that's still not a wave , just increasing and decreasing due to the gravity of the two stars causing a fluctuation in the gravity field of the binary system ...
neither stars gravity would fluctuate but because of the rotation there would be a fluctuation observed from outside the binary system.
think of it as a planetary alignment in our solar system
Now you are doing what Bill G did to you with waves. Yes technically that is a wave but we tend to call them orbital resonances. It does get frustrating using these stupid layman terms which have such wide meaning.
https://en.wikipedia.org/wiki/Orbital_resonanceUsing your layman concepts that effect would be felt as a change in the local value of gravity here and you describe it as such. LIGO measures the expansion and contraction between two fixed points on earth. That sort of effect you are describing would just role thru the detector sort of not noticed (there is a hand waving in that statement it does require analysis). What they are measuring directly is the expansion and contraction of space itself which is what a GR gravity wave is.
If you prefer we could use the term ripples in space and time rather than gravity waves which is more accurate to what they are measuring and gets rid of the layman wave concept.
To a degree your sort of gravity wave is self evident by the fact we have tides on our oceans etc. The irony is Earth/Moon must make GR gravity waves according to GR but it's to small for even LIGO to detect. So if GR is right both your sort and the GR ripple in time and space wave are created by the moon/earth movement, the second being to small to measure with our current instruments.
So I guess all I can say is your sort of gravity wave is way off topic since we are talking about GR and LIGO detection.
