Vector databases have been designed and optimized for cloud environments; however, emerging scientific AI workloads (e.g., molecular search, meteorological trajectory detection, and literature-driven hypothesis generation) demand efficient, scalable execution on HPC systems. We present a large-scale evaluation of three state-of-the-art vector databases -- Qdrant, Milvus, and Weaviate -- on two production supercomputers, scaling to 256 distributed workers across 64 compute nodes. We evaluate representative workload patterns -- mixed read/write and write-then-read -- using popular benchmarks, multimodal embeddings, and a novel real-world scientific dataset. Our results reveal that workload characteristics can limit latency reduction, additional cores can reduce query throughput by up to 30.67%, and scaling from 16 to 256 workers (16x) only yields a 5.46x improvement. This scaling paradox exposes the fundamental mismatch between cloud-oriented designs and HPC systems, highlighting the need for new, HPC-aware vector database designs.

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