Abstract
A spatial theory is proposed for the linear transient growth of disturbances in a parallel boundary layer. Following from the consideration of a signaling problem, the spatial development of disturbances downstream of a source may be presented as a sum of decaying eigenmodes and Tollmien-Schlichting (TS) like instability modes. Therefore, the problem of optimal disturbances may be considered as an initial value problem on the subset of the decaying eigenmodes and a TS wave, and a standard optimization procedure may be applied for evaluation of the optimal transient growth. The results indicate that the most significant transient growth is associated with stationary streamwise vortices. Numerical examples illustrate that favorable pressure gradient decreases the overall amplification. Effects of compressibility and the wall cooling are investigated as well.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 2097-2104 |
| Number of pages | 8 |
| Journal | Physics of Fluids |
| Volume | 13 |
| Issue number | 7 |
| DOIs | |
| State | Published - Jul 2001 |
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ASJC Scopus subject areas
- Mechanics of Materials
- Computational Mechanics
- Physics and Astronomy(all)
- Fluid Flow and Transfer Processes
- Condensed Matter Physics
Cite this
Spatial theory of optimal disturbances in boundary layers. / Tumin, Anatoli; Reshotko, E.
In: Physics of Fluids, Vol. 13, No. 7, 07.2001, p. 2097-2104.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Spatial theory of optimal disturbances in boundary layers
AU - Tumin, Anatoli
AU - Reshotko, E.
PY - 2001/7
Y1 - 2001/7
N2 - A spatial theory is proposed for the linear transient growth of disturbances in a parallel boundary layer. Following from the consideration of a signaling problem, the spatial development of disturbances downstream of a source may be presented as a sum of decaying eigenmodes and Tollmien-Schlichting (TS) like instability modes. Therefore, the problem of optimal disturbances may be considered as an initial value problem on the subset of the decaying eigenmodes and a TS wave, and a standard optimization procedure may be applied for evaluation of the optimal transient growth. The results indicate that the most significant transient growth is associated with stationary streamwise vortices. Numerical examples illustrate that favorable pressure gradient decreases the overall amplification. Effects of compressibility and the wall cooling are investigated as well.
AB - A spatial theory is proposed for the linear transient growth of disturbances in a parallel boundary layer. Following from the consideration of a signaling problem, the spatial development of disturbances downstream of a source may be presented as a sum of decaying eigenmodes and Tollmien-Schlichting (TS) like instability modes. Therefore, the problem of optimal disturbances may be considered as an initial value problem on the subset of the decaying eigenmodes and a TS wave, and a standard optimization procedure may be applied for evaluation of the optimal transient growth. The results indicate that the most significant transient growth is associated with stationary streamwise vortices. Numerical examples illustrate that favorable pressure gradient decreases the overall amplification. Effects of compressibility and the wall cooling are investigated as well.
UR - http://www.scopus.com/inward/record.url?scp=0035397849&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0035397849&partnerID=8YFLogxK
U2 - 10.1063/1.1378070
DO - 10.1063/1.1378070
M3 - Article
AN - SCOPUS:0035397849
VL - 13
SP - 2097
EP - 2104
JO - Physics of Fluids
JF - Physics of Fluids
SN - 0031-9171
IS - 7
ER -