Analyzing Ocean Currents on Icy Moons, Europa and Enceladus

Abstract

This study investigates the rotational dynamics of ocean currents on Jupiter’s and Saturn’s icy moons, Europa and Enceladus. The research aims to quantify the relationships between ocean depth, rotational forces, and the transit times of nano-sized silica particles. Numerical simulations were conducted to model the subsurface ocean dynamics of these moons. Python libraries, including Matplotlib for visualization and NetCDF for data management, were employed to process and analyze time-series data, enabling the examination of particle transit times in relation to varying ocean depths and rotational forces. The results demonstrate that the Rossby number governs particle transit times, adhering to distinct power laws: Ro*^(−3/2) for small Rossby numbers and Ro*^(−2/3) for large ones. Within the tangent cylinder (a region aligned with the moon’s rotational axis), a structured east-west zonal flows facilitated efficient particle transport. In contrast, areas outside this region exhibited less efficient, chaotic flow patterns. These findings provide insights into how rotational fluid mechanics influence material distribution in icy moon oceans, contributing to the understanding of their potential habitability.

Research Period
January 2022 – August 2022

Research Guidance
Guidance under Professor John Marshall, Massachusetts Institute of Technology (MIT)

Hypothesis
The central hypothesis was that the rotation of icy moons and their ocean depths significantly affect ocean currents, which in turn influence the transit times of nano-sized silica particles. We specifically hypothesized that particles within the “tangent cylinder”—a region influenced by the planet’s rotation around its rocky core—would exhibit different movement characteristics compared to those outside this cylinder due to the rotational fluid dynamics.

Motivation
My fascination with fluid dynamics and its role in planetary environments drives my research into the subsurface oceans of icy moons like Europa and Enceladus. By exploring how rotational forces influence ocean currents on these moons, I aim to uncover insights into their potential habitability and the broader processes that shape planetary systems.

Research Breakdown
The research problem was deconstructed into several manageable tasks:

  1. Initial Graphing:
    I began by creating graphs of the zz-coordinate of particles over time to visualize their vertical motion.
  2. Particle Motion Visualization:
    To better understand the motion of particles, I made a movie showing the yy- and zz-positions of a particle over time.
  3. Transit Time Distribution:
    I generated a probability density plot of transit times (in rotation periods of icy moons) for all particles. This revealed that transit times follow a Gaussian distribution.
  4. Impact of Meridional Displacement:
    I created additional probability density plots of transit times for particles released from various meridional displacements (latitudes). This analysis showed two distinct scenarios:
    • Particles released more than ~100 km from the equator had transit times peaking at ~1000 rotation periods with a long tail.
    • Particles released near the equator had transit times peaking at ~250 rotation periods with a smaller tail.
  5. Analysis of Simulation Data:
    I analyzed data from 12 simulations run by a Ph.D. student I collaborated with. These simulations varied ocean parameters, such as depth and Rossby number. Using the data, I created probability density plots for each simulation and found the following:
    • For small Rossby numbers (Ro* ≪ 1), the normalized transit time of particles follows a power law: Ro*^(-3/2).
    • For large Rossby numbers (Ro* ≫ 1), the transit time follows a different power law: Ro*^(-2/3).

This systematic approach allowed me to identify the underlying physical mechanisms driving particle transit times in icy moon oceans.

Quantifiable Outcomes
1. Rossby Number and Transit Time: I established that the Rossby number, which is a function of ocean depth and moon rotation rate, plays a crucial role in particle movement. My findings verified that:
– For small Rossby numbers (Ro* << 1), the normalized transit time of particles follows a power law, specifically Ro*^(-3/2).
– For large Rossby numbers (Ro* >> 1), the transit time follows a different power law, Ro*^(-2/3). (See the accompanying graph for detailed results.)
2. Dynamics Within the Tangent Cylinder: Particles inside the tangent cylinder exhibited distinct transit times and displacement patterns compared to those outside, due to more vigorous current systems. This suggests that rotational dynamics within the tangent cylinder significantly influence particle distribution and deposition.

Skills Acquired

1. Data Analysis: Developed skills in handling large datasets, particularly time-series data essential for tracking particle movement. This skill was critical for interpreting complex graphs and charts. 
2. Parameter Relationships: Learned to derive and interpret relationships between non-dimensional parameters like the Rossby number, enhancing my understanding of fluid dynamics and planetary science.
3. Visualization and Interpretation: Developed expertise in visualizing complex data through graphs, charts, and animations, enhancing my ability to communicate research findings effectively.

Key Learnings

1. Rotational Fluid Mechanics: Acquired a deep understanding of how rotational forces influence fluid motion, crucial for modeling planetary phenomena and understanding the Coriolis effect. 
2. Data Analysis from Numerical Simulations: Developed skills in analyzing simulation data, identifying patterns, and validating theoretical predictions about particle behavior in varying conditions. 
3. Numerical Modeling and Simulation: Acquired introductory exposure to numerical modeling, including basic concepts of grid-based methods and discretization of fluid motion equations.
4. Application of Theory: Applied theoretical knowledge from planetary science and fluid mechanics to practical problems, reinforcing the real-world applicability of these theories in planetary exploration and the search for extraterrestrial life.

Graphs and Visualization

y-position vs. z-position for a particle

Probability density of the transit times for simulation 1 below. The colors show different y-values the particles are released from. The grey represents particles released from y=-350 km, and the brown represents particles released from y=350 km. Every color represents an increment of 50 km.




Graphed Rossby number vs transit time for each experiment in the table.


Transit times taken for each simulation. Particles are released from y = -350 km.