Transition to Deterministic Chaos in a Hydrodynamic System
Nonlinear hydrodynamic systems often exhibit transition to chaotic behaviour when a properly defined stress parameter is increased. According to an idea due to Landau (1) the route to chaos has been conjectured to consist of a sequence of bifurcation points at which many incommensurate frequencies are gradually introduced. At variance with this, Lorenz (2) and Ruelle and Takens (3) have sugqested that fluid turbulence is associated with the existence of a strange attractor in phase space. Therefore chaotic behaviour is actually caused by finite dimensional deterministic dynamics and is a consequence of the sensitivity of the solutions to the initial conditions.
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