About generalized scaling for passive scalars in fully developed turbulence

In this paper we use a simple normal form approach of scale invariant fields to investigate scaling laws of passive scalars in turbulence. The coupling equations for velocity and passive scalar moments are scale covariant. Their solution shows that passive scalars in turbulence do not generically follow a general scaling observed for velocity field because of coupling effects.

Turbulent passive scalar field of a small prandtl number

The statistical-mechanics theory of the passive scalar field convected by turbulence, developed in an earlier paper [Phys. Fluids 28, 1299 (1985)], is extended to the case of a small molecular Prandtl number. The set of governing integral equations is solved by the equation-error method. The resultant scalar-variance spectrum for the inertial range is F(k)~x−5/3/[1+1.21x1.67(1+0.353x2.32)], where x is the wavenumber scaled by Corrsin's dissipation wavenumber. This result reduces to the − (5)/(3) law in the inertial-convective range. It also approximately reduces to the − (17)/(3) law in the inertial-diffusive range, but the proportionality constant differs from Batchelor's by a factor of 3.6.

A passive scalar field convected by turbulence

Classical statistical mechanics is applied to the study of a passive scalar field convected by isotropic turbulence. A complete set of independent real parameters and dynamic equations are worked out to describe the dynamic state of the passive scalar field. The corresponding Liouville equation is solved by a perturbation method based upon a Langevin–Fokker–Planck model. The closure problem is treated by a variational approach reported in earlier papers. Two integral equations are obtained for two unknown functions: the scalar variance spectrum F(k) and the effective damping coefficient (k). The appearance of the energy spectrum of the velocity field in the two integral equations represents the coupling of the scalar field with the velocity field. As an application of the theory, the two integral equations are solved to derive the inertial-convective-range spectrum, obtaining F(k)=0.61 −1/3 k−5/3. Here is the dissipation rate of the scalar variance and is the dissipation rate of the energy of the velocity field. This theoretical value of the scalar Kolmogorov constant, 0.61, is in good agreement with experiments.

Compatibility of Glyphosate with Galerucella calmariensis; a Biological Control Agent for Purple Loosestrife (Lythrum salicaria)

By integrating Galerucella calmariensis with glyphosate there is potential to achieve both immediate and sustained control of purple loosestrife (Lythrum salicaria). The objective of this study was to determine the compatibility of glyphosate on the oviposition and survival of adult G. Calmariensis and on the ability of G. calmariensis third instar larvae to pupate to teneral adults. Our results revealed glyphosate (formulated as Roundup) at a concentration of 2% (2.43L/acre) and 4% solution (4.86 L/acre) had no impact on the ability of G. calmariensis third instar larvae to pupate to new generation adults. To examine the effect of a 2% solution of glyphosate on adult G. calmariensis oviposition and survival, adults were randomly divided between a direct contact group (adults sprayed directly), an indirect contact group (host plants with adults were sprayed), and a control group. Our results revealed that glyphosate does not impact G. calmariensis oviposition or adult survival. The results of this study indicate that G. calmariensis is compatible with glyphosate indicating that further field studies examining integrated control strategies for purple loosestrife are warranted.