Symmetry analysis of the turbulent dissipation rate

In 1935, G. I. Taylor invoked rotational symmetry to derive a remarkable formula for the turbulent dissipation rate. That derivation, though ingenious, leaves it unclear if the formula truly conforms with rotational symmetry. We use the machinery of Lie groups to furnish a rigorous derivation of Taylor's formula under rotational symmetry and also under a symmetry not considered by Taylor, reflectional symmetry.