The mayor shall be the chief executive officer of the city, and shall exercise all powers and perform all duties conferred and imposed upon him by this charter, the ordinances of the city and laws of the state. He shall be recognized as the official head of the city for all ceremonial purposes, by the courts for the purpose of serving civil processes, and by the governor for the purpose of martial law. He shall study the operations of the city government and shall report to the council any neglect, dereliction of duty or waste on the part of any officer or department of the city. In time of public danger or emergency he may, with the consent of the council take command of the police, maintain order, and enforce the law. In the event of a vacancy in the office of the mayor, whether by death, resignation, or any other cause, the council shall appoint a mayor for the unexpired term, but in case of a recall the vacancy shall be filled in the manner provided in this charter.