Suppression of jet spectra or jet quenching in high-energy heavy-ion collisions is caused by jet energy loss in the dense medium. The azimuthal anisotropy of jet energy loss in noncentral heavy-ion collisions can lead to finite values of jet anisotropic flow coefficients. This is investigated within the linear Boltzmann transport model, which simulates both elastic scattering and medium-induced gluon radiation based on perturbative quantum chromodynamics for jet shower and medium recoil partons as well as radiated gluons as they propagate through the quark-gluon plasma. The dynamical evolution of the quark-gluon plasma in each event of heavy-ion collisions is provided by the $(3+1)$-dimensional CLVisc hydrodynamic model with fully fluctuating initial conditions. This framework has been shown to well describe the suppression of single inclusive jet spectra. We calculate in this study the elliptic $({v}_{2}^{\mathrm{jet}})$ and triangular $({v}_{3}^{\mathrm{jet}})$ anisotropy coefficients of the single inclusive jet spectra in $\text{Pb}+\text{Pb}$ collisions at the Large Hadron Collider energies. We investigate the colliding energy, centrality, jet transverse momentum dependence of the jet anisotropy, as well as their event-by-event correlation with the flow coefficients of the soft bulk hadrons. An approximate linear correlation between jet and bulk ${v}_{2}$ is found. The effect of the bulk ${v}_{n}$ fluctuation on ${v}_{n}^{\mathrm{jet}}$ is found negligible. We also investigate the effect of jet-induced medium excitation, which is influenced by radial flow, on jet ${v}_{2}^{\mathrm{jet}}$. The sensitivity of jet elliptic anisotropy ${v}_{2}^{\mathrm{jet}}$ to the shear viscosity of the bulk medium is also studied.
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