Dep. ENERGY : Transition to turbulence
Mines Nancy - 3rd Year - Master 2 -
Département Énergie
Academic Year 2022-2023
Transition to turbulence in
thermoconvection
and
aerodynamics
Syllabus
ARCHE page
Find here the latest pdf version of
my lecture notes, with elements of solution of most exercises and problems.
In these lecture notes,
some equations and figures are empty and should be filled or realized
by the students themselves: `DIY' means `Do it yourself' !
A `full' version of the lecture notes, without blank spaces
and with the complete figures,
may be asked by mail to
Emmanuel Plaut.
On this dynamic web page,
I sketch the planning and the program of the module.
Further informations will be published regarding
the assessment - grading methods,
using, in particular, homeworks.
Starting from session 2,
the students will use
Mathematica
on their laptop
to plot fields,
perform formal (symbolic) and numerical computations.
A Mathematica
licence specific to Mines Nancy will be used:
you should receive before session 1 a mail from
Wolfram Research, who produces and distributes
Mathematica.
For session 1, a pocket calculator will be sufficient.
All lectures and the exam will take place in room P318.
Session 1 Thursday September 29
Natural thermoconvection,
Rayleigh - Bénard thermoconvection: setup of the
linear stability analysis with slip boundary conditions
[ Slides of session 1 ]
Session 2 Thursday October 6
Rayleigh - Bénard thermoconvection with slip boundary conditions:
linear stability analysis
Preparatory work: theory
Try to solve by yourself the beginning of ex. 1.1:
find the coefficient of degree 1
and the constant coefficient of the characteristic equation (1.32).
Preparatory work: computing
Install and configure
Mathematica
on your laptop, if this has not been done last week.
Learn how to use it with tutorials,
and by trying to do a few things by yourself;
for instance look at
-
ce notebook interactif par Olivier Deck (que je remercie);
-
this Wolfram's fast introduction for programmers;
-
this Wolfram's tutorial on algebraic calculations;
-
this Wolfram's tutorial on symbolic calculations;
-
this Princeton's tutorial on symbolic computation...
During session 2 we were supposed to
do contour plots, and some formal computations
of ex. 1.1,
hence all items above were presumably relevant.
At least they are relevant for session 3 !
[ Slides of session 2 ]
Session 3 Thursday October 13
Rayleigh - Bénard thermoconvection: linear and
weakly nonlinear analysis, supercritical patterning bifurcation,
elements on further transitions and on the case of no-slip boundary conditions;
Lorenz model & chaos; confined geometry - flow reversals...
Preparatory work:
Terminate ex. 1.1.
[ Slides of session 3, without overlays since they are numerous ]
Session 4 Thursday October 20
Transition in open shear flows: generalities,
the case of plane Poiseuille flow
[ Slides of session 4 ]
Session 5 Thursday October 27
Transition in plane Poiseuille flow:
linear stability analysis,
Tollmienn - Schlichting waves
[ Slides of session 5 ;
PPF-LinAn.m : script Mathematica with
a partial solution of pb. 2.1 ;
commands.m : script Mathematica
called in PPF-LinAn.m ]
Session 6 Thursday November 10
Transition in plane Poiseuille flow:
weakly nonlinear stability analysis,
subcritical bifurcation
to Tollmienn - Schlichting waves,
subcritical & saddle-node bifurcations.
Transition in open shear flows...
Preparatory work:
Advance pb. 2.1 as far as possible,
starting with PPF-LinAn.m.
[ Slides of session 6 - all of them
to give you solutions of pb and exs ! ]
Examination Thursday November 24 9h30-11h30 in room P318
This time slot corresponds to the standard exam of duration
1 hour 30 mins... plus 30 mins for one student who has a bonus of 1/3 of the duration.
All students will start at 9h30 and should bring their laptop
for Mathematica and ARCHE, nothing else,
plus the lecture notes given at the beginning of the module.
Homework
The homework will be realized in groups.
A hand-written solution will be requested.
Some plots realized preferentially with
Mathematica could be added,
moreover, a notebook could be sent by email.
- Ex. 1.2 General linear stability analysis of slip RBT
...
for 3 students, after session 2.
Scoring scale: 1: 4 points | 2: 6 points
Total: 10 points + max 1 point of bonus for good english
- Ex. 1.11 Stability analysis of a fluid layer
with different thermal stratifications
...
for 4 students, after session 2.
Scoring scale: 1: 1 point | 2: 1.5 points | 3: 3 points
| 4: 0.5 point | 5: 3.5 points | 6: 0.5 point
Total: 10 points + max 1 point of bonus for good english
- Ex. 2.7 3D linear stability analysis of 2D viscous open shear flows:
Squire's transformation and theorem
...
for 4 students, after session 5.
Scoring scale: 1: 0.75 point | 2: 0.75 point | 3: 1.75 points
| 4: 1 point | 5: 3.5 points | 6: 2.25 points
Total: 10 points + max 1 point of bonus for good english
Grading methods
- The number of + got during the whole session,
to measure your participation, yields a score
NP over 15 = the maximum of + over the 11 students .
-
Your homework score multiplied by 2
yields a score over 20 points,
NH .
-
Your examination score will be, over 20 points,
NE .
-
Your module score will be something like
(the coefficients might be slightly modified)
NM =
0.2 NP +
0.4 NH +
0.6 NE .
-
A grade G = A, B, C, D, E, F or FX
will be deduced from NM.
I will give some infos (histograms, thresholds, etc.) on the
ARCHE page of the module...
Emmanuel Plaut