WAVES AND WAVE RESISTANCE OF THIN BODIES MOVING AT LOW SPEED: THE FREE-SURFACE NONLINEAR EFFECT

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Abstract

THE LINEARIZED THEORY OF FREE-SURFACE GRAVITY FLOW PAST SUBMERGED OR FLOATING BODIES IS BASED ON A PERTURBATION EXPANSION OF THE VELOCITY POTENTIAL IN THE SLENDERNESS PARAMETER EPSILON WITH THE FROUDE NUMBER F KEPT FIXED.IT IS SHOWN THAT, ALTHOUGH THE FREE-WAVE AMPLITUDE AND THE ASSOCIATED WAVE RESISTANCE TEND TO ZERO AS F#0, THE LINEARIZED SOLUTION IS NOT UNIFORM IN THIS LIMIT: THE RATIO BETWEEN THE SECOND AND FIRST-ORDER TERMS BECOMES UNBOUNDED AS F#0 WITH EPSILON FIXED.THIS NON-UNIFORMITY (CALLED 'THE SECOND FROUDE NUMBER PARADOX' IN PREVIOUS WORK) IS RELATED TO THE NONLINEARITY OF THE FREE-SURFACE CONDITION.CRITERIA FOR UNIFORMITY OF THE THIN-BODY EXPANSION, COMBINING EPSILON AND F, ARE DERIVED FOR TWO-DIMENSIONAL FLOWS.THESE CRITERIA DEPEND ON THE SHAPE OF THE LEADING (AND TRAILING) EDGE: AS THE SHAPE BECOMES FINER THE LINEARIZED SOLUTION BECOMES VALID FOR SMALLER F.UNIFORM FIRST-ORDER APPROXIMATIONS FOR TWO-DIMENSIONAL FLOW PAST SUBMERGED BODIES ARE DERIVED WITH THE AID OF THE METHOD OF CO-ORDINATE STRAINING.THE STRAINING LEADS TO AN APPARENT DISPLACEMENT OF THE MOST SINGULAR POINTS OF THE BODY CONTOUR (THE L EADING AND TRAILING EDGES FOR A SMOOTH SHAPE) AND, THEREFORE, TO AN APPARENT CHANGE IN THE EFFECTIVE FROUDE NUMBER.(A)

Original languageEnglish
Pages (from-to)MAY 27, 1975
JournalJournal of Fluid Mechanics
Volume69
Issue number2
StatePublished - 1975

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