OpenOceanModels

On Feb 2, 1979, the Global Drifter Program began, launching satellite-tracked buoys to monitor ocean currents. A key tool for climate and ocean research 🌊 Read more: https://oceanofisica.ulpgc.es/efemeride/inception-global-drifter-program

OpenOceanModels/Exercises/NS_nonlinearadvection_pressure at main · fjmachin/OpenOceanModels Contribute to fjmachin/OpenOceanModels development by creating an account on GitHub.

📎 Code: bit.ly/NS_nonlinear...

🎥 Video: youtu.be/jjFHG5EJeFc

#OpenOceanModels #NavierStokes #FluidDynamics #Bernoulli #Venturi #Oceanography #CFD

5️⃣ In the animation, we increase the slope of the pressure field progressively, and observe how the velocity field reacts.

This helps visualize how fluid adjusts locally to maintain balance with external forcing.

4️⃣ This setup echoes classic cases like the

Venturi effect

Bernoulli principle

Both describe how pressure energy converts into kinetic energy in steady flows—here derived directly from the Navier–Stokes equations.

3️⃣ The result is a spatially varying velocity field.
Regions with steeper pressure gradients require stronger changes in velocity to maintain balance.

The velocity field is not evolving in time—it adjusts in space to compensate for pressure.

2️⃣ We impose a pressure that increases linearly with
𝑥. This creates a horizontal pressure gradient.

Our goal is to compute the velocity field 𝑢(𝑥) that balances this gradient—so that there's no acceleration, and the flow remains in a steady state.

1️⃣ We focus on two terms of the Navier–Stokes momentum equations: the nonlinear advection term and the pressure gradient term.

We remove everything else: no viscosity, no Coriolis, no time acceleration.

🧵 Thread — Exercise #10: Pressure vs Nonlinear Advection

What happens when pressure increases steadily in space—but doesn’t change in time—while velocity adapts to maintain balance?

In this episode of OpenOceanModels, we isolate a classic fluid dynamic balance.
🧵👇

Next, we’ll explore what happens when nonlinear advection interacts with other forces. Stay tuned.

#NavierStokes #FluidDynamics #NonlinearAdvection #Oceanography #OpenOceanModels

YouTube video by OpenOceanModels Exercise #9. Nonlinear Advection: When Velocity Deforms Itself

🎥 Watch the simulation:
www.youtube.com/watch?v=VTZK...

💻 Code and explanation:
bit.ly/NS_nonlinear...

This is pure nonlinear dynamics in action.
No net momentum is created—just redistributed through self-advection.

We start from rest—no viscosity, no pressure gradient, no Coriolis force. Just a sharp velocity front.

The result?
The front deforms: faster regions overtake slower ones, turning a step into a ramp.

🌊 OpenOceanModels – Case #9
This time, we isolate nonlinear advection in the Navier–Stokes equations.
What happens when the flow transports itself?

6/
This is entry #8 in the OpenOceanModels series, where we isolate individual terms from Navier–Stokes to better understand geophysical flows.

#OpenOceanModels #NavierStokes #FluidDynamics #Viscosity #OceanModeling #Python #NumericalSimulation

5/
💻 Run the simulation yourself. The Python code is here:
bit.ly/OOM_momentum...

4/
🔬 A clean setup to understand how viscosity operates in a fluid.
📽️ Watch the full animation:
www.youtube.com/watch?v=BA4j...

3/
The higher the curvature of velocity, the stronger the diffusion.
That’s why the center of the Gaussian decays first and fastest.

2/
We start with a Gaussian velocity pulse and watch it evolve.
No wave, no drift.
Just smoothing.
Just spreading.
This is momentum diffusion in its purest form.

1/
What happens when we isolate only viscosity in the Navier–Stokes equations?
In this case, we strip everything else—no Coriolis, no pressure gradients, no advection. Just local acceleration and viscous diffusion.

YouTube video by OpenOceanModels Exercise #7. Acoustic Wave: Pressure-Driven Acceleration in Navier–Stokes Equations

💻 Code (Python):
bit.ly/OOM_acoustic...

🎥 Full simulation:
www.youtube.com/watch?v=1aJa...

#OpenOceanModels #NavierStokes #Acoustics #Sound #FluidDynamics #Oceanography #Python

🌬 In the atmosphere, this mechanism is central.
🌊 In the ocean, it’s usually negligible — which is why many models filter it out.

But conceptually?
It’s a clean, beautiful example of how pressure alone can create motion.

In this setup:
✖ No Coriolis
✖ No viscosity
✖ No advection
Just pressure pushing fluid parcels and generating motion.

By focusing only on how pressure drives motion, we recover the classical wave equation.
This governs how sound waves propagate in air — or any compressible medium.

YouTube video by OpenOceanModels Exercise #7. Acoustic Wave: Pressure-Driven Acceleration in Navier–Stokes Equations

🔊 What does an acoustic wave look like in its purest form?
In Exercise #7 of OpenOceanModels, we isolate just two terms of the Navier–Stokes equations:
🟢 Local acceleration
🟢 Pressure gradient
🎬 www.youtube.com/watch?v=1aJa...
🧵👇

6/6 🔜 Next episodes: we'll progressively add other terms (pressure, viscosity, etc.) to build a deeper intuition of ocean & atmospheric fluid dynamics.

#OpenOceanModels #Oceanography #FluidDynamics #InertialOscillation #Science

5/6 💻 Want the code? Find it here:
bit.ly/OOM_inertial...

YouTube video by OpenOceanModels Exercise #6. Inertial Oscillations: Isolating Terms in Navier–Stokes Equations

4/6 🎥 See inertial oscillations in action:
youtu.be/Vw8OAoujJm0

3/6 🌀 In this episode, we focus on just the time derivative and the Coriolis term. The resulting motion? Inertial oscillations—fluid parcels moving in circular paths due solely to Earth's rotation.

2/6 💡 By simplifying! We isolate terms in the equations to see what happens when only specific forces act on fluid parcels.