Existing underwater image enhancement (UIE) methods typically prioritize improving image quality at the expense of algorithmic efficiency. In this paper, we propose a fusion-based, channel-wise isotropic convergent UIE method designed for real-time performance. The proposed approach comprises three key modules: (i) a non-linear transformation module that corrects color casts and aligns the pixel distribution with the gray-world assumption (GWA); (ii) a channel-wise isotropic convergence scheme that reduces intensity distribution disparities across channels, promoting balanced convergence; and (iii) a patch-based enhancement strategy that divides the image into smaller patches to better capture local features and improve adaptability to non-uniform degradation. Moreover, certain critical steps in our method are optimized to achieve O(1) time complexity, allowing it to meet real-time requirements. Extensive experiments validate the effectiveness of each module in the proposed method, showcasing its superiority when compared to the existing state-of-the-art (SOTA) approaches. Code has been released at https://github.com/JohnChenS/FCICE_UnderwaterImageEnhancement.