LYRICS EXPLANATIONS

VERSE 1

I am coming here… with high-Reynolds-number stamina

…I can beat these rap folks whose flows are… laminar

[I can beat rap folks who have simple laminar flows, which are easily studied,

I am coming here with the stamina for very complex turbulent flows.]

In the video the water flow is laminar – as evidenced by the clear stream you see. This is because the water particles flow in distinct "layers" which do not mix. More on laminar/turbulent flows here: ·

• Un-Mixing a Laminar Flow:

https://fyfluiddynamics.com/2015/10/this-video-demonstrates-one-of-my-favorite/ ·

• An Introduction to Turbulence from 3blue1brown:​

https://fyfluiddynamics.com/2018/11/with-some-help-from-physics-girl-and-her-friends/ ·

• The Reynolds number, illustrated:

https://fyfluiddynamics.com/2013/09/the-dimensionless-reynolds-number-is-a-key-concept/ 

I like fluid mechanics, so go ahead call me a nerd,

But my flow's got power… proportional to its velocity to the third

[Call me a nerd, but I have powerful flows. In fact, since the power of the flow is proportional to velocity cubed, when I double my flow speed, my flow power increases by a factor of 8.]

And I can spit rhymes so fast you can't even understand me mate,

Because at these speeds, as spit spins it also starts to cavitate

[And my flows have a lot of power because their speed is high. So high, that due to the high velocity, there are areas in the flow in which the pressure drops to a point that liquid water turns to vapor. In other words, it cavitates. You would typically see cavitation occur first in the core of vortices where the fluid (e.g., water) spins at high speeds. For example, the bubbles shown behind propellers in movies depict cavitation. The same thing happens in your blender! Cavitation is also associated with noise - just like other rappers I "spit" rhymes, but my ones may be difficult to understand because of the noise associated with cavitation.]

Cavitation is shown in this music video. More on cavitation here:

• Watch cavitation destroy a bottle in slow motion:

https://fyfluiddynamics.com/2014/04/this-high-speed-video-shows-the-cavitation-that/

• Cavitation collapse and how bubbles break surfaces:

https://fyfluiddynamics.com/2019/08/cavitation-collapse/ 

But I can rap faster, cuz I am doctor of flow… apart from being a master

And I can accelerate my flow to the point that you definitely know that my speech reached a supersonic speed, so here you go

[I have an MS degree and a PhD degree, both of which are earned by researching flows, hence I am Doctor and a Master of flow. And I can increase the speed of my flow to the point that it is faster than the speed of sound, or supersonic, and you know that because of the sonic boom.]

These compressible flows, they ain't no joke

Because as the high pressures get higher, you should be less likely to choke

[Compressible flows (e.g., supersonic flows) are flows in which the density of the fluid (e.g., air) varies significantly as the particles move. These flows are no joke – the changing density makes them more difficult to study. In order to achieve supersonic flow in a channel (e.g., within a fighter jet engine) the flow needs to be pushed at high pressure. If the pressure is not sufficient, the flow may abruptly become subsonic (choking). The higher the pressure that pushes the flow is, the less likely the flow will choke – in contrast, rappers are more likely to "choke" (be unable to perform) when the pressure on them is higher.]

More on compressible and supersonic flows here:

• Shock waves form in supersonic flows, as pictured here:

​https://fyfluiddynamics.com/2019/03/this-week-nasa-released-the-first-ever-image-of/

• See how supersonic flow forms in a rocket nozzle:

https://fyfluiddynamics.com/2013/11/when-supersonic-flow-is-achieved-through-a-wind/ 

​

That's why I bring the turbulence to haters like a vortex generator

So don't blame me if your game is lame, just make your Reynolds number greater

[Vortex generator are objects put in the flow to create more turbulence, essentially increasing the Reynolds number - with this song I am bringing turbulence to everyone, including the people who may not necessarily like flows.]

What’s a vortex generator? They’re those little fins on airplane wings:

https://fyfluiddynamics.com/2012/10/ever-look-out-an-airplanes-window-and-wondered/

CHORUS

Fast cars - it's all, it's all about flow

Private jets, drones - it's all about flow

Beaches, waves, yachts - it's all about flow

Beer, wine, liquor - it's all about flow

Submarines, ships - it's all about flow

Wind turbines - it's all, it's all about flow

The air you breathe - it's all, it's all about flow

Even this rap thing - it's all about flow

​

[Flows are extremely important in all these and many other areas - automotive,  aeronautical, and naval industries, environmental flows (e.g., ocean flows), drinks, power generation, biological flows (e.g., blood flow).

Rapping includes flows too but in another sense.]

