A Caltech Library Service

The Role of Coordinate Systems in Boundary Layer Theory


Kaplun, Saul (1954) The Role of Coordinate Systems in Boundary Layer Theory. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/9QZM-8W36.


The boundary layer approximation to a given flow problem is not invariant if different coordinate systems are used in the approximation process. However, a correlation theorem (Theorem 1) is given, which states that the boundary layer solution with respect to any given system can be found, by a simple substitution, from that with respect to any other system. On the basis of this theorem, the dependence of the solution on the choice of coordinates is investigated in detail. The skin friction is invariant, but the flow field is not invariant. At large distances from the wall, the flow field given by boundary layer theory depends almost entirely on the choice of coordinates, rather than on the physical problem. This dependence may be used to obtain a complete matching between the boundary layer solution and the external flow, in the following sense: Theorem 2 states how a coordinate system can be found such that the boundary layer solution with respect to this system is valid as an approximation for the entire flow field. It contains the external flow and the flow due to displacement thickness. The discussion is restricted to steady, two-dimensional, incompressible flow without separation. These restrictions, however, are not essential for many of the results.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Aeronautics and Mathematies)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Aeronautics
Minor Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Lagerstrom, Paco A.
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1954
Record Number:CaltechETD:etd-12032003-111930
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4738
Deposited By: Imported from ETD-db
Deposited On:10 Dec 2003
Last Modified:08 Jun 2023 23:51

Thesis Files

PDF (Kaplun_s_1954.pdf) - Final Version
See Usage Policy.


Repository Staff Only: item control page