On Sunday mornings, Joan the turnip seller will come to your town. Buy as many White Turnips as possible. If the turnips stay in your inventory until the following Sunday, they will rot and cannot be sold to Tom Nook. However, if you want your turnips to live forever, first into your house and go next to a table that can have items placed on it. Drop a tool item (fishing rod, shovel, axe, etc.) under you, then go into your inventory and drop the desired amount of turnips. If done correctly, the turnips should land on the table and stay there. Since they are not in your pockets, they will not rot and die. When Tom Nook has good prices for the Stalk Market, grab the turnips from the table and sell them.