With evapo-transpiration rates up about 4mm/day and the need to get water penetration into the soil it makes sense to apply at least 8mm in a single cycle. Applying less daily barely covers the days water loss and so does not get in to any depth where it will not be lost quickly.
Two applications a week would give 16mm which is about 50% of evapo-transpiration losses. Where possible irrigation should be during the night. Any aerating to improve water penetration should be avoided until there are good moisture levels in the soil – opening dry soil only increases the water losses putting grass under greater stress.