Center for Integrative Planetary Studies Seminar

Fall 2024
By Aathreya Kadambi
Expanding on Lectures by Professor Philip Marcus and Others

This fall I’m thinking of joining this CIPS seminar. I think the wonderful thing about seminars is that they illustrate how dependent human hearing and perception is on you actually knowing context and background well.

3D Models and Solutions to the Equations of Motion of Julipter’s Great Red Spot

Why is the GRS of interest?

Vortices widely exist in systems of geophysical fluid dynamics. The GRS is the oldest and largest known vortex.

Voyager fly-bys imaged cloud motions of this thing and these were turned into velocity vectors. It also found a cool temperature anomaly at the top of the GRS. At berkeley Advected Corrected Image Velocimetry was used to make much denser velocity maps.

Something about getting unstratified and the nstratified when going from bottom to top or something.

We are not going to take into account any dynamical effects. Zonal flows are amazingly steady in time. Measuring them now is very similar to measuring them in like the 1970s. In the James Web Telescope, they didn’t see much variation in the zonal flows between the top and bottom of the red spot.

Some graphs with Pressure on the $y$ axis and other things on the $x$ axis, for example temperature. Something about the Brunt-Vaisala frequency 👀. Something oscillates vertically, and when that frequency goes to zero, we get something else. So apparently this frequency square, $N^2$, determines the convective zone or something like that, although I low key don’t really know what that is or what is oscillating vertically or anything tbh.

Between 700 millibar apparently there is no reliable data. The hubble telescope monitors moving clouds, and that’s what we want to do. To find out the cloud height requires cloud modeling and radiative transfer. AYY stuff that I like. But then he said some stuff that I don’t completely get. I don’t really know what “Cloud Decks” are though.

Now we’re going to talk about the good, the bad, and the ugly about 2D, Quasi-Geostrophic, an 3D Boussinesq Numerical Simluations. hehehe.

Quasigeostrophic approximation comes in two flavors, assumes there is a bound between horizontal pressure gradients, and accelerations due to the corillosi effects. If you combine with vertical hydrostatic equillibrium, you get Thermal Wind Equation. That relates some stuff oof he changed the slide…

The Good: 2D Moore-Saffman Relation. A good homework problem for first year graduate fluid dynamics students. Only important parameters of the flow are $\sigma$, the shear of Zonal Flow, and $\omega$, the vorticity of vortex. Aspect ratio $\frac{L_x}{L_y} \approx 1 + \frac{\sigma}{\omega}$. It turns out when you do 3D numerical calculations, you get something that I didn’t totally hear gg. There was some picture of a cylinder shaped thing.

The Bad: Stability. Rayleigh theorem wrt angular momentum is not valid in 2D. Not stable if radii is something.

I had to respond to someone for a second and missed something oof.

What makes 3D numerical simulations possible: big time steps, some other things. We use spectral analysis. High spatial resolution spectral code $384^3$ spectral collation points or something. Equivalent to $4000^3$ finite-difference points, equivalent to less 100km in latitude and longitude and 0.15 km in vertical. Previous studies use EPIC.

Create 2D equilibria that solve the Euler equation, equation of state, continuity equation, dissipationless energy equation (with no vertical velocity). Stack the 2D solutions on top of each otehr to get a 3D flow. This 3D approximation of a vortex solves all the equations of motion except the neergy equation. Solutions t the initial value code are not unique. There can be many, steady stable vortices with different heights of their midplanes, different horizontal areas, strengths and vertical thicknesses Stacking layering across the rotational axis are stable, but the other way are not stable. Another factor that goes into stacking is constant area vortex (CA) versus constant velocity vortex (CV).

Which model is close to equilibrium?

Something about 3D hollow vortices and making things hollow. Global circulation models had a big dilemma because older chips couldnt resolve the physics that was going on. Then everyone’s tsuff started to match up.

The goal after getting some hollow vorticees things was to get vortices at some cloud deck level that can reproduce the hollow vorticity field in some of the pitures or something. So apparently there are types of cloud decks, like HST and JWST cloud decks.

All small vortices in on jupyter are surrounded by bright rings in this picture but no the red spot.

Some vortices are stable and hollow, but others are stable and non-hollow. What we find is that our hollow vortex, when we change a parameter, will become non-hollow, and when we change it even more it will become un-hollow. Apparently that migh be important and stuff.

New Temperature Observations show that the cold lid is much lower in the atmosphere than we had assumed. Something about moving vortices closer to the convective zone. There are some parts, dynamical top, cold lid, midplane, hot floor, and dynmaical bottom. we measure pressure differences and stuff and temperature differences and see what happens.

