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``Exact'' laws for evaluating cascade rates, tracing back to the Kolmogorov``4/5'' law, have been extended to many systems of interest includingmagnetohydrodynamics (MHD), and compressible flows of the magnetofluid andordinary fluid types. It is understood that implementations may be limited bythe quantity of available data and by the lack of turbulence symmetry.Assessment of the accuracy and feasibility of such ``third-order'' (or Yaglom)relations is most effectively accomplished by examining the von Karman-Howarthequation in increment form, a framework from which the third-order laws arederived as asymptotic approximations. Using this approach, we examine thecontext of third-order laws for incompressible MHD in some detail. The simplestversions rely on the assumption of isotropy and the presence of a well-definedinertial range, while related procedures generalize the same idea to arbitraryrotational symmetries. Conditions for obtaining correct and accurate values ofthe dissipation rate from these laws based on several sampling and fittingstrategies are investigated using results from simulations. The questions weaddress are of particular relevance to sampling of solar wind turbulence by oneor more spacecraft.

Strategies for determining the cascade rate in MHD turbulence: isotropy, anisotropy, and spacecraft sampling