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We report the finding of a scaling relation among the cosmic-web anisotropyparameter $A$, the linear density rms fluctuation sigma(r) and the lineargrowth factor D(z). Using the tidal field derived from the MillenniumSimulation on 512^{3} grids at z=0, 2, 5 and 127, we calculate the largesteigenvalues $\lambda$ of the local tidal tensor at each grid resolution andmeasure its distance-averaged two-point correlation function, xi_{lambda}, as afunction of the cosines of polar angles cos(theta) in the local principal axisframe. We show that xi_{lambda} is quite anisotropic, increasing toward thedirections of minimal matter compression, and that the anisotropy ofxi_{lambda} increases as the redshift, z, decreases and as the upper distancecutoff r_{c} decreases. Fitting the numerical results to an analytic fittingmodel \xi_{\lambda}(\cos\theta)\propto (1+A\cos^{n}\theta)^{-1}, it is foundthat the best fit value of A, dubbed the cosmic-web anisotropy parameter,varies systematically with sigma(r_{c}) and D(z), allowing us to determine thesimple empiral scaling relation A(r_{c},z)=0.8, D^{0.76}(z), sigma (r_{c})$.

A Scaling Relation of the Evolving Tidal Fields in a LCDM Cosmology