This study, employing a numerical approximation, computationally describes 2D melt fracture as elastic instability in the flow along and outside a straight channel. In the preceding research (Kwon, 2018, Numerical modeling of two-dimensional melt fracture instability in viscoelastic flow, J. Fluid Mech. 855, 595–615) several types of unique instability and corresponding bifurcations such as subcritical and chaotic transitions have been illustrated with possible mechanism presumed. However, the 1^st bifurcation from stable steady to unstable periodic state could not be accurately characterized even though its existence was proven evident. The analysis herein aims at verification of this 1^st transition to temporally (and also spatially) periodic instability, utilizing the same numerical technique with attentive control of flow condition. As a result of scrutinizing the solutions, the steady elastic flow described by the Leonov rheological model passes through supercritical Hopf bifurcation at the Deborah number of 10.42 and then transforms to the state of the 1^st weak periodic instability. It has also been confirmed that near this bifurcation point it takes extremely long to completely develop into either steady state (in the stable case) or periodic instability, which obstructed immediate characterization of the transition in the previous work.

这项研究采用数值逼近，以计算方式将2D熔体破裂描述为沿直线通道和沿直线通道的流动中的弹性不稳定性。在前面的研究（权，2018年，在粘弹性流动二维熔体破裂不稳定性的数值模拟，J.流体机甲。 855，595-615）几种类型的独特的不稳定和相应分叉如亚临界和混乱的过渡已经示出推测可能的机制。然而，1^日从稳定到稳定不稳定周期状态分叉不能准确地表征，即使它的存在被证明是明显的。本文的分析旨在验证这^第一个利用相同的数值技术并仔细控制流动条件，过渡到时间（以及空间）周期性不稳定性。仔细研究溶液的结果，Leonov流变模型描述的稳定弹性流以Deborah数为10.42的超临界Hopf分叉通过，然后转变为^第一个弱周期不稳定性状态。还已经证实，在这个分叉点附近，要完全发展成稳态（在稳定的情况下）或周期性的不稳定性都需要极长时间，这阻碍了先前工作中过渡的直接表征。