Hydrodynamic Solitons: Untangling Knots on an Endless Rope

managers: Pranav Chandrashekar, Havyn Ancelin

contact: pranavc2576@g.ucla.edu, havynancelin@g.ucla.edu

Learning Objectives: Wave Mechanics, Linear Hydrodynamics & Acoustics, Water Waves in a Gravitational Field

Suggested Prerequisites:

Mathematics 32B, 33A, 33B,

Physics 105A, 105B, 131

Video Links:

Non-Propagating Hydrodynamic Soliton Pt.1

Non-Propagating Hydrodynamic Soliton Pt.2

Preoccupied by a very angry cactus at the Mildred E. Mathias Botanical Garden, you hear an unusual splash. You peer into the pond and find a turtle waddling up a muddy slope; it is headed right for you! Fearlessly, you stand your ground and patiently wait as the turtle makes his way to you. 

“Consider the following description—”, the turtle speaks with its mouth, 

“A measurable quantity of energy confined within a definite region of space”. 

After a turtle-sized yawn, he continues, “It can move around space and sail through time, with no inclination to dissipate, it maintains its shape.” 

“Is this a riddle?”, you ask.

“Yes . . .”, the turtle sighs. “In the event that a pair of these collide, we find them unaltered, gliding right past our sight, wherever they might. When opposites collide, they could disappear, leaving neither in sight.” 

“There’s an opposite thing?”

“There’s an opposite thing. Anyhow, what did I just describe?” it asks, and swiftly slides back into the pond.

Did the turtle just describe the properties of elementary particle/anti-particle pairs? Perhaps, but that’s no riddle. What is a riddle, however, is the other class of physical objects that demonstrates each of these properties — hydrodynamic solitary waves. Also known as ‘solitons’, these waves can be observed on the surface of a macroscopic fluid such as water! 

As opposed to a standing wave, in which every point along the wave has a constant phase but varies only in amplitude, a solitary wave has constant phase across a continuous, definite region of space. The phenomenon of solitons has been extensively studied by Professor Seth Putterman at UCLA’s Physics department.

The project will begin by working as a group to develop the equations that describe the state of an ideal fluid, starting from macroscopic first principles. Once we have gathered a set of equations, we will explore the linearized motion of ideal liquids and gases, which will include hydrostatics, vortices, acoustics, and dispersive water waves in a uniform gravitational field. Hydrodynamic solitons are an inherently non-linear phenomena, so we will conveniently approach that after the linear phenomena. We will also build experimental setups for generating parametrically driven hydrodynamic solitons because they are quite fun to watch!