advective and diffusive terms contribute very little to the change of N with time, and hence a direct measure of the local rate of change of the concentration N represents a good approximation of . Under conditions of an equilibrium where the standing concentration is steady then must must balance the dispersion of N by advective and diffusive processes. The magnitude of N in this case, like the size of ones bank account, does not serve as a direct reflection of the rate of turnover.
In passing, it is of interest to inquire into the meaning of Eq. (IIA-2) if applied to marine life which does have means of locomotion. The equation may concievably apply if we regard as a statistical mean applying to the relative migrations of the creatures in question. The factor controlling the in this case is quite different from that in the case of the inanimate constituents, and seems to be in fact just the opposite-the tendency being for grouping together rather than for dispersion. However, the migratory motion of the groups as a whole is dependent upon the physiological adaptation to the environment as well as upon the apparently psychological controls. The diurnal, vertical migrations of the so-called scattering layer, which is evidently a grouping of marine life capable of locomotion, is a case in point.