Before I start I'm not a mathematician so bear with me...
I have an equation that takes the form of a tornado shape, its described by the following equation: $$z = 2\ln(x^2 + y^2)$$ I want to add a twist to this curve in cartesian corrdinates but have no idea how to do it. Is there a way to change this curve to add a twist whilst describing the whole object in a single cartesian equation?
Just for clarification heres the kind of twist i am refering to
