1. A method of operating a data storage system to write file system data of an internal file system to an underlying storage volume, comprising: writing the file system data as sequential data and non-sequential data to the storage volume, the sequential data being stored in windows each having a predetermined number of consecutive data blocks and being allocated dynamically as the sequential data is written; and maintaining and using a window cache to identify existing windows for storing respective newly written sequential file system data in sequence with respective earlier-written file system data for which the existing windows were previously allocated, the window cache including a set of entries indexed by an identifier of (1) a file of the file system and (2) a window-size region of the file to which sequential data is being written, the entries including respective physical window addresses identifying respective ones of the existing windows and being obtained by lookup operations using respective values of the identifier.