Spatial variations of a passive tracer in a random wave field

Abstract

The effect of random wave fields on passive tracer spatial variations is studied. We derive a closed-form expression for the spatial autocorrelation function (or power spectrum) of the tracer fluctuations that is quantitatively accurate so long as wave field nonlinearities are small. The theory is illustrated for the case of long internal gravity waves in the ocean. We find that even if the (rear face of the) spectrum of the advecting velocity field is a pure power law, the tracer spectrum has two separate power law subranges. Most important to oceanographic applications, in the larger scale subrange, the effective horizontal compressibility of the wave velocity field becomes a dominant factor of the tracer variations. In such cases, the concentration spectrum becomes approximately proportional to the spectrum of the wave potential energy. The latter, which decays with increasing wavenumber much more rapidly than that known for two-dimensional eddy turbulence, is confirmed by satellite observations in wave-dominated ocean regions. As an additional confirmation of the theory, we demonstrate the occurrence of spectral peaks at wavenumbers corresponding to the semi-diurnal tide frequency.