You can find more about flows related to these and other topics here:

• Testing a supersonic car:

https://fyfluiddynamics.com/2015/02/how-do-you-test-a-supersonic-car-like-the/

• Quadcopter aerodynamics:

https://fyfluiddynamics.com/2017/05/schlieren-photography-is-a-classic-method-of-flow/

• How waves travel:

https://fyfluiddynamics.com/2019/08/how-waves-travel/

• Tears of wine:

https://fyfluiddynamics.com/2016/02/give-your-wine-glass-a-swirl-and-afterward-you-may/  

• Champagne physics:

https://fyfluiddynamics.com/2013/12/champagne-owes-much-of-its-allure-to-its-tiny/

• Measuring wind turbines with snowfall:

https://fyfluiddynamics.com/2014/01/one-of-the-challenges-in-large-scale-wind-energy/

• The mysterious acoustics of Carnegie Hall:

https://fyfluiddynamics.com/2018/08/for-nearly-a-century-the-acoustics-of-carnegie/

• Inside singing:

https://fyfluiddynamics.com/2017/03/these-are-the-vocal-folds-of-a-woman-singing/

​

VERSE 2

When it comes to CFD, it often makes me feel like home

I am fluent with Fluent, and I do a lot with OpenFOAM

[One way to study and predict flows is by using computer simulations - Computational Fluid Dynamics. I have been using two of the most popular programs used for that - Fluent and OpenFOAM.]

More on CFD here: 

https://fyfluiddynamics.com/tagged/computational-fluid-dynamics/

When you talk about my area, it has a well-defined border

And my scheme, it's not all about the MUSCL, but I often use a second order

[In simulations one needs to clearly identify the area of the flow that has to be simulated. There are different ways to convert the equations that govern flows to equation that can be solved by a computer. These ways (schemes) have different accuracy (shown by their order - higher is better) depending on how closely they depict the actual equations. MUSCL is the name of one scheme, but there are many others that can be used. Unlike some other rappers, my “scheming” is not all about the muscle.]

I rap pretty fast, so sometimes I just have to be explicit

And here is a part of my philosophy - you don't want to miss it

[When simulating flows that change with time, we picture the flow at different moments of time separated by small intervals of time, or time steps. When working with faster flows, these time steps have to be smaller. While large time steps can be taken with so-called implicit schemes, that will result in poor accuracy, so sometimes I have to use explicit schemes which require much smaller time steps (better resolution in time) to make my flow more accurate and detailed.]

I have big ambitions, I am only limited by boundary conditions

When life gets too complex, I just do a Proper Orthogonal Decomposition

[When solving problem related to flow we need to know what some parameters, like incoming flow speed and pressure, are and where we have solid boundaries - these are called boundary conditions and dictate (to a certain degree) what happens with the flow. In a similar way, I am only limited by my surroundings and circumstances - whether they are favorable or not, I still have big ambitions that I strive for. When life gets too complex, I try to analyze and simplify the complexity by focusing on the most significant issues - similarly to Proper Orthogonal Decomposition (POD) which represents a complex flow by a few main components (modes), which capture the majority of the flow physics.]

I am direct like DNS, and resolve the big stuff like a large eddy simulation

And just like with RANS, sometimes I take a chance, and if doesn't work out, I have patience

[Simulating flows usually requires simplifying the equations so that computers can solve them within a reasonable amount of time (usually days or weeks). Direct Numerical Simulations (DNS) use the exact equations but DNS can only be used for simple, small-scale flow geometries; Large Eddy Simulations (LES) use the exact equations on larger scales and modeled equations on smaller scales,

where the model can do a better job compared to the larger scales. Weather models, for example, are largely based on LES. RANS (Reynolds Averaged Navier Stokes) equations are often used for modeling flow, but in some cases they are not very stable, meaning that a solution may not be reached, and hence requiring more of a "trial and error" approach. I am direct and say things just the way they are like DNS, focus on the big issues like in LES, and sometimes take a chance, like I do when simulating using RANS, but if things don't work out for me, I am patient and keep trying.]

More on DNS, LES, RANS, here: 

• Simulating Turbulence with DNS:

https://fyfluiddynamics.com/2011/08/turbulent-flows-are-complicated-to-simulate/ 

• Simulating Urban Environments with LES:

https://fyfluiddynamics.com/2014/09/anyone-who-has-spent-much-time-in-an-urban/

• Cars and cyclists, seen through RANS:

https://fyfluiddynamics.com/2015/07/this-years-tour-de-france-opened-with-an/

Bottom line is: When it comes to flows, I have complete domination

Because I got my back covered… by partial differential equations

[The equations that govern flows are partial differential equations, so I dominate flows, because I use those equations - and I literally got my back covered by them.]

