A second-order Lagrangian stochastic model formulated in terms of the mean dissipation rate and satisfying the well-mixed condition for a Tsallis distribution of Lagrangian accelerations is shown to be incompatible with Kolmogorov's similarity theory. This difficulty does not arise when, following the approach advocated by Beck ͓Phys. Rev. Lett. 87, 180601 ͑2001͔͒, the Tsallis distribution is recovered from a Gaussian model through the employment of a distribution of dissipation rates. The

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... ts caused by ignoring fluctuations in dissipation along trajectories are evaluated in numerical simulations in which Lagrangian accelerations and dissipation histories evolve jointly as a Markovian process. Sawford 1 introduced a second-order Lagrangian stochastic ͑LS͒ model, for simulating the trajectories of fluid particles in turbulent flows, i.e., for the joint evolution of a fluid particle's acceleration, velocity, and position ͑A,u,x͒. The quantity d is a white noise process with mean zero and variance dt. The timescales pertaining to the energy-containing and dissipation scales of motion are T L ϭ2 u 2 /C 0 and t ϭC 0 /2a 0 t E where u 2 and A 2 ϭa 0 /t E are the velocity and acceleration variances, is the mean rate of dissipation of turbulent kinetic energy divided by fluid density, t E ϭ(/) 1/2 is the Eulerian dissipation timescale, and is the kinematic viscosity. According to Kolmogorov's similarity theory both the Lagrangian velocity structure constant, C 0 , and the parameter a 0 are universal for turbulence at high Reynolds number. However, at Reynolds numbers attainable in direct numerical simulations against which model predictions will be compared, a 0 is found to be a strong function of Reynolds number with numerical estimates being well described by a 0 ϭ0.13 Re 0.64 where Re ϭ u / is the Reynolds number based on the Taylor microscale, ϭ(15 u 2 /) 1/2 . 2 By construction Sawford's model is exactly consistent with the dissipation and inertial-subrange forms of the La-grangian velocity structure function as determined by Kolmogorov's similarity theory and has been shown 1 to be in remarkably close agreement with data from direct numerical simulations ͑DNS͒ 2 ͑see Figs. 1 and 2; compared dotted lines and symbols͒. The model is also exactly consistent with independent Gaussian distributions for acceleration and velocity 3 and consequently is at variance with recent experimental studies 4 which indicate that unconditional Lagrangian accelerations have a highly non-Gaussian distribution at high Reynolds number (Re Ͼ10 2 ) that is well represented by a Tsallis distribution, 5 This discrepancy can be resolved by invoking a natural generalization of Thomson's well-mixed condition 3 to construct a second-order model with such acceleration statistics and having Gaussian velocity statistics. This nonlinear model is given by For Re ϭ90 this model is seen in Fig. 1 ͑compare dashed lines and symbols͒ to produce a Lagrangian velocity function, D(t), in close agreement with the DNS data 2 while at lower Reynolds numbers better agreement is seen to be obtained with a Gaussian distribution for unconditional accelerations ͑compare dotted lines and symbols͒. This shortcoming can be attributed to the inappropriateness of the Tsallis a͒ LETTERS The purpose of this Letters section is to provide rapid dissemination of important new results in the fields regularly covered by Physics of Fluids. Results of extended research should not be presented as a series of letters in place of comprehensive articles. Letters cannot exceed four printed pages in length, including space allowed for title, figures, tables, references and an abstract limited to about 100 words. There is a three-month time limit, from date of receipt to acceptance, for processing Letter manuscripts. Authors must also submit a brief statement justifying rapid publication in the Letters section.