ETD Collection

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Author: search.filters.author.Kokela, Lady NomvulaSubject: search.filters.subject.Differential equations, Partial.

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    Double reduction of partial differential equations with applications to laminar jets and wakes
    (2016) Kokela, Lady Nomvula
    Invariant solutions for two-dimensional free and wall jets are derived by consid- ering the Lie point symmetry associated with the appropriate conserved vectors of Prandtl's boundary layer equations for the jets. For the two-dimensional jets we also consider the comparison, advantages and disadvantages between the standard method that uses a linear combination of all the Lie point symme- tries of Prandtl's boundary layer equations to generate the invariant solution with the new method explored in this paper which uses the Lie point sym- metry associated with a conserved vector to generate the invariant solution. Invariant solutions for two-dimensional classical and self-propelled wakes are also derived by considering the Lie point symmetry associated with the appro- priate conserved vectors of Prandtl's boundary layer equations for the wakes. We also consider and discuss the standard method that uses a linear combi- nation of all the Lie point symmetry of Prandtl's boundary layer equations to generate the invariant solutions for the classical and self-propelled wakes.