Can anyone explain what is meant by Gauaian Invariance, and how is it noermall applied to N.S equations

Thanks in advance

Tensors do not change when expressed in a different coordinate system. For example, a vector should still have the same magnitude and direction when expressed in Cartesian coordinates or cylindrical polar coordinates. Not sure of your context, but it is typically applied to models of turbulent transport equations to formulate/check terms and behaviour.