CHORUS

​

VERSE 3

The players try to impress the ladies but they don't care,

Because they stare at me when I start talking about boundary layers

[When there is a flow over a solid surface, the flow near the surface is slower. In fact, the layer of fluid closest to the surface does not move (significantly). This area of slower flow is called a boundary layer and is of particular importance due to its influence on drag.]

One of the locations where the video was shot is the University of New Hampshire Flow Physics Facility which is the largest facility in the world for studying boundary layers - because of its size (8 ft by 20 ft by 250 feet) the boundary layers are very large and can be more easily studied. The tunnel can be used for many other studies as well - e.g., wind turbine arrays and flow around full-size cyclists.

• More on the FPF here:

https://www.unh.edu/unhtoday/news/release/2010/11/15/slow-flow-new-wind-tunnel-largest-its-type

• See a turbulent boundary layer in action:

https://fyfluiddynamics.com/2013/05/in-experiments-it-can-be-difficult-to-track/ 

And I am talking about millions for Reynolds number because we got big fans

I don't give a 50 cent about those rappers whose Reynolds number is... 10

[We can achieve very large Reynolds numbers - values in the order of millions, because we have big fans in the FPF. In comparison, other rappers have simple flows comparable to a Reynolds number of 10 which would imply laminar flow. I am making a reference to the rapper 50 cent but I am not implying that his flows are simple.]

The fans of the FPF are two 400-horsepower fans, each moving 250,000 cubic feet of air per minute, seen in the video.

They perform rap, well, I perform rap and PIV,

And occasionally - I do some Laser Doppler Velocimetry

[In addition to rap I do Particle Image Velocimetry (PIV), this is a popular experimental technique in which a laser illuminates the area of the flow of interest. Particles in the flow reflect the light and images of these particles are taken. Taking many images allows us to figure out how each particle moves, what the speed of the flow is in each location, as well as more information about the flow. Occasionally I use another technique - Laser Doppler Velocimetry in which two laser beams cross each other and as a result, form a pattern of bright and dark areas. As particles flow through that pattern they reflect light when passing through the bright areas. We can detect that and determine the speed of the particles.]

A PIV system (covered by laser protection curtains} and an LDV system are shown in the video. Notice the protective goggles which are required for safety.

• Laser goggles for parrotlets:

https://fyfluiddynamics.com/2016/12/many-experimental-techniques-in-fluid-dynamics-use/ 

I am hot like a hotwire, you got something to say?

Talk to my homie Johny, who worked with 100 models… in his wind turbine arrays

[Hot wires are also used to study flows experimentally – A thin wire is kept hot, and as air passes by, the wire cools. To maintain the wire’s temperature in faster flows, more energy must be put in to the wire. This is used to determine the flow speed. I am hot like a hotwite, and I work with models… and if anyone knows about working with models, that's my friend John Turner V who worked with 100 models studying wind turbine arrays and how the turbines downstream are affected by the turbines upstream.]

John is shown in the video in the FPF with some of the model turbines set up on the floor.

• A look at hotwires:

https://fyfluiddynamics.com/2011/03/hotwire-anemometry-is-used-in-experimental-fluid/ 

This is not a mainstream rap, that would be somewhat simpler and fake

Because the real complexity of the flow is not in the free stream… it's in the wake

[The flow behind an object (the wake area) is much more complex and is very important in understanding the flow around the object - in this rap I am bringing up the important issue of flows, which we encounter constantly in our daily lives. That is more relevant, and more complex, compared to other topics, just like the wake flows are more complex but also more important for understanding the flow around the object.]

• Delta wing wake, visualized:

https://fyfluiddynamics.com/2019/11/trails-from-a-delta-wing/

• Complex flow behind a cylinder:

https://fyfluiddynamics.com/2013/11/flow-over-blunt-bodies-produces-a-series-of/

• Wakes behind fish:

https://fyfluiddynamics.com/2012/02/which-matters-more-form-or-function-this/

And my flows are so fast and complex, you probably lost me

But you can find me at the University of New Hampshire representing Bill George and Team Wosnik

[While this rap may be too difficult to understand at first, you can easily learn more and ask me more. Currently I am at the University of New Hampshire, where I teach. I received my PhD from there as well under the supervision of Prof. Martin Wosnik (shown in the video). Prof. Bill George, a leading and widely-recognized expert in the field of turbulence, was his advisor and was my professor during my Master's degree studies at Chalmers University of Technology, Sweden – Prof. Bill George has been instrumental for my success and was the one who connected me with Prof. Wosnik.]