Bjorken flow attractors with transverse dynamics

In the context of longitudinally boost-invariant Bjorken flow with transverse expansion, we use three different numerical methods to analyze emergence attractor solutions in an ideal gas massless particles exhibiting constant shear viscosity entropy density ratio $\eta / s$. The fluid energy is initialized using a Gaussian profile plane, while $\chi = \mathcal{P}_L \mathcal{P}_T$ between longitudinal and pressures set at initial time $\tau_0$ value $\chi_0$ throughout system employing Romatschke-Strickland distribution. We introduce hydrodynamization $\delta \tau_H (\tau_H - \tau_0)/ \tau_0$ based on $\tau_H$ when standard deviation $\sigma(\chi)$ family reaches minimum point maximum convergence solutions. $0+1{\rm D}$ setup, \tau_H$ exhibits scale invariance, being function only $(\eta s) (\tau_0 T_0)$. With find similar computed respect local temperature, $T_0(r)$. highlight transition regimes where expansions dominate. that required for solution be reached increases distance from origin, as expected properties defined by conditions. argue predominantly effect significantly influenced dynamics small systems or large values