Eddy

Unit 5 Cohesion

Eddy

Juan Juan
12 min read
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Eddies are swirling, rotational structures that form within a flowing gas or fluid, where coherent vortices emerge and persist despite the surrounding chaotic motion. They are the Mid Cohesion force in Superphysics’ Gas Relationalities — the rotational, structure-forming action of the gaseous medium as it organizes itself through aetherspace and space.

Unlike convection (linear/displacement), eddies are rotational and self-sustaining — gas curls back on itself, forming stable loops that trap momentum and energy.

The Equation: Vorticity and Eddy Formation

Vorticity (Micro Origins, Macro Manifestation)

ω=∇×v \omega = \nabla \times \mathbf{v}

Where:

Symbol Meaning Unit
ω \omega Vorticity (local rotation rate) s−1 \text{s}^{-1}
v \mathbf{v} Velocity field m/s \text{m}/\text{s}
∇× \nabla \times Curl operator —
∂ω∂t+(v⋅∇)ω=(ω⋅∇)v+ν∇2ω \frac{\partial \omega}{\partial t} + (\mathbf{v} \cdot \nabla)\omega = (\omega \cdot \nabla)\mathbf{v} + \nu \nabla^2 \omega

Here ( (\omega \cdot \nabla)\mathbf{v} ) is the vortex stretching term — the mechanism that intensifies eddies. Viscosity ( \nu \nabla^2 \omega ) diffuses rotation, acting as cohesive damping.

Reynolds Number (Transition to Eddy Formation)

Re=ρvLμ Re = \frac{\rho v L}{\mu}
Symbol Meaning Unit
Re Reynolds number (ratio of inertial to viscous forces) —
ρ \rho Gas density kg/m3 \text{kg}/\text{m}^3
v v Flow velocity m/s \text{m}/\text{s}
L L Characteristic length m \text{m}
μ \mu Dynamic viscosity Pa⋅s \text{Pa} \cdot \text{s}

When Re > 2000, laminar flow breaks into eddies — cohesion emerges from displacement.

Kolmogorov Scale (Smallest Eddy Size)

η=(ν3ε)1/4 \eta = \left( \frac{\nu^3}{\varepsilon} \right)^{1/4}

Where

ε \varepsilon

is the energy dissipation rate. Below

η \eta

, viscosity smooths out rotation.

Key Properties of Eddies

Property Explanation
Rotational Fluid curls around a local axis — pure cohesion
Self-sustaining Vortices feed on shear and persist until viscosity dissipates them
Hierarchical Large eddies spawn smaller eddies (energy cascade)
Momentum-trapping Eddies carry trapped mass and momentum over distances
Pressure-linked Low pressure at vortex core (Bernoulli)
Temperature-dependent Higher ( T ) → lower ( \nu ) → eddies persist longer
Scale-dependent Eddy size determines lifetime and energy content

Energy Cascade (Richardson)

E(k)∝k−5/3 E(k) \propto k^{-5/3}

Energy flows from large eddies (small ( k )) to small eddies (large ( k )) until viscosity dissipates it as heat.

Real-Life Examples

Example How Eddies Work
1. Smoke rings A puff of smoke forms a toroidal vortex that travels intact
2. Turbulence behind aircraft Wingtip vortices spiral behind planes, dangerous to following aircraft
3. Ocean eddies Large swirling currents (e.g., Gulf Stream rings) trap warm water
4. Jupiter’s Great Red Spot A persistent anticyclonic eddy larger than Earth
5. Kármán vortex street Alternating eddies shed behind a cylinder in flow
6. Tornadoes Intense vertical eddies formed from wind shear
7. Coffee cup swirls Stirring creates eddies that persist after spoon removed
8. Atmospheric cyclones Low-pressure systems with rotating eddy structure
9. River rapids Rocks create standing eddies in flowing water
10. Dust devils Small, short-lived eddies formed by surface heating

Summary

Question Answer
What is an eddy? A coherent rotational vortex in a flowing medium
What law describes it? Vorticity equation: ( \frac{\partial \omega}{\partial t} + (\mathbf{v} \cdot \nabla)\omega = (\omega \cdot \nabla)\mathbf{v} + \nu \nabla^2 \omega )
What type of force? Mid Cohesion (rotational, Rule 2 + 4)
What drives it? Shear, instability, vortex stretching, energy cascade
Real examples? Smoke rings, wingtip vortices, Jupiter’s Great Red Spot, tornadoes
What’s its displacement counterpart? Convection (Mid Displacement)

Bottom line: Eddies are the rotational, self-sustaining curls of the gaseous medium — the Mid Cohesion force that pairs with convection’s linear displacement in Superphysics’ Gas Relationalities.

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