# Resonant drag instability of grains streaming in fluids

## TL;DR

This paper introduces the concept of resonant drag instabilities (RDI), showing that grains streaming faster than fluid waves can cause generic, rapid instabilities across various physical systems, with a simple formula for their growth rates.

## Contribution

The paper derives a universal expression for RDI growth rates and introduces a matrix-based resonance formalism applicable to diverse fluid and nonfluid systems.

## Key findings

- Identified conditions for generic streaming instabilities in fluids.
- Derived a simple analytic formula for RDI growth rates.
- Proposed applications across astrophysical and atmospheric systems.

## Abstract

We show that grains streaming through a fluid are generically unstable if their velocity, projected along some direction, matches the phase velocity of a fluid wave (linear oscillation). This can occur whenever grains stream faster than any fluid wave. The wave itself can be quite general--sound waves, magnetosonic waves, epicyclic oscillations, and Brunt-V\"ais\"al\"a oscillations each generate instabilities, for example. We derive a simple expression for the growth rates of these "resonant drag instabilities" (RDI). This expression (i) illustrates why such instabilities are so virulent and generic, and (ii) allows for simple analytic computation of RDI growth rates and properties for different fluids. As examples, we introduce several new instabilities, which could see application across a variety of physical systems from atmospheres to protoplanetary disks, the interstellar medium, and galactic outflows. The matrix-based resonance formalism we introduce can also be applied more generally in other (nonfluid) contexts, providing a simple means for calculating and understanding the stability properties of interacting systems.