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We investigate the decay of freely-evolving, isotropic turbulence whose spectrum takes the form E(k→0)∼Ik, I being Loitsyansky's integral. We report numerical simulations in a periodic domain whose dimensions, l, are much larger than the integral scale of the turbulence, l. We find that, provided l≫l and Re≫1, the turbulence evolves to a state in which Loitsyansky's integral is approximately constant and Kolmogorov's decay law, u∼t, holds true. The approximate conservation of I in fully-developed turbulence implies that the long-range interactions between remote eddies, as measured by the triple correlations, are very weak.

Posts around the world have been confronted with arguments that they receive competitive advantages and better treatment under domestic law than private sector operators. Independent bodies in several industrialized countries have issued recommendations urging governments to promote competitive equality principles under domestic law. While many critics urge that the playing field be leveled, they often do not take account of the many costly public responsibilities that postal operators must fulfill. The opinion reaffirms that the USPS is a federal government entity and is not subject to competition laws applicable to private sector providers. As a governmental entity, the USPS must fulfill many social policies. Unlike private sector providers in the United States, it must execute universal service obligations. Postal rates must also reflect many noncommercial considerations, and product pricing is driven by social policy as opposed to economic principles. As an employer, the USPS must observe significant, costly restrictions on its ability to set wage and benefit policies. As a purchaser of billions of dollars of goods and services, the USPS must fulfill numerous socio-economic policies that make it less able to acquire goods and services efficiently and at the lowest possible cost. The “level playing field” debate cannot be fairly understood without recognizing the counterbalancing social policy responsibilities borne by postal operators.

Posts around the world have been confronted with arguments that they receive competitive advantages and better treatment under domestic law than private sector operators. Independent bodies in several industrialized countries have issued recommendations urging governments to promote competitive equality principles under domestic law. While many critics urge that the playing field be leveled, they often do not take account of the many costly public responsibilities that postal operators must fulfill. The opinion reaffirms that the USPS is a federal government entity and is not subject to competition laws applicable to private sector providers. As a governmental entity, the USPS must fulfill many social policies. Unlike private sector providers in the United States, it must execute universal service obligations. Postal rates must also reflect many noncommercial considerations, and product pricing is driven by social policy as opposed to economic principles. As an employer, the USPS must observe significant, costly restrictions on its ability to set wage and benefit policies. As a purchaser of billions of dollars of goods and services, the USPS must fulfill numerous socio-economic policies that make it less able to acquire goods and services efficiently and at the lowest possible cost. The “level playing field” debate cannot be fairly understood without recognizing the counterbalancing social policy responsibilities borne by postal operators.

Posts around the world have been confronted with arguments that they receive competitive advantages and better treatment under domestic law than private sector operators. Independent bodies in several industrialized countries have issued recommendations urging governments to promote competitive equality principles under domestic law. While many critics urge that the playing field be leveled, they often do not take account of the many costly public responsibilities that postal operators must fulfill. The opinion reaffirms that the USPS is a federal government entity and is not subject to competition laws applicable to private sector providers. As a governmental entity, the USPS must fulfill many social policies. Unlike private sector providers in the United States, it must execute universal service obligations. Postal rates must also reflect many noncommercial considerations, and product pricing is driven by social policy as opposed to economic principles. As an employer, the USPS must observe significant, costly restrictions on its ability to set wage and benefit policies. As a purchaser of billions of dollars of goods and services, the USPS must fulfill numerous socio-economic policies that make it less able to acquire goods and services efficiently and at the lowest possible cost. The “level playing field” debate cannot be fairly understood without recognizing the counterbalancing social policy responsibilities borne by postal operators.

We investigate the decay of freely-evolving, isotropic turbulence whose spectrum takes the form E(k→0)∼Ik, I being Loitsyansky's integral. We report numerical simulations in a periodic domain whose dimensions, l, are much larger than the integral scale of the turbulence, l. We find that, provided l≫l and Re≫1, the turbulence evolves to a state in which Loitsyansky's integral is approximately constant and Kolmogorov's decay law, u∼t, holds true. The approximate conservation of I in fully-developed turbulence implies that the long-range interactions between remote eddies, as measured by the triple correlations, are very weak.

