I'm having a problem where rivulets are forming in the lower section of my yard, giving it a fragmented like appearance. I assume this is caused my runoff from the upper section of my yard, which is sloped downwards towards the flat, lower section. The rivulets don't form in the all-grass portion of my yard, but instead form right at the base of a landscaped portion that is entirely composed of various vines and ground cover. At the boundary of this ground-cover portion are large, decorative rocks. My assumption was that I could place a layer of small rocks/rock chips/gravel between the decorative rocks and my grass and this would disrupt the flow of the water and remove the small rivers that I assume are forming and causing the large gashes in the yard.
I drew the image above to better illustrate the situation. Would this work and be a good long-term solution?