RE: questions
Kerstein, Alan
The general answer to these questions is that the ODT velocity components do not advect fluid. Formally, they evolve as passive scalars. Their effect on advection is indirect, through their appearance in the eddy rate expression. Nevertheless, they evolve in a manner that causes them to behave analogously to physical velocity components, so they are interpreted as such in data reduction.
This explains the absence of the terms you mention in questions (1) and (3). It would have been reasonable and perhaps preferable to include the buoyancy term in the w equation (question 2), but in the present context the effect is minor.
In this formulation, the mechanisms of advection, here meaning vertical displacement of fluid parcels, are triplet maps and subsidence, where the latter is nonconservative - it removes fluid throughout the domain and replaces it with mass in a different thermodynamic state at the top boundary. Thus the evolution is nonconservative only in that it is not a closed system - it has inflow/outflow. Otherwise, the applicable conservation laws are obeyed.
Alan
-----Original Message-----
From: Sorbjan, Zbigniew [mailto:zbigniew...@marquette.edu]
Sent: Thursday, April 02, 2009 8:27 AM
To: Kerstein, Alan
Subject: RE: questions
Hi Alan,
Referring to your B-LM paper (2006), I have a few questions:
(1) formally, the convective terms d(wX)/dz should be included in each equation for X in system (1)-(4)
(2) the w equation (3) should also include the buoyancy term.
(3) the continuity equation should be included to relate the density (temperature) fluctuations with the vertical velocity.
Were do you include these constrains?
Zbig
Kerstein, Alan
To rephrase my point, the conservation laws of the model are not expressed by the usual equations because properties do not evolve by the usual processes. This requires a 'back to basics' approach, starting with control volume analysis. There is no w * grad (.) advection process in the model, so properties of w have no bearing on the occurrence or non-occurrence of imbalances. Of course, the physical w does obey conservation laws so the model w cannot emulate the physical w in all respects, but it turns out well nevertheless because the physical flow has more degrees of freedom in 3D so the conservation laws are not highly constraining with respect to the statistics of a given component. This addresses your items (1) and (2).
Concerning (3), I include subsidence because it was part of the specifications for some of the intercomparison cases I have run, and also it is handy for forcing a statistically steady state for cases when that is mathematically useful irrespective of its physical relevance. It is unrelated to the considerations you mention, which are not a concern, as I mentioned above.
I will read the attachment you sent and comment on it later.
Alan
-----Original Message-----
From: Sorbjan, Zbigniew [mailto:zbigniew...@marquette.edu]
Sent: Thursday, April 02, 2009 4:45 PM
To: Kerstein, Alan
Subject: RE: questions
(1) Since w is different at each level, then dw/dz is not zero, Because horizontal div V=0, we are getting imbalance.
What consequence does such a imbalance have?
(2) Integrating the w equation with respect to z shows that d<w>/dt=n(dw/dz|top - dw/dz|bottom) which is not zero.
So the first (deterministic) step does not conserve the vertical velocity in time.
(3) We usually disregard subsidence in BLM. How important is it for a model to include it? Is it introduced just to balance the imbalance described above, and force w=0 at the top?
Z.
________________________________________
From: Kerstein, Alan [ark...@sandia.gov]
Sent: Thursday, April 02, 2009 4:56 PM
To: Sorbjan, Zbigniew
Cc: odt-re...@googlegroups.com
Subject: RE: questions