Grass Patches... and a Few Trees. The savanna is characterized by its variety of grasses. However, it is not the lush grasses of grasslands that extend as far as the eye can see. Instead, the grasses are often in thick clumps with bare ground and shrubs in between.There are many types of grasses in the savanna, such as Rhodes grass, red oats grass and lemon grass.The Bermuda grass that many plant in their lawns is native to the African savanna as is elephant grass, which can grow 10 feet (3 m) tall.nstead, the grasses are often in thick clumps with bare ground and shrubs in between. There are many types of grasses in the savanna, such as Rhodes grass, red oats grass and lemon grass.