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

Table 2

Behavior of solutions without 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, “P” a stable periodic orbit, and “CP” a transitional behavior from chaotic to periodic.

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