Asymptotic Behavior of a Viscoelastic Fluid in a Closed Loop Thermosyphon: Physical Derivation, Asymptotic Analysis, and Numerical Experiments

Table 3

Behavior of solutions with diffusion (𝜈≠0) for different values of the viscoelastic characteristic time, 𝜀 (rows), and the temperature gradient, B (columns). We introduce the following notation to account for the obtained numerical results: “C” denotes a fully chaotic behavior, “CS” a transition from chaotic outburst to stable equilibria, and “P” a periodic orbit.

𝐵/𝜀	10^−4	10^−3	10^−2	10^−1	10^0	10^1	10^2
1	CS	CS	CS	CS	CS	CS	CS
10	CS	CS	CS	CS	CS	CS	CS
20	CS	CS	CS	CS	CS	CS	CS
30	CS	CS	CS	CS	CS	CS	CS
40	P	P	P	CS	CS	CS	CS
50	P	P	P	CS	CS	CS	CS
100	P	P	P	CS	CS	CS	CS
1000	P	P	P	CS	CS	CS	CS
10000	P	P	P	CS	CS	CS	CS