哈克定律背後至少有兩種互補的解釋。其一是由義大利水文學家安德烈亞·里納爾多等人在1990年代提出的「最優水道網絡」理論，認為河流在大尺度上呈現狹長形態，是因為這是將水向下坡輸送最節能的方式。其二是景觀演化模型：水流侵蝕岩石時，微小的地形差異導致某些水道捕獲更多徑流，進而加速侵蝕、吸引更多水流，經過數千年的局部調整，整個排水網絡逐漸重組為能量耗散最小的最優配置。
2026年的一項新發現將哈克定律的適用範圍進一步擴展。德克薩斯大學的田東及其合作者發現，哈克定律不僅適用於河流的支流網絡，也適用於河口三角洲的分流網絡——河道長度與其「滋養面積」的0.6次方成正比。支流網絡與分流網絡本質上是相反的過程，一個匯聚沉積物，一個分散沉積物，卻遵循相同的數學規律。這種簡單確定性與混沌隨機性的共存，正是河流最優結構如此迷人的原因所在。
Rivers, like all transport networks, follow a universal mathematical structure that gives them a fractal-like appearance. In 1957, U.S. Geological Survey scientist John Hack discovered the most important law governing river networks: a stream's length is proportional to its drainage area raised to the power of 0.6 (L ~ A⁰·⁶). This relationship, known as Hack's law, holds worldwide regardless of geological characteristics, and reveals that larger basins become progressively more elongated rather than maintaining the same proportions as smaller ones.
At least two complementary explanations underlie Hack's law. The "optimal channel network" theory, proposed by Italian hydrologist Andrea Rinaldo and colleagues in the early 1990s, argues that elongated large-scale river networks represent the most energy-efficient configuration for transporting water downhill. Landscape evolution models provide the mechanism: as water erodes rock, small topographic irregularities cause some channels to capture more runoff, erode faster, and attract still more water. Over thousands of years, these local adjustments gradually reorganize the entire drainage network into a configuration that minimizes energy dissipation — one that conforms to Hack's law.
A 2026 discovery extended Hack's law into new territory. Tian Dong of the University of Texas, Rio Grande Valley and collaborators found that the law applies not only to rivers' tributary networks but also to their deltas — the fan-shaped structures formed where rivers meet the sea. In deltas, channel length scales with nourishment area (the area supplied with sediments) raised to the power of 0.6. Tributary and distributary networks are essentially opposites — one collects sediment while the other distributes it — yet both obey the same mathematics. This coexistence of simplicity and determinism with chaos and randomness is what makes the optimal structure of rivers so captivating.