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Sally Zhu

The Harker School
San Jose, California

About Sally Zhu

Sally studied the patterns made by the waves that flow below the water’s surface, called internal waves, in a hypothetical two-dimensional fish tank, and how they can go from choppy to smooth as they bounce off the tank’s walls. Sally believes that this could help scientists analyze waves in the ocean.

On the Smoothness and Regularity of the Chess Billiard Flow and the Poincaré Problem

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Sally Zhu, 17, of Saratoga, made waves with her Regeneron Science Talent Search mathematics project. Many people are familiar with how waves move on the surface of water in a fish tank, but there are also waves that travel below the surface, called internal waves. Understanding these waves mathematically is difficult because they bounce off of walls in an extremely complex way. In her project, Sally addressed this difficulty by showing that internal waves that undergo “chess billiard flow” in a two-dimensional square fish tank will always go from choppy to smooth if a certain number, called the rotation number, of the tank is a Diophantine number (an irrational number that cannot be neatly approximated with rational numbers). Not only did Sally add to the field theoretically, but she also performed numerical experiments on a computer and generated plots to intuitively explain her theoretical results, which she hopes will help scientists in fluid dynamics and oceanography.

The daughter of Huican Zhu and Hong Wei, Sally attends The Harker School in San Jose.

Beyond the Project

Sally is a published first-author in Research Notes of the American Astronomical Society. She is also editor-in-chief for her high school’s online news site, the Harker Aquila.

FUN FACTS: Sally has a “pretty extensive” puzzle collection that includes Rubik’s cubes, jigsaw puzzles and more! When she needs to de-stress, she says she turns on music and works on a puzzle.

STS 2023 Finalist Sally Zhu, Illustration by Amy Wike