Turbulent diffusion in stably stratified non-decaying turbulence

We develop a Lagrangian model of both one-particle dagger and two-particle turbulent diffusion in high Reynolds number and low Froude number stably st ratified nondecaying turbulence. This model is a kinematic simulation (KS) that obeys both the linearized Boussinesq equations and incompressibility. Hence, turbulent diffusion is anisotropic and is studied in all three direc tions concurrently with incompressibility satisfied at the level of each an d every trajectory. Horizontal one-particle and two-particle diffusions are found to be indepen dent of the buoyancy (Brunt-Vaissala) frequency N. For one-particle diffusi on we find that <(x(i)(t) - x(i)(t(0)))(2)> similar to u'(t - t(0))(2) for t - t(0) much le ss than L/u', and <(x(i)(t) - x(i)(t(0)))(2)> similar to u'L(t - t(0)) for t - t0 > L/u', where i = 1,2 and u' and L are a r.m.s. velocity and a length-scale of the energy-containing motions respectively, and <(x(3)(t) - x(3)(t(0)))(2)> similar or equal to u'(2)/N-2 = (LFr2)-Fr-2 for 2 pi/N much less than t - t0 This capping of one-particle vertical diffusion requires the consideration of the entire three-dimensional flow, and we show that each and every traje ctory is vertically bounded for all times if the Lagrangian vertical pressu re acceleration a(3) is bounded for all times. Such an upper bound for a(3) can be derived from the linearized Boussinesq equations as a consequence o f the coupling between vertical pressure acceleration and the horizontal an d vertical velocities. Two-particle vertical diffusion exhibits two plateaux. The first plateau's scaling is different according to whether the initial separation Delta(0) b etween the two particles is larger or smaller than eta, the smallest length -scale of the turbulence: [GRAPHICS] The second plateau is reached when the two particles become statistically i ndependent, and therefore <Delta(3)(2)> similar or equal to 2L(2)Fr(2) for t - t(0) much greater than L/u'. The transition between the two plateaux coincides with the time when the tw o particles start moving significantly apart in the horizontal plane.