Known as "the hidden half", plant roots are fundamental contributors to the riparian ecosystem functioning. Roots show an extraordinary architectural complexity that recalls their remarkable ability to adapt to environmental heterogeneity, resources availability, and climate. In fluvial environments, phreatophytes and hydrophytes cope with flow and sediment processes, and hydrotropism and aerotropism are the main drivers for root growth. In this work, we show how the vertical root density distribution in riparian plants is the result of how plants respond to the random fluctuations of river flows. A root data set from field and controlled outdoor experiments is used in combination with a physically based analytical model to demonstrate that the root vertical density distribution can be ascribed to the interplay of randomness and determinism in a simple mathematical form. The shape of the distribution reflects the profitability of plant roots to grow in different soil layers depending on the soil moisture availability. For the first time, this model helps understanding in an analytical manner the adaptation strategy of plant roots to different scenarios, paving the way for the comprehension of the effects of future changes in climate and environmental conditions.