I would like to know the theoretical justification of using convective vorticity vector or the moist vorticity vector. Some literature state that due to slant of the moist isotropics the vorticity need to be crossed with the gradient of moist potential temperature to describe deep convection. I would like to know is there theoretical justification of to cross the vorticity and gradient of potential temperature in order to explain deep convection in the atmosphere????
The idea of the "slantwise convection" rather corresponds to a competition between two restore forces: the one which tends to "conserve" the angular momentum and the other one which corresponds to "moist-adiabatic (and then moist-isentropic, and then equal potential temperature) processes". Thus, to my mind, it is more complicated than a "cross of vorticity and gradient of potential temperature". Am I right?
On the other hand, if you speak of natural (vertical convection), the problem of "slantwise convection" becomes useless, since the vertical acceleration due to the buoyancy force is the dominant one in that case. Am I right?
A power-point :
https://www.google.fr/url?sa=t&rct=j&q=&esrc=s&source=web&cd=14&ved=0ahUKEwjvtc2Do5fSAhWLzRoKHcFbChQ4ChAWCDMwAw&url=http%3A%2F%2Fwww.meteo.psu.edu%2F~pmm116%2Ftalks%2Fcsi_talk_nws_20dec05.ppt&usg=AFQjCNFVcHqEWvWkFvLUCLMXIu-T0a8qUg&sig2=6V2gROtUYGVwLAEq8ULvKg&bvm=bv.147448319,d.d2s
Dear Philbert,
It is better to use the generalized moist potential vorticity (GMPV) defined in the following paper (please consult the text around eq. 4)
http://ac.els-cdn.com/S1002007108003808/1-s2.0-S1002007108003808-main.pdf?_tid=6a6ed2d6-f51d-11e6-a0c9-00000aacb35f&acdnat=1487341917_33353c8aaf34e735b51099ebec549e21
As far as the discussion of the slantwise convection is concerned I agree with the comment of Pascal. The deck of slides illustrating the role of centrifugal instability is yet another example of the intricacies introduced to any mechanical system by rotation.
Sincerely, Janusz
Dear Pascal thank you for the good answer and the power point about CSI. For natural convection from bouyance force is there theoretical; justification that they can be explained by the cross of vorticity and gradient of temperature?
Dear Janusz, thank you for the publication. The question arose from the convective vorticity vector, why crossing vorticity and gradient of temperature. Is there theoretical justification that the vector resulting from the cross product of vorticity and gradient of temperature will explain the natural convection
Dear Philbert,
After some extensive search in the literature I believe that there are several reasons for using a cross product of vorticity with gradient of the moist potential temperature. One of the best discussions of this subject is in Ran et al. (2013), JGR Atmospheres vol. 118, pp 5710-5723 (available from Google after the search with keyword: Ran PV-based diagnostic quantities). Below I have extracted 4 main reasons for using CVV derived by Ran et al. (2013) (You can find the corresponding text after Eq (28)):
"Solenoidal Vorticity (SV) and Potential Solenoidal Vorticity (PSV) are both closely related to Convective Vorticity Vector (CVV) in both dry and moist atmosphere"
"the direction of $\nabla p$ is almost vertical, therefore SV represents the predominantly the vertical component of CVV"
"PSV represents predominantly the horizontal component of CVV."
"The vertical component of CVV has been shown by Gao et al. [2004a, 2007] to describe the evolution of tropical convection and to indicate areas of heavy rainfall".
The entire construction presented by Ran et al. (2013) starts as usually, in such a studies, from the vorticity equation; it is well presented and very easy to follow.
Please note that we do not need to refer to the slantwise convection in order to justify the use of CVV as the essential diagnostic tool for convection.
I hope that the above reference will help you in resolving your problem.
Sincerely, Janusz
PS Please let me know if you have problems downloading this paper; I believe that the text in the open domain but it was not easy to get the file.
Dear Janusz thank you very much for this paper. Just read the preamble and grasped that before PV [dot] the vorticity and the temperature gradient are in vector form, to describe better atmospheric flow, after the dot results into scalar quantity which can describe large atmospheric flow where the isentropic surface are horizontal and gradient of temperature in the horizontal
In mesoscale the scalar quantity can not explain the evolution of vorticity therefore need for the cross of vorticity and temperature gradient to form another vector that describe the vorticity vector and temperature vector, am I right??.
Thank you very. Please send me the PDF file of this paper.
Dear Janusz thank you very much. It is a bit clear to be now. It is good to learn different orientations of the isentropic surfaces in large and mesoscale convective system. I did small experiment, the verical component of potential vorticity in the tropics (Tanzania) (f+zeta)dT/dP was small compared to the horizontal components. This explained due to the isentropic are mainly vertical and the only vorticity that can be explained is the horizontal and the vertical part is ignored [should noted that verical is not completely zero but small]. The CVV find a vector that will be perpendicular to the horizontal vector in PV therefore resolve the ignored vorticity.
Thank you please send me the pdf file of this paper
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