Could this be the Charles Rose named by his uncle, commander James Rose, RN, as an heir in his will,
available from the British National Archives. James Rose states that Charles, son of his brother Alexander Rose, was a lieutenant RN and is in Canada. The will dates from 1838, with an update increasing the sum to be inherited by Charles, in 1840. James Rose is from Nairn Scotland, I have not found his brother Alexander, but the entries so far suggests this Charles could be the same who later drowned.