Why does the absence of diabatic heating rate and frictional terms make the zonal and vertical velocity identically zero?

The Curious Case of Still Air: Why Zonal and Vertical Winds Just… Vanish

Ever wondered why those super-simplified weather models always seem to have perfectly still air moving east-west or up-down? It all boils down to what happens when you strip away some key ingredients: diabatic heating and friction. Turns out, ditching those, makes both the zonal (east-west) and vertical components of wind velocity just… vanish. Poof! But why does this happen? Let’s dig in, shall we?

First, we need to get a handle on a couple of concepts that form the bedrock of how we understand the atmosphere: geostrophic and hydrostatic balance. Think of them as the atmosphere’s way of trying to stay in equilibrium.

• Geostrophic Balance: High up in the atmosphere, far from the ground, things get interesting. The pressure gradient force (PGF) – that push of air from high to low pressure – and the Coriolis force (that weird deflection caused by the Earth spinning) are usually locked in a near-perfect tug-of-war. The result? Wind that flows parallel to those isobars (lines of equal pressure), with high pressure sitting to your right if you’re in the Northern Hemisphere. It’s like the wind is trying to fall downhill (towards low pressure) but keeps getting pushed sideways by the Earth’s rotation.
• Hydrostatic Balance: This one’s all about vertical equilibrium. Imagine the atmosphere as a stack of pancakes. Hydrostatic balance basically says that the weight of all the pancakes above is perfectly balanced by the pressure pushing up from below. Simple, right?

Now, these balances are captured in a set of equations called the primitive equations. Think of them as the atmosphere’s operating system. They’re incredibly complex, so to actually understand what’s going on, we often make some… let’s call them “strategic” simplifications.

So, what happens when we decide to ignore diabatic heating and friction? What exactly are we throwing out the window?

• Diabatic Heating: This is any process that adds or removes heat from the air. Think sunshine warming the ground, or water vapor releasing heat as it turns into rain.
• Friction: This is the drag the air feels as it rubs against the Earth’s surface, and even the internal friction within the air itself. It’s like trying to run through mud – it slows you down.

Basically, we’re imagining a perfectly isolated, frictionless world. An air parcel can move without any outside interference. Sounds a bit boring, doesn’t it? And that’s precisely the point.

Here’s the kicker: in this super-simplified world, the zonal and vertical winds disappear. Why?

Now, before you start thinking that weather forecasting is a piece of cake, remember these are HUGE simplifications!

• Diabatic heating, especially when water vapor condenses into clouds, is a major player in creating vertical motion and driving weather patterns. Think thunderstorms!
• Friction is essential for slowing down the wind near the surface and creating that turbulent boundary layer we all experience every day.

So, while this theoretical exercise is helpful for understanding the basics, it’s a far cry from the real, messy, complicated atmosphere we live in.

The takeaway? When you switch off diabatic heating and friction, you’re essentially hitting the “pause” button on atmospheric motion in those directions. It shows just how crucial these seemingly small processes are in making our atmosphere the dynamic, ever-changing place it is. Even if it’s just an idealized view.