I had the same problem in my home. I live in sausalito,ca. by san francisco bay with a southern exposure. In winter we get 40 plus winds and pouring rain. The rain paired with the wind has even blown in through the top of the window casement.
Two years ago I found what I call window baffles, by accident, through the vermont country store co. they are wonderful! We have just endured 16 days of torrential rain and over 50 mile an hour winds. The top of the window casement leaked, but not my window baffles.
I couldn't find them at the vermont country store. But, I did see them online. Go to google and type; window screens that keep out the rain. The first thing you will see on the top right are; different drawings of screens. the one named thermwell products aws1207 adjustable screen window with ventilator looks like mine.
It's a regular screen on the backside and the louvred baffles face inside. I have found that it works well with the baffles facing up. Then just slam your window down hard on the baffle. this makes a good seal. good luck, you're going to love these.