The onset of aperiodic or chaotic behaviour in viscoelastic fluids is
examined in the context of the Rayleigh-Benard thermal convection setu
p. A truncated Fourier representation of the conservation and constitu
tive equations, for an Oldroyd-B fluid, leads to a four-dimensional sy
stem that constitutes a generalization of the classical Lorenz system
for a Newtonian fluid. It is found that, to the order of the present t
runcation and below a critical Deborah number De(c), the critical Rayl
eigh number Ra(c), for the onset of steady thermal convection does not
depend on fluid elasticity or retardation. For De > De(c), it is show
n that steady convection does not exist, with the fluid becoming overs
table instead. Fluid overstability, namely when the convective cell st
ructure is time periodic, and which is attributed to fluid elasticity,
is found to set in at a Rayleigh number that depends on the Deborah n
umber and fluid retardation, and may be much smaller than Ra(c). It is
also found that fluid elasticity tends to destabilize the convective
cell structure, precipitating the onset of chaotic motion, at a Raylei
gh number that may be well below that corresponding to Newtonian fluid
s.