unit of sigma in nonadiabatic calculation

[anwesha]

Hi,
I am a bit confused with the units of the non-adiabatic exp(-i*sigma*t) term

mode period = 2*pi/sigma (from documentation) --> so here sigma is the angular frequency having unit (1/rad)
now the output omega by gyre is dimensionless.
sigma = omega*sqrt(GM/R^3) --> sqrt(GM/R^3) has unit of (1/s) --> so sigma here is the normal frequency having unit of (1/s)

what am I missing here in my understanding?

[rhtownsend]

Hi Anwesha --

Thanks for your questions!

mode period = 2*pi/sigma (from documentation) --> so here sigma is the angular frequency having unit (1/rad)

In fact, the unit of sigma is rad/second (since sigma = 2*pi/period). That's sometimes also written as 1/second, since radians are unitless.

now the output omega by gyre is dimensionless.
sigma = omega*sqrt(GM/R^3) --> sqrt(GM/R^3) has unit of (1/s) --> so sigma here is the normal frequency having unit of (1/s)

The 1/second you mention here is the same as the 1/second I give above.

Hope this answers your question!

cheers,

Rich

[anwesha]

Hi Rich,

thank you so much for the clarification. So, if I want the eigen frequencies in 'rad/s' to compare with lamb and Brunt Vaisala (both of which I have found in rad/s) that would simply mean I will be using sigma (without having any additional factor of 2pi)?

[rhtownsend]

Yes, that's right -- assuming the Brunt is also in rad/s.