Field-induced anomaly in the anisotropic non-Fermi-liquid normal state of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>UBe</mml:mi> <mml:mn>13</mml:mn> </mml:msub> </mml:math>

We report the results of high-resolution dc magnetization and specific-heat measurements at very low temperatures for a single crystal \color{black} of UBe$_{13}$ in magnetic fields applied along the [001] and [111] directions, in both the normal and superconducting states. In the normal state, magnetic susceptibility $χ(T) = M/H$ exhibits a logarithmic temperature dependence over a wide temperature range (1-20 K). However, with increasing field, this non-Fermi-liquid (NFL) behavior of $χ(T) $ at low temperatures is suppressed. Moreover, a susceptibility maximum occurs below 4 T, whereas Fermi-liquid coherence is recovered above 8 T. In addition, thermodynamic anomalies ($T_{\rm A}$ and $H_{\rm A}$) occur in both magnetic susceptibility and specific heat at intermediate fields (6--10 T) along the [111] direction. Furthermore, a nontrivial fifth-order nonlinear susceptibility is observed in the normal-state magnetization of UBe$_{13}$. These results suggest a close relationship between the field-induced multipolar correlations of $5f$-electron degrees of freedom and the Fermi-surface reconstruction accompanying the crossover from the NFL state to the Fermi-liquid state in UBe$_{13}$.