In studies of binary black hole (BBH) mergers in eccentric orbits, the mean anomaly, traditionally regarded as less significant than eccentricity, has been thought to encode only the orbital phase, leading to the assumption that it exerts minimal influence on the dynamics of eccentric mergers. In a previous investigation, we identified consistent oscillations in dynamical quantities peak luminosity $L_{\mathrm{peak}}$, remnant mass $M_{\mathrm{rem}}$, spin ${\alpha }_{\mathrm{rem}}$, and recoil velocity $V_{\mathrm{rem}}$—in relation to the initial eccentricity $e_0$. These oscillations are associated with integer orbital cycles within a phenomenological framework. In this paper, we aim to explore the underlying physical nature of these oscillations through gravitational waveforms. Our examination of remnant mass and spin reveals that, while the initial Arnowitt, Deser, Misner (ADM) mass $M_{\mathrm{ADM}}$ and orbital angular momentum $L_0$ exhibit gradual variations with $e_0$, the radiated energy $E_{\mathrm{rad}}$ and angular momentum $L_{\mathrm{rad}}$ display oscillatory patterns akin to those observed in $M_{\mathrm{rem}}$ and ${\alpha }_{\mathrm{rem}}$. By decomposing the waveforms into three distinct phases—inspiral, late inspiral to merger, and ringdown—we demonstrate that these oscillations persist across all phases, suggesting a common origin. Through a comparative analysis of $E_{\mathrm{rad}}$ and $L_{\mathrm{rad}}$ derived from numerical relativity, post-Newtonian (PN) waveforms, and orbital-averaged PN fluxes during the inspiral phase, we identify the initial mean anomaly $l_0$ as the source of the observed oscillations. This effect, which is averaged out in orbital-averaged flux calculations, significantly influences $M_{\mathrm{rem}}$, ${\alpha }_{\mathrm{rem}}$, and $V_{\mathrm{rem}}$, with its impact increasing as $e_0$ rises. Further, we find that by continuously varying $l_0$ within the parameter space $[0,2\pi ]$, we can construct an envelope that encompasses the original oscillations of these radiative quantities, indicating that the oscillations originate from the specific initial condition $l_0$. We synthesize and analyze the relationships between dynamical quantities and mass ratio for orbital BBH mergers, integrating data from both eccentric and circular orbits. Our findings emphasize that eccentricity and mean anomalies induce oscillations and ranges in dynamical quantities relative to circular orbits. We interpolate the maximum and minimum values of the dynamical quantities to delineate the vicinities of these quantities for eccentric orbits compared to circular orbits. Notably, the vicinities intensify with higher mass ratios ($q=m_1/m_2\le 1$, $m_1$, and $m_2$ are component masses of the BBH) for $M_{\mathrm{rem}}$, ${\alpha }_{\mathrm{rem}}$, and $L_{\mathrm{peak}}$, reaching maximum effects for $q\approx 1/3$ on $V_{\mathrm{rem}}$. By quantifying the residual deviations relative to circular orbits, we highlight significant differences between the vicinities and the polynomial modeling of circular orbits, underscoring the importance of this effect, which cannot be overlooked and has a broad impact.

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• General relativity
• Gravitation
• Gravitational waves