NONLINEAR SHIP-WAVE THEORIES BY CONTINUOUS MAPPING.

THE EXACT EQUATIONS OF STEADY INVISCID FLOW PAST A SHIP HULL ARE FORMULATED IN A REFERENCE DOMAIN, ONTO WHICH THE FLOW DOMAIN IS MAPPED.A THIN-SHIP PERTURBATION ANALYSIS IS PERFORMED IN THE REFERENCE DOMAIN, AND THE FIRST- AND SECOND-ORDER SOLUTIONS ARE DERIVED.THE CLASSICAL THIN-SHIP THEORY IS OBTAINED AS THE CONSISTENT, MAPPING-INDEPENDENT, PERTURBATION SOLUTION IN THE PHYSICAL SPACE.GUILLOTON'S METHOD IS INTERPRETED AS AN INCONSISTENT, MAPPING-DEPENDENT, SECOND-ORDER APPROXIMATION.A NEW INCONSISTENT APPROXIMATION IS OBTAINED BY EXPLOITING THE FREEDOM IN THE MAPPING OF THE FLOW DOMAIN ONTO THE REFERENCE DOMAIN.FURTHER IMPROVEMENTS ARE SUGGESTED.(A)