On the O'Brien-Jarrett-Marchi law

The relationship between the total water volume entering a lagoon during a characteristic tidal cycle (i.e., the prism) and the size of its inlet is well established empirically since the classic work of O'Brien and Jarrett widely cited in the geomorphic and hydrodynamic literature. Less known is a rather deep theoretical explanation proposed by Marchi. This paper reviews the empirical and theoretical evidence on which the relation is based, setting the various theoretical approaches so far pursued within the general framework ensured by Marchi's theoretical treatment of the problem. We conclude that the depth of the empirical and theoretical validations and the breadth and the importance of its implications suggest that the O'Brien-Jarrett-Marchi law relating the minimum inlet cross-sectional area and the tidal prism flowing through it may be referred to thereinafter.