Liquid metal convection is essential to processes like Earth’s dynamo, solar thermal power, and liquid metal batteries. Yet, key aspects—such as coherent flow structures and heat/momentum transport—remain poorly understood due to the difficulty of measuring turbulent flows in opaque liquids. This dissertation investigates ultrasound imaging techniques to advance open questions in this field. A computational ultrasound imaging system is proposed that incorporates three main approaches. First, ultrasound image velocimetry (UIV) is used to capture time-resolved velocity fields, enabling decomposition of characteristic flow oscillations and validation of theoretical scaling laws. However, UIV’s spatial resolution is limited by its interrogation area size. To overcome this, ultrasound localization microscopy (ULM) was adapted, achieving vector flow mapping at 188 µm resolution. ULM was able to measure boundary layer recirculation and velocity fields previously inaccessible, with an average uncertainty of 4.2%. To address data volume challenges in long-term or volumetric imaging, a novel compression technique—external angle-dependent resonator (EAR)—was introduced. EAR uses multimode waveguides to encode spatial information onto temporal signals, reducing data by 98.5% without significantly sacrificing temporal and spatial resolution. This dissertation incorporates significant advancements in ultrasound imaging for state-of-the art and future MHD flow studies. Furthermore, the investigated compression technique can enhance the application of volumetric medical imaging by its unique advantage of using only a few receiving elements. This is especially relevant in highly integrated systems, opening new perspectives in biomedical lab-on-chip or wearable ultrasound applications.