Ridge waveguide with TE01 mode

Hello,

I don't know how to theoretically explain following behaviour of TE01 mode in a square ridged waveguide:

When I select width of a ridge to be considerable compared to the size of a waveguide (e.g. 1/3, 1/2) and simultaneously I am increasing the height of a ridge (parameter v in a picture) the cutoff frequency is changing according to the attached picture.
And that's a point where I get lost. I have no idea why this happens, why the cutoff frequency rises at first and then drops.
Could anyone try and explain this?

Thanks for every help !