Thermodynamic Speed Limit

[Caleb Routt]

This is a pretty advanced topic but can anyone explain to me what the "Thermodynamic Speed Limit" is in tornadoes?

 

[Stan Rose]

You'll have to be more specific because it's unclear what you're asking. The 'thermodynamic speed limit' is a hypothetical limit for the speed of the tornado based on an assumed vortex and the pressure difference in the vortex--obviously the greater the pressure difference the higher the winds will be. In turn, if you know the CAPE, or the potential energy available to the storm, you can use this to determine the strength of the updraft and therefore that pressure difference. Problem is, the basic idea assumes things like hydrostatic balance or cyclostrophic flow are present, and that may not be the case. So in reality, the tornado might have a higher wind speed than what the basic idea presumes.

 

[Caleb Routt]

Okay that makes sense.. However what is Hydrostatic balance? I know what cyclostrophic balance is.

 

[Jeshua Everett]

Think of a volume of air and the forces acting on it. The weight of the volume of air is a downward force, the pressure from the air above the volume is a downward force, and the pressure of air below the volume is an upward force. When these forces keep the volume at rest (static) it is said to be in hydrostatic balance or equilibrium. Pretty much it's the pressure gradient balancing the gravitational force. Hopefully I explained well enough, I am still just learning from every text book I can get my hands on.

Okay that makes sense.. However what is Hydrostatic balance? I know what cyclostrophic balance is.

 

[Ashwin D]

Inside the tornado - is the hydrostatic balance valid at that microscale ?

http://paoc.mit.edu/12307/mass wind/hydrostatic notes/hydrostatic.pdf

"
It can become suspect, however, in very vigorous small-scale systems in both the
atmosphere and ocean (
e.g.
, tornados, violent thunderstorms and deep, polar convection in
the ocean)"

and this study does a exhaustive analysis on hydrostatic balance validity and tornadoes - https://opensky.ucar.edu/islandora/object/manuscripts:870/datastream/PDF/view


Generally mesoscale systems show a tendency to depart from hydrostatic balance owing to the strong lift.

 

[Jeff Duda]

Inside the tornado - is the hydrostatic balance valid at that microscale ?

http://paoc.mit.edu/12307/mass wind/hydrostatic notes/hydrostatic.pdf

"
It can become suspect, however, in very vigorous small-scale systems in both the
atmosphere and ocean (
e.g.
, tornados, violent thunderstorms and deep, polar convection in
the ocean)"

and this study does a exhaustive analysis on hydrostatic balance validity and tornadoes - https://opensky.ucar.edu/islandora/object/manuscripts:870/datastream/PDF/view


Generally mesoscale systems show a tendency to depart from hydrostatic balance owing to the strong lift.

Hydrostatic balance is strictly a balance between gravity and the vertical pressure gradient force (i.e., involving no other forces but those two). Whenever buoyancy is added to the situation, hydrostatic balance goes away. So that includes any and all deep, moist convection and yes, tornadoes and hurricanes, too. In general, hydrostatic balance applies to large scale and quiescent conditions and generally does not apply on the mesoscales or below.

In addition, the anelastic (and frictionless) approximation to the equations of motion can break down inside a tornado since speeds can occasionially approach the order of magnitude of the speed of sound (e.g., O(100 m/s)).

 

[Royce Sheibal]

It would be really interesting to see how the formulas for drag related to terminal velocity and power to overcome drag could be applied to tornadic scenarios. With drag being a v^2 and power being a v^3 -based equations, it would seem that there would be rapid diminishing returns at high velocities. I wonder what the Reynolds numbers range from in a tornado depending on temperature/dust/moisture/debris? And as Jeff mentions aerodynamics goes all to hell around 100 m/s (222mph) because of compressible flow, which throws all sorts of other curve balls into tornado dynamics. Stupid physics.

https://brian-f-farrell.fas.harvard.edu/files/brian_f_farrell/files/structure.pdf

Edit: Article talking about Reynolds numbers and vortexes - Good Read.