Nonlinear free fall of one-dimensional rigid bodies in hyperviscous fluids

TL;DR

This paper demonstrates that combining dimensional reduction with hyperviscous regularization enables a well-posed mathematical model for the free fall of slender rigid bodies in viscous fluids, overcoming classical limitations.

Contribution

It introduces a novel DR/HR approach that allows rigorous analysis of free fall of slender bodies, which was not possible with classical models.

Findings

Hyperviscous term enables a proper definition of viscous forces on 1D bodies.

The DR/HR method results in a well-posed fluid-structure interaction problem.

The approach effectively models the free fall of slender rigid bodies in fluids.

Abstract

We consider the free fall of slender rigid bodies in a viscous incompressible fluid. We show that the dimensional reduction (DR), performed by substituting the slender bodies with one-dimensional rigid objects, together with a hyperviscous regularization (HR) of the Navier--Stokes equation for the three-dimensional fluid lead to a well-posed fluid-structure interaction problem. In contrast to what can be achieved within a classical framework, the hyperviscous term permits a sound definition of the viscous force acting on the one-dimensional immersed body. Those results show that the DR/HR procedure can be effectively employed for the mathematical modeling of the free fall problem in the slender-body limit.