The GYRE Forums

Dear Rich

Does GYRE 5.0 still have the option to return the "normalized rotation kernel" (parameter "K") in the output mode files?
GYRE 4.4 had this option, but version 5.0 doesn't seem to have this parameter. Did you maybe remove this feature on purpose?

Best regards
Mathias

Mathias wrote:Dear Rich

Does GYRE 5.0 still have the option to return the "normalized rotation kernel" (parameter "K") in the output mode files?
GYRE 4.4 had this option, but version 5.0 doesn't seem to have this parameter. Did you maybe remove this feature on purpose?

Best regards
Mathias

GYRE 5.0 returns either the Ledoux coefficient (C) or its gradient (dC_dx). The gradient is equivalent to the unnormalized rotation kernel.

My recollection is that K can be reproduced by some combination of these -- but you may have to do some digging. I haven't touched this code for a while.

cheers,

Rich

I've been looking into this today; to recover a normalized rotation kernel K from dC_dx, you can divide dC_dx by (C * Rstar) where C is the integral of dC_dx from x=0 to x=1.

edit: I posted a confusing paragraph here earlier; suffice it to say that evidently C / (4*pi) gives beta_nl. Should that normalization be put in and these variables be renamed dbeta_dx and beta?


chris

mankovich wrote:I've been looking into this today; to recover a normalized rotation kernel K from dC_dx, you can divide dC_dx by (C * Rstar) where C is the integral of dC_dx from x=0 to x=1.

edit: I posted a confusing paragraph here earlier; suffice it to say that evidently C / (4*pi) gives beta_nl. Should that normalization be put in and these variables be renamed dbeta_dx and beta?


chris

Thanks for sharing your thoughts, Chris. From my math, the definition of dC_dx in gyre_mode.fpp means that

K_nl = dC/dx / C

...where C is the integral of dC_dx over 0 < x < 1. Likewise,

beta_nl = C

(but there's no factor of 4*pi, can you point out where that creeps in?).

I probably shouldn't have used C as my symbol, since the Ledoux splitting coefficient is

C_nl = 1 - beta_nl = 1 - C

(cf. Aerts 2010, 3.361). In fact, your suggestion of dbeta_dx is much better -- I'll make the change once we agree on the 4pi.

cheers,

Rich

rhtownsend wrote:

mankovich wrote:I've been looking into this today; to recover a normalized rotation kernel K from dC_dx, you can divide dC_dx by (C * Rstar) where C is the integral of dC_dx from x=0 to x=1.

edit: I posted a confusing paragraph here earlier; suffice it to say that evidently C / (4*pi) gives beta_nl. Should that normalization be put in and these variables be renamed dbeta_dx and beta?


chris

Thanks for sharing your thoughts, Chris. From my math, the definition of dC_dx in gyre_mode.fpp means that

K_nl = dC/dx / C

...where C is the integral of dC_dx over 0 < x < 1. Likewise,

beta_nl = C

(but there's no factor of 4*pi, can you point out where that creeps in?).

I probably shouldn't have used C as my symbol, since the Ledoux splitting coefficient is

C_nl = 1 - beta_nl = 1 - C

(cf. Aerts 2010, 3.361). In fact, your suggestion of dbeta_dx is much better -- I'll make the change once we agree on the 4pi.

cheers,

Rich

OK, the 4pi comes in because of the way Aerts et al define the inertia in terms of \tilde{xi} = xi/sqrt(4pi), not xi. My expressions are correct... BUT I've decided to follow the Aerts convention, so I'll be making changes accordingly.

cheers,

Rich