AI 中文总结
该研究在有理扩展热力学的双曲幂律弛豫模型中，分析非等温动力学对激波结构及流动指数阈值的影响，推导特征排序恒等式，确定激波厚度分类不变，参考温度等因素会影响临界马赫数和激波厚度。
AI 中文摘要
我们研究在有理扩展热力学的双曲幂律弛豫模型中，当考虑完整的非等温动力学时，先前为等温激波剖面发现的两个流动指数阈值是否仍然存在。非等温剖面问题在结构上与等温对应问题不同：恢复能量平衡决定了行波沿程的温度，并将其反馈到压力、弛豫产生项、温度相关的一致性系数以及特征结构中。在热力学稳定性条件$p_\theta\neq0$和约化雨贡纽压力严格凸性的情况下，不存在非平凡的恒温压缩剖面能满足完整方程。我们推导了一个精确的全局特征排序恒等式，并证明正的非平衡特征速度在未受扰动的上游状态处具有严格的全局最小值。因此，当$1<M_0<\text{Mst}$时存在单调连续剖面，而当$M_0>\text{Mst}$时，Boillat--Ruggeri定理排除了$C^1$剖面，任何可允许的分段光滑连接必须包含亚激波。尽管存在热机械耦合，激波厚度分类保持不变：$m=2$是弱激波阈值，当$M_0\nearrow\text{Mst}$时$m=1$是近临界阈值。在当前类别中，对应的指数与本构无关，而有限极限值和前置因子取决于状态方程、内能以及温度相关的一致性系数。对于Tait--Murnaghan实例，当量纲化的粘性-弛豫尺度固定时，提高参考温度会降低临界马赫数，并且对于所考虑的热变薄定律，会减小解析得到的激波厚度。
英文摘要
We investigate whether the two flow-index thresholds previously found for isothermal shock profiles persist when the full nonisothermal dynamics is taken into account in a hyperbolic power-law relaxation model of Rational Extended Thermodynamics. The nonisothermal profile problem is structurally different from its isothermal counterpart: restoring the energy balance determines the temperature along the traveling wave and feeds it back into the pressure, the relaxation production, the temperature-dependent consistency coefficient, and the characteristic structure. Under thermodynamic stability, $p_θ\ge0$, and strict convexity of the reduced Hugoniot pressure, no nontrivial constant-temperature compressive profile can satisfy the full equations. We derive an exact global characteristic-ordering identity and prove that the positive nonequilibrium characteristic speed has its strict global minimum at the unperturbed upstream state. Consequently, a monotone continuous profile exists for $1<M_0<\Mst$, whereas for $M_0>\Mst$ the Boillat--Ruggeri theorem excludes a $C^1$ profile and any admissible piecewise-smooth connection must contain a subshock. Despite the thermomechanical coupling, the shock-thickness classification remains unchanged: $m=2$ is the weak-shock threshold and $m=1$ the near-critical threshold as $M_0\nearrow\Mst$. The corresponding exponents are constitutive-independent within the present class, while finite limiting values and prefactors depend on the equation of state, internal energy, and temperature-dependent consistency coefficient. For the Tait--Murnaghan example, increasing the reference temperature lowers the critical Mach number when the dimensional viscous--relaxation scale is fixed and, for the thermally thinning law considered, reduces the resolved shock thickness.
Comments25 pages, 6 figures
