# Unified transport scaling laws for plasma blobs and depletions

## TL;DR

This paper derives and validates unified scaling laws for plasma blob and depletion dynamics, revealing how size, amplitude, and compressibility influence their velocities and accelerations in a gravitational field.

## Contribution

It introduces a comprehensive empirical model that unifies the scaling laws for plasma blobs and depletions, accounting for compressibility effects and matching numerical simulations.

## Key findings

- Radial velocity scales with the square root of size and amplitude for incompressible flows.
- Compressibility alters the velocity scaling, making it linear with amplitude for certain ratios.
- Depletions accelerate faster than blobs due to reduced inertia.

## Abstract

We study the dynamics of seeded plasma blobs and depletions in an (effective) gravitational field. For incompressible flows the radial center of mass velocity of blobs and depletions is proportional to the square root of their initial cross-field size and amplitude. If the flows are compressible, this scaling holds only for ratios of amplitude to size larger than a critical value. Otherwise, the maximum blob and depletion velocity depends linearly on the initial amplitude and is independent of size. In both cases the acceleration of blobs and depletions depends on their initial amplitude relative to the background plasma density, is proportional to gravity and independent of their cross-field size. Due to their reduced inertia plasma depletions accelerate more quickly than the corresponding blobs. These scaling laws are derived from the invariants of the governing drift-fluid equations and agree excellently with numerical simulations over five orders of magnitude. We suggest an empirical model that unifies and correctly captures the radial acceleration and maximum velocities of both blobs and depletions.