We give an upper bound for the number of nested ovals of a real tetragonal curve $R$ embedded in an Hirzubruch surface in terms of the genus of the curve.
"Real elliptic surfaces with double section and real tetragonal curves." Bull. Belg. Math. Soc. Simon Stevin 19 (3) 445 - 460, september 2012. https://doi.org/10.36045/bbms/1347642375