Introduction
A vortex is one of the most persistent and revealing patterns in nature. Wherever energy moves through matter under constraint, rotation emerges. From whirlpools in a sink to tornadoes, hurricanes, atmospheric circulation, ocean currents, and even galaxies, vortices appear across an extraordinary range of scales.
At first glance, vortices seem simple—things go around in circles. In reality, vortices are among the most complex structures studied in physics. They are inherently nonlinear, often chaotic, and dominated by momentum rather than heat.
This page began decades ago as an exploration of classical vortex physics. Over time, it became clear that vortices are not merely curiosities of fluid mechanics, but a powerful framework for understanding complex systems—including the accelerating dynamics of Earth’s climate.
Modern climate change is often framed as a problem of temperature. Increasingly, it is revealed to be a problem of motion. Much of today’s damage is caused not directly by heat, but by moving mass: wind, water, and rotation.
Climate change behaves less like a thermostat and more like a vortex— spiraling faster as feedbacks reinforce one another. It is a vector problem, not a scalar one.
Vortices: Basic Formulae
velocity = distance / time
acceleration = change in velocity / time
Forced vortex:
circulation (τ) = 2ωA
ω = angular velocity (vector)
A = area enclosed by the contour
Free vortex:
circulation = 2πC
These describe idealized systems. Real vortices interact with turbulence, boundaries, and changing mass distributions—often leading to instability and chaos.
Vortex Prose
Vortex Flow: Vortex flow is non-potential. The integral of tangential velocity around a closed contour is nonzero—energy is stored in rotation.
Singularities: Ideal vortices contain a singularity at the core where velocity becomes undefined.
vtangential = a / r
vradial = 0
At r = 0, classical equations break down—signaling the limits of idealized models.
Historical Note: Huygens and Descartes envisioned gravity and motion as emerging from vortices. Determinism dominated physics for centuries—until chaos and uncertainty intervened.
Acceleration, Momentum, and Climate
Climate change is not simply warming. It is a redistribution of mass and energy that increases momentum in the system.
Many modern climate disasters are driven by violent motion— storms, floods, and wind—rather than heat alone.
Momentum (p = mv) can increase without increasing speed. Direction, mass, and structure matter.
How do we change the momentum of human civilization—and the climate system— without accelerating further in the wrong direction?