AN UNSTEADY CAVITY FLOW 



D. P. Wang 



The Catholic University of America 

 Washington^ B.C. 



I. INTRODUCTION 



A perturbation theory for two-dimensional unsteady cavity 

 flows has been formulated by the present author and Wu [ 1965] . In 

 that formulation we regard the unsteady part of the motion as a 

 small perturbation of a steady cavity flow already established. This 

 already established steady cavity flow will be called as the basic 

 flow. Our perturbation expansion is carried out in terms of a set 

 of intrinsic coordinates {s,n) of the basic flow. The coordinate s 

 is the arc length measured along a streamline in the direction of the 

 basic flow, and n the distance measured normal to a streamline. 

 An illustration is given in Fig. 1 , where the solid lines represent 

 the basic flow configuration, AB represents the wetted side of the 

 solid body, AI and BI, the two branches of the cavity Weill which 

 is a free surface. Also shown in Fig, 1 is the unsteady perturbed 

 flow configuration represented by dotted lines. The unsteady 



Fig. i Illustration of an unsteady perturbation flow 



This paper will henceforth be referred to as W. 



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