The department may, upon its own motion or at the request of the attorney general or upon complaint of not less than 10 owners of property on any inland public water in the state, make a preliminary investigation of conditions affecting the use and enjoyment of any such public water whenever it shall be of the opinion that such investigation would be in the public interest. If, as a result of any such preliminary investigation, it shall appear to the department that the management and control of any outlet of any such public water and the connected instrumentalities are carried on or used in such manner that the value of shore property above or riparian rights below such outlet or the enjoyment of such water by the public is seriously and adversely affected, it may make further investigation with a view to ascertaining the respective rights of all interested parties, including the public. If, as a result of such further investigation after public hearing, the department shall be of the opinion that such management and control is lawful, but that changes in the manner of the exercise of the right of management and control would be of benefit to others without undue injury to the owner of the outlet, it shall direct such changes as in its opinion would be of benefit to the public and private interests concerned.