Onsager's point vortex model of two dimensional turbulence is extended by the inclusion of time dependent vortex circulations. If the time dependence of the circulations is governed by statistically independent Onstein-Uhlenbeck processes we observe the emergence of scaling regimes for the structure functions of the Eulerian and the Lagrangian velocity increments. Fully developed turbulent flows are flux equilibrium systems leading to selfsimilarity and scaling behaviour of correlation functions. The probability distributions corresponding to the simplest case of idealized, i.e. homogeneous, isotropic, and stationary fully developed flows are unknown although the underlying fluid dynamical equations and its statistical counterparts are well-established [1]. Fluid motions can be treated either from an Eulerian or a Lagrangian point of view. Most analytical theories have been formulated in the Eulerian framework. Point vortex models (see e.g. [2]), which have been extensively investigated especially for the case of two dimensional flows, essentially make use of a Lagrangian description. Since the point vortex equations of an ideal two dimensional fluid, which is not stirred, are of Hamiltonian nature, a statistical treatment based on the microcanonical ensemble can be established. This has been discussed for the first time by Onsager [3]. The purpose of the present Letter is to show that an extension of Onsager's point vortex model, which allows for fluctuating circulations of the point vortices, leads to a state which shows scaling behaviour of the structure functions.

We derive the exact solution for the Burgers equation with a time dependent forcing, which depends linearly on the spatial coordinate. For the case of a stochastic time dependence an exact expression for the joint probability distribution for the velocity fields at multiple spatial points is obtained. We present numerical results for fixed boundary conditions, and analyze the formation of shocks.

Posts around the world have been confronted with arguments that they receive competitive advantages and better treatment under domestic law than private sector operators. Independent bodies in several industrialized countries have issued recommendations urging governments to promote competitive equality principles under domestic law. While many critics urge that the playing field be leveled, they often do not take account of the many costly public responsibilities that postal operators must fulfill. The opinion reaffirms that the USPS is a federal government entity and is not subject to competition laws applicable to private sector providers. As a governmental entity, the USPS must fulfill many social policies. Unlike private sector providers in the United States, it must execute universal service obligations. Postal rates must also reflect many noncommercial considerations, and product pricing is driven by social policy as opposed to economic principles. As an employer, the USPS must observe significant, costly restrictions on its ability to set wage and benefit policies. As a purchaser of billions of dollars of goods and services, the USPS must fulfill numerous socio-economic policies that make it less able to acquire goods and services efficiently and at the lowest possible cost. The “level playing field” debate cannot be fairly understood without recognizing the counterbalancing social policy responsibilities borne by postal operators.

Posts around the world have been confronted with arguments that they receive competitive advantages and better treatment under domestic law than private sector operators. Independent bodies in several industrialized countries have issued recommendations urging governments to promote competitive equality principles under domestic law. While many critics urge that the playing field be leveled, they often do not take account of the many costly public responsibilities that postal operators must fulfill. The opinion reaffirms that the USPS is a federal government entity and is not subject to competition laws applicable to private sector providers. As a governmental entity, the USPS must fulfill many social policies. Unlike private sector providers in the United States, it must execute universal service obligations. Postal rates must also reflect many noncommercial considerations, and product pricing is driven by social policy as opposed to economic principles. As an employer, the USPS must observe significant, costly restrictions on its ability to set wage and benefit policies. As a purchaser of billions of dollars of goods and services, the USPS must fulfill numerous socio-economic policies that make it less able to acquire goods and services efficiently and at the lowest possible cost. The “level playing field” debate cannot be fairly understood without recognizing the counterbalancing social policy responsibilities borne by postal operators.

Onsager's point vortex model of two dimensional turbulence is extended by the inclusion of time dependent vortex circulations. If the time dependence of the circulations is governed by statistically independent Onstein-Uhlenbeck processes we observe the emergence of scaling regimes for the structure functions of the Eulerian and the Lagrangian velocity increments. Fully developed turbulent flows are flux equilibrium systems leading to selfsimilarity and scaling behaviour of correlation functions. The probability distributions corresponding to the simplest case of idealized, i.e. homogeneous, isotropic, and stationary fully developed flows are unknown although the underlying fluid dynamical equations and its statistical counterparts are well-established [1]. Fluid motions can be treated either from an Eulerian or a Lagrangian point of view. Most analytical theories have been formulated in the Eulerian framework. Point vortex models (see e.g. [2]), which have been extensively investigated especially for the case of two dimensional flows, essentially make use of a Lagrangian description. Since the point vortex equations of an ideal two dimensional fluid, which is not stirred, are of Hamiltonian nature, a statistical treatment based on the microcanonical ensemble can be established. This has been discussed for the first time by Onsager [3]. The purpose of the present Letter is to show that an extension of Onsager's point vortex model, which allows for fluctuating circulations of the point vortices, leads to a state which shows scaling behaviour of the structure functions.