## What is/are Isotropic Invariant?

Isotropic Invariant - An approximation of isotropic invariants, bypassing the solution of a quartic equation or computation of tensor square roots, allows stretches, rotations, stresses, and balance laws to be written in terms of derivatives of position.^{[1]}The turbulent states for each B R has been compared using an anisotropic invariant map in the horseshoe vortex regime, top surface regime and in the wake regime.

^{[2]}We also study the effect of introducing a further dependence of the energy on the anisotropic invariants related to the square of the Cauchy–Green strain tensor.

^{[3]}The anisotropic invariant maps show the near bed anisotropy inclining to be a two-component isotropy subjected to no seepage and seepage flow.

^{[4]}The approach helps us successfully in determining the fiber strains, for a family of symmetrically and asymmetrically oriented fibers, with the aid of a single anisotropic invariant.

^{[5]}Anisotropic invariant map (AIM) has been plotted; nature of turbulence is found to be non-homogeneous and anisotropic even at low Re (= 3200) and non-homogeneity increases as Re increases.

^{[6]}The ground substance is the common so-called compressible neo-Hooke model and the standard reinforcement part is augmented by second order anisotropic invariants.

^{[7]}

## isotropic invariant map

The turbulent states for each B R has been compared using an anisotropic invariant map in the horseshoe vortex regime, top surface regime and in the wake regime.^{[1]}The anisotropic invariant maps show the near bed anisotropy inclining to be a two-component isotropy subjected to no seepage and seepage flow.

^{[2]}Anisotropic invariant map (AIM) has been plotted; nature of turbulence is found to be non-homogeneous and anisotropic even at low Re (= 3200) and non-homogeneity increases as Re increases.

^{[3]}