All public landings and all streets bounding and abutting (or the termination thereof), upon the harbor line, as before specified, or upon the line of survey of the ship channel and old river bed, or upon such portion of the Ohio canal, or Lake Erie, as lies within the limits of the City, at or upon which no bridges exist or shall be constructed by the authority of Council, are hereby designated and set apart as public landings, and as such are to be under the control of the Harbor Master or such other officers as Council shall provide, under such rules and regulations as Council shall prescribe.