As a first step in understanding the instabilities which are observed when oil is contained in the presence of a shear flow, the problem of finding the mean shape of a pool of oil in front of a barrier moving in water of infinite depth is considered. The author presents experimental evidence that this problem is one of a gravity current in which no head loss takes place outside of a relatively thin boundary layer, and that irrotational flow theory can be used in the water phase. The oil phase is considered to be hydrostatic. An equilibrium equation is developed which balances frictional, dynamic, and hydrostatic forces. A Green's function approach is used, in which the slick is assumed to be slender. Flow quantities are expressed as a perturbation series in terms of integrals of an assumed friction coefficient and low order solutions. Numerical solutions are presented for several assumed friction distributions. The problem of non-uniform convergence near the leading edge is considered, and possible approaches toward obtaining an inner expansion valid there are discussed.

  • Corporate Authors:

    Massachusetts Institute of Technology

    Department of Ocean Engineering, 77 Massachusetts Avenue
    Cambridge, MA  United States  02139
  • Publication Date: 1976-9

Subject/Index Terms

Filing Info

  • Accession Number: 00142339
  • Record Type: Publication
  • Source Agency: Massachusetts Institute of Technology
  • Report/Paper Numbers: PhD Thesis
  • Files: TRIS
  • Created Date: Nov 23 1976 12:00AM