Horizontal roll vortices influence the distribution of turbulence, with turbulence variances and fluxes concentrated in regions of positive roll vertical velocity ωr. This “modulation” of turbulence can be explained simply in terms of the advection of turbulence-generating elements by rolls.
A budget equation is derived for the roll-modulated turbulence energy. Evaluations of various terms in the equation shows that the modulation of turbulence variance is accounted for primarily by a similar modulation in mechanical and buoyancy production near the surface and by vertical transport at higher levels (∼100 m). Energy exchange between rolls and turbulence is relatively unimportant. That is, the rolls modulate, turbulence energy mainly by redistributing turbulence and turbulence-producing elements, rather than by exchanging energy.
Similarly, it is shown that the exchange of energy between rolls and roll-modulated turbulence contributes considerably less to the energy equation of rolls than does the major term, buoyancy.