Advancements in Understanding Gravity Currents Using AI

Gravity currents are flows in the ocean that occur when fluids of different densities mix. This happens in places like ocean overflows or hydrothermal vents. To predict how these currents behave, we need to measure both pressure and velocity at the same time. This helps us understand energy transport, mixing, and the overall movement of fluids.

In this context, a new method called Physics Informed Neural Networks (PINNs) is being used. PINNs blend physical laws with data from experiments to better predict pressure and velocity in gravity currents. This method helps overcome the challenges of gathering data, especially when measurements can be noisy or sparse.

#The Challenge of Measuring Gravity Currents

To accurately study gravity currents, we usually rely on several techniques like Particle Image Velocimetry (PIV), Planar Laser Induced Fluorescence (PLIF), and Light Attenuation Technique (LAT). These methods allow us to gather data about velocity and density in two dimensions. However, they can be very expensive and difficult to use together in real-world settings. Additionally, using these methods often means we have to deal with complex inverse calculations to find pressure from density measurements, making it hard to create a clear picture of the flow.

Previous research has looked into ways to extract pressure fields under certain assumptions. However, many of these methods fail when faced with complex flows or when the density differences are not simple to handle. Traditional approaches struggle with transient features, which means they cannot capture the flow's rapid changes effectively.

#The Promise of Deep Learning

Recent advancements in deep learning have opened doors for better analysis of fluid mechanics. Neural networks, in particular, can learn complex relationships in data, making them suitable for tackling these fluid dynamics problems. However, the unpredictable nature of flows often makes it hard for data-driven models to provide accurate results.

PINNs have emerged as a promising solution. By embedding physical laws into the learning process, they can solve mathematical equations related to fluid behavior along with making predictions based on observed data. This method works well with noisy data and helps in situations where data availability is limited.

#Key Objectives of the Research

The main goals of this research were twofold. First, we wanted to validate the velocity fields obtained through PINNs. To do this, we combined LAT and PIV measurements from the same experiments and trained a PINN model to infer velocity and pressure based on density measurements. We then compared these inferred values with the data we got from PIV for validation.

The second goal was to use this approach to calculate Energy Flux, which is crucial for understanding how energy moves through these non-linear flows.

#Experimental Setup

In the experiments, a tank was filled with freshwater, and a barrier separated it from a saltwater solution. When the barrier was removed, the different densities caused a gravity current to form at the bottom of the tank. The intensity of this current and the mixing action that happens is affected by the Reynolds number, which tells us about the flow's behavior.

To gather data accurately, we used a specific computational method called Nek5000, which allows for high-quality simulations of how the fluid flows. This process generates synthetic data that we can use to train our models.

#Investigating Noise Robustness

To see how robust our PINN model is against noisy data, we tested different levels of added noise to our simulated data. We found that even with significant noise, the PINN model could still accurately predict the necessary fields like density, velocity, and pressure. This suggests that PINNs are resilient and can handle real-world data that might not be as clean or perfect.

#Training with Experimental Data

The next step was to apply our PINN model to real experimental data obtained from the LAT measurements. We set up the experiment with precise cameras and light sources to collect data on both density and velocity.

By assuming the flow is mostly uniform in one direction, we simplified the problem to focus on the two-dimensional aspects of the flow. The model used LAT data to infer the necessary fields and match them with PIV measurements for validation, allowing us to assess how well the PINNs could predict real-world scenarios.

#Results from the Experimental Data

When we analyzed the results, we saw that the predicted density values matched closely with our measurements. However, the velocity predictions were particularly interesting. Even without prior information about the flow, the model managed to successfully predict the current's speed and direction with reasonable accuracy.

Nonetheless, we discovered some inaccuracies, particularly in certain areas. This led us to adjust our model to account for these discrepancies, which improved the results significantly.

#Exploring Energy Flux

One of the crucial aspects we looked at was energy flux, which helps us understand how energy transfers within the gravity current. By analyzing the inferred pressure fields, we could see areas where energy is being both transferred to and absorbed from surrounding fluids.

The results highlighted transitions in energy flow, indicating zones of high and low energy within the gravity current. This information is valuable for understanding the dynamics of how these currents mix and interact with the environment.

#Conclusion

This research showcases the effectiveness of Physics Informed Neural Networks in tackling challenges related to gravity currents in marine environments. By blending physical laws with experimental data, we can predict key characteristics of fluid behavior, even in noisy or incomplete data scenarios.

Our findings show that PINNs can not only work well with simulated data but also provide meaningful insights when applied to experimental results. While there are still challenges to address, particularly in capturing all the nuances of three-dimensional flows, the potential for this approach in ocean modeling is promising.

As we continue to refine these methods and apply them to real-world data, we can enhance our understanding of complex ocean dynamics, potentially leading to improved models for predicting how these flows behave in nature.