Apparently, stability requires $D_{\text{top}} > |(g/T)(\Delta T)_{\text{top}} / N^2_{\text{top}}|$ at the top and exactly the same at the bottom but with $\text{bot}$ instead of $\text{top}$. So like as $N$ goes to zero, we get closer and closer to unstableness.

Very little wiggle room in GRS parameters so that it is almost unique.

Heavy Ion Outflow in the Earth-Moon System

She wanted to bring this to the Earth Geospace system because the moon has been excluded from the geospace system for a long time.

The moon is sometimes in the Earth’s magnetosphere and other times it is not. Earth and moon system is the reason that Earth has a very stable atmosphere right now and it might be connected to its habitability.

Source of the Plasma: Solar Wind (hydrogen, helium, oxygen and other ions), and Atmosphere/Ionosphere (hydrogen, helium, nitrogen, oxygen, NO and other ions).

Christon et al 2017, they find lots of different ions in the Earth’s atmosphere.

The thing is, this doesn’t account for the contribution of the Moon’s plasma to the magnetosphere.

Ionospheric outflow. To maintain the atmospheric consistency, they have some flux flow or something. Theres also something called trapped cold ions and polar wind outflow.

Modeling atmospheric escale: PWOM. Polar Wind Outflow Model, developed to solve the ison escape along the open magnetic field lines.

Lunar soil contributions are actually relevant. Lunar soil has lots of minerals which might be contributing during impacts from meteriorites and stuff.

Summary:

• Contributions of ionispheric outflow and lunar pickup ions to Earth’s magnetosphere are compared
• Heavy ions are sourced from Earth’s atmosphere
• More consistent source of ions, doesn’t depend on solar cycles

Funny remark: someone asked a difficult question, and she said “this is a good question because I was trying to skip that point”. I thought that was funny and cool/interesting lol.

Magnetotail Electrons

Mentioned Electron Precipitation Ionosphere

Solar wind electrons in the magnetotail, showed a “parabola plot”

Uncover mechanisms in the martian tail are the works in her PhD.

Perform a large statistical study, spent a long time making a database of 10 years of electron energization in the Martian magnetotail. You are more likely to observe energized electrons in the Southern hemisphere.

Building more robust models of the Martian nightside ionosphere by M. Marquette

• Mars has no intrinsic dipole field
• Mars has locally strong, inhomogeous crustal magnetic fields (or smth)
• electron impact ionization is the main source of ionization or something

“We now model 137 different electron impact processes”

Topology types of magnetic fields. Categories like day closed, night closed, open to night, draped, cross terminator closed, night closed-void, and open to day.

night closed field lines are most common on the night side.

behavior of the electrons really depends on magnetic fields or something.

open to day topology on the night side apparently? Actually I don’t completely get the relationship to these topologies and the sides, or why they are called what they are called.

Looking for Water on Present Day Mars

• Valley networks
  • Evidence of sustsained flow: fans, meander bends, scroll bars
• Outflow channels

A question I have is, despite seeing these geographic features, how do we know that it was water flowing, rather than some other fluid? I guess we’ve found water on Mars.

• I don’t understand the exact deduction, but he mentioned hydrothermal systems and stuff like that
• Minerology

basically evidence for a “cryosphere”

Something about permeability and some other quantities relating to aquifers.

Howdoespermeabiliy vary with depth?

Wait he’s talking about induced seismicity, but why are we making earthquakes intentionally?

Repeated marsquakes in Marsian upper mantle

We can actually image the underground parts of mars by using seismic waves. How do we use this to look for water? $v_o =\sqrt{\frac{\text{Bulk Modulus} + \frac{4}{3}\text{Shear Modulus}}{\text{Bulk Density}}}$ and another for the $s$ waves speed $v_s$.

Apparently the Rock Physics Handbook with three authors my eyes fail to read is a good book.

What controls seismic velocities in sediments? Lot’s of things to be honest, he had a whole list.

Markov Chain Monte Carlo inversion approach was used to explore some parameters, pore shape aspect ratio, porosity, water saturation, mineral bulk modulus, mineral shear modulus, and one more.

Conclusions:

• No ice-saturated cryosphere in upper 300 m up to 40% of fractures filled with ice
• No ice-saturated cryosphere in upper crust;up to 10% of pores filled with ice
• Liquid water more likely than not in mid-curst crust; if correct, more water than hypothesized oceans

some evidence of not seeing a cryosphere with watre underneath it or something.