## 1 Introduction  
Emerging applications, including water quality monitoring [1], offshore asset monitoring [2], biodiversity monitoring [3], oil field exploration [4], biogeochemical process exploration [5], and the extensive deployment of acoustic modoms with their efficient computing and denoising capabilities [6], have attracted significant investments of time, finances, and intellectual resources from both industry and academia in recent years. These investments aim to develop viable underwater acoustic communication (UWAC) systems. However, the complex nature of water, the slow propagation speed of acoustic waves through water, limited bandwidth availability, complex noise sources, and delay-Doppler effects make it much more challenging to design and deploy a reliable UWAC system compared to traditional terrestrial radio systems [7, 8]. The only way forward is to design dedicated signal processing algorithms and network protocols specifically for UWAC scenarios, which are validated across a variety of scenarios. Running actual experiments in seas, rivers, or lakes presents significant financial and logistical challenges [9]. Border security protocols among multiple nations sharing a water body can sometimes make it nearly impossible to conduct trials, especially during the design stage. Therefore, it is crucial for system engineers to test their designs using emulator platforms that are both controllable and offer realistic and comprehensive simulations. Channel emulator platforms allow designers to evaluate the performance of different algorithms across a broad range of parameters. They also provide ample samples to assess how the system performs and evolves over time through thorough empirical evaluations [10]. Once the robustness of the designed system has been synthetically validated, experimental demonstrations can be arranged in a specific environment with significantly reduced time, financial, and logistical commitments. Developing channel emulators for the UWAC environment poses significant challenges due to the absence of a typical underwater environment. Water characteristics vary based on factors such as depth, salinity, density, and geographical location. The acoustic signal is subjected to fluctuations in attenuation, absorption, delay, Doppler effects, and noise, influenced by the diverse underwater characteristics, as well as sea-surface and sea-bottom contours [11; 12]. Therefore, instead of separately characterising each environmental parameter and its impact, we propose the development of a mathematical model that utilises the principles of the medium's physics and acoustic signal propagation. This model aims to accurately map the interaction between the aquatic medium and the travelling signal. Several UWAC channel modelling software and platforms have been developed over the years to realistically represent different UWAC communication scenarios. One very popular open-source platform is BELLHOP [13], which utilises beam tracing to emulate acoustic pressure fields in specific underwater environments. Another widely used platform is the Ulrick model [14], which calculates distance-related spreading loss and frequency-related absorption loss for UWAC links. Other UWA network simulators, such as DESERT [15], SUNSET [16], and WOSS [17], also provide researchers with valuable insights into the UWAC environments. However, there is no single unified platform that comprehensively captures the flow of the acoustic signals through various aquatic environments. Such a platform would provide valuable insights into how the signal interacts with the environment, how it evolves over time and distance, and how these changes impact the overall design of the communication system. The primary contribution of this paper is the integration of mathematical modelling, specifically how acoustic signals propagate through water, with the generation of channel samples using the sum-of-sinusoids (SOS) approach [18] in a generalised yet manageable channel emulator platform.