Laboratory rivers extremize friction and are cosmological analogues

TL;DR

This paper draws a formal analogy between laboratory river profiles and cosmological models, revealing that river friction extremization relates to a cosmological Friedmann equation and energy dissipation.

Contribution

It introduces a novel cosmological analogy for river profiles, linking fluid dynamics with cosmological equations and providing insights into friction and energy dissipation extremization.

Findings

River cross-sections satisfy a Friedmann-like differential equation.

Extremizing the action corresponds to maximizing friction force and energy dissipation.

The extremum identified is a maximum, not a minimum.

Abstract

In the shallow water approximation, the cross-sectional profiles of laboratory rivers satisfy a differential equation here shown to be formally the Friedmann equation of cosmology ruling the evolution of Anti-de Sitter universe. The ensuing cosmic analogy provides a counterintuitive Lagrangian for the transverse river profile. Extremizing the corresponding action corresponds to extremizing the friction force on the river bottom and the energy dissipation rate. Analysis of the second variation establishes that this extremum is a maximum.