The visual system of underwater intelligent vehicles promotes the development of ocean science and engineering. Currently, most of the methods used in visual systems are based on supervised learning. However, it is challenging to obtain high-quality underwater datasets. In this work, we propose a network named suirSIR (semi-supervised underwater image reconstruction and enhancement network based on a Simulated Image Re-degradation process, suirSIR) to reduce the dependence of network training on paired datasets. To address the issue of pseudo labels with negative effects misleading the network during semi-supervised learning, we first revise the physical image formation model and embed it into the proposed network, which consists of two pairs of student-teacher nets. The proposed network is then used to estimate the parameters of the revised model and simulate the re-degradation of images to ensure the stability of supervised and unsupervised training. Further, we design a prompt SwinTransformer module by combining the prompt tensors to achieve stronger nonlinear modeling capability in feature processing. Besides, our teacher net can generate more than one kind of pseudo label to guide the student net. Numerous experiments and analyses validate the superiority of our method compared to other state-of-the-art UIE (Underwater Image Enhancement, UIE) methods. Furthermore, extended experiments such as object detection, image segmentation and real-time underwater video enhancement demonstrate the potential of our method for applications. Our code and enhanced videos are available at: https://github.com/jacezhang66/OctopusAI-suirSIR-network.