THE DISSIPATION OF FLUCTUATING TRACER VARIANCES

The evolution of the covariance of two tracers involves a quantity cal led codissipation, proportional to the covariance of the gradients of the two tracers, and analogous to the dissipation of tracer variance. The evolution of the variance of a composite tracer-a linear combinati on of two simple, primary tracers-depends on the ''composite dissipati on,'' a combination of the individual simple tracer dissipations and t he codissipation. The composite dissipation can be negative (implying growth of the variance of the composite tracer) for structures in whic h the correlation of the simple tracer gradients are large enough (i.e ., large codissipation). This situation occurs in the phenomena of dou ble diffusion and salt fingering. A particular composite tracer called watermass variation, a measure of water-type scatter about the mean t racer versus tracer relationship, lacks production terms of the conven tional form-tracer flux multiplying tracer gradient-in its variance ev olution balance. Only codissipation can produce variance of watermass variation. The requirements that watermass variance production and dis sipation be in equilibrium, and that no other composite tracer varianc e be tending to grow due to codissipation, lead to a particular relati on among codissipation and the simple dissipations and between the sim ple dissipations themselves. The latter are proportional to one anothe r, the proportionality factor being the square of the slope of the mea n tracer versus tracer relation. The same results can be obtained by m odifying Batchelor's argument to give the equilibrium cospectrum of tw o tracer gradients at high wavenumbers in a well-developed field of is otropic turbulence. As a consequence of these arguments, the turbulent eddy tracer fluxes are also proportional, with the mean tracer-tracer slope as proportionality factor. Further, the ratio of turbulent diff usivities of two tracers is unity. The dissipation of buoyancy, a comp osite tracer constructed from temperature and salinity, is proportiona l at equilibrium to thermal dissipation multiplied by a factor that de pends on the stability ratio. This previously established result is ob tained here under less restrictive conditions.