# fluid mechanics

How can maths help to understand the Southern Ocean, a vital component of the Earth's climate system?

How do green algae manage a perfect breaststroke even though they haven't got a brain? Enter the maths of synchronisation.

How does a smooth flow suddenly become turbulent? The Reynolds number helps understand the transition.

How does water, or indeed any fluid, move? The Euler equations let us look beneath the surface and mark the beginning of modern fluid dynamics.

New research shows that ventilation is crucial and that masks are effective.

How do green algae manage a perfect breaststroke even though they haven't got a brain? The maths of synchronisation explains and even sheds light on human physiology and evolution.

Ocean waves are not moving walls of water. Instead, it's some kind of energy that moves along. But then, what happens to the water itself? This isn't just an idle question to ponder while watching the ocean — its answer may help protect us from it too. And it requires some sophisticated maths.

Few things in nature are as dramatic, and potentially dangerous, as ocean waves. The impact they have on our daily lives extends from shipping to the role they play in driving the global climate. From a theoretical viewpoint water waves pose rich challenges: solutions to the equations that describe fluid motion are elusive, and whether they even exist in the most general case is one of the hardest unanswered questions in mathematics.

**Jerry Gollub**tells

*Plus*about a new discovery which combines experiment with sophisticated maths.