Citation:

PANGAEA.949070

Name: Optimal growth (Re=2000,A=1,Wo=15): value of TG as function to and tf (computed)
Published: 2022-09-26
License: https://creativecommons.org/licenses/by/4.0/
Keywords: nonlinear instability; transition to turbulence

Always quote citation above when using data! You can download the citation in several formats below.

Published: 2022-09-26 • DOI registered: 2023-01-13

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Abstract:

The data are obtained via an in-house Matlab script (developed by Dr. Baofang Song) to compute the non-modal transient growth of disturbances in pulsatile and oscillatory pipe flows. In this study, a Newtonian fluid driven by pulsatile and oscillatory flow rate flows in a straight pipe. In pulsatile flow, there are three governing parameters: steady Reynolds number (defined by the steady flow component), pulsation amplitude (ratio of oscillatory and steady flow component) and Womersley number (dimensionless pulsation and oscillation frequency). In oscillatory flow, due to vanishment of steady flow component, oscillatory Reynolds number (defined by the oscillation flow component) and Womersley number. The Reynolds number defined by the thickness of Stokes layer is alternatively used for the oscillatory Reynolds number. The study was carried out in a manner that one governing parameter varies while other governing parameters are fixed.

The data file 't0_TG_contour.dat' shows the maximum energy amplification over modes in the parameter regime of initial time and final time.

This file includes three columns: the first column indicates initial time of perturbations normalized by pulsation period; the second column indicates the evolution time of the perturbation normalized by period; the third column indicates the energy amplification corresponding to the initial time (first column) and the evolution time (second column).

Keyword(s):

nonlinear instability; transition to turbulence

Comment:

#t0:initial time; tf:end time; tau:time duration, tau=tf-t0

VARIABLES = "t0/period", "(tf-t0)/period", "G(t0,tau)"

ZONE T="data", I=21, J=21

Parameter(s):

#	Name	Short Name	Principal Investigator
1	Time of pertubartion by pulsation period	t0/T	Xu, Duo
2	Time of perturbation energy maximum - Time of perturbation by pulsation period	(tf-t0)/T	Xu, Duo
3	Transient energy growth	TG	Xu, Duo

License:

Creative Commons Attribution 4.0 International (CC-BY-4.0)

Status:

Curation Level: Enhanced curation (CurationLevelC) * Processing Level: PANGAEA data processing level 2 (ProcLevel2)

Size:

1323 data points

Data

Download dataset as tab-delimited text — use the following character encoding:

1 t0/T	2 (tf-t0)/T	3 TG
0.05	0.00000000	1.00000000
0.05	0.05013381	6.09679787
0.05	0.09981999	20.69355408
0.05	0.14995380	42.83560452
0.05	0.20008761	61.24542627
0.05	0.25022141	74.94932595
0.05	0.29990760	88.53452186
0.05	0.35004140	104.45624785
0.05	0.40017521	120.54558707
0.05	0.44986139	138.79622040
0.05	0.49999520	155.91312661
0.05	0.55012901	174.02647141
0.05	0.59981519	190.37100436
0.05	0.64994900	204.89664879
0.05	0.70008281	217.21851257
0.05	0.75021661	227.23022643
0.05	0.79990280	234.88390424
0.05	0.85003660	240.42951063
0.05	0.90017041	243.98120725
0.05	0.94985659	245.77875893
0.05	0.99999040	246.13108214
0.10	0.00000000	1.00000000
0.10	0.05013381	6.10242645
0.10	0.09981999	19.62054851
0.10	0.14995380	38.58330716
0.10	0.20008761	54.20942385
0.10	0.25022141	68.54203530
0.10	0.29990760	86.16043394
0.10	0.35004140	104.14128030
0.10	0.40017521	124.28256009
0.10	0.44986139	142.89311167
0.10	0.49999520	162.55416039
0.10	0.55012901	180.68573437
0.10	0.59981519	196.73991654
0.10	0.64994900	210.72564407
0.10	0.70008281	222.34189679
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0.10	0.85003660	243.29759758
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0.10	0.99999040	247.78838523
0.15	0.00000000	1.00000000
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0.15	0.14995380	35.23170644
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0.15	0.29990760	88.10065425
0.15	0.35004140	109.12409860
0.15	0.40017521	129.61495530
0.15	0.44986139	149.68789900
0.15	0.49999520	169.35908722
0.15	0.55012901	187.17893654
0.15	0.59981519	202.67210533
0.15	0.64994900	215.92184536
0.15	0.70008281	226.72211968
0.15	0.75021661	235.14106657
0.15	0.79990280	241.30069784
0.15	0.85003660	245.55025288
0.15	0.90017041	248.10717630
0.15	0.94985659	249.26321749
0.15	0.99999040	249.32280755
0.20	0.00000000	1.00000000
0.20	0.05013381	6.89253209
0.20	0.09981999	18.91425642
0.20	0.14995380	34.36697384
0.20	0.20008761	52.63056018
0.20	0.25022141	72.75205412
0.20	0.29990760	92.99552970
0.20	0.35004140	115.25708582
0.20	0.40017521	136.21259685
0.20	0.44986139	156.08641812
0.20	0.49999520	175.43869153
0.20	0.55012901	192.68373595
0.20	0.59981519	207.43833679
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0.20	0.70008281	229.84587600
0.20	0.75021661	237.52972120
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0.20	0.90017041	249.26005856
0.20	0.94985659	250.37660636
0.20	0.99999040	250.55934293
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0.30	0.99999040	251.68378266
0.35	0.00000000	1.00000000
0.35	0.05013381	10.23691028
0.35	0.09981999	28.61450702
0.35	0.14995380	48.27125774
0.35	0.20008761	69.81417524
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0.35	0.29990760	116.26894124
0.35	0.35004140	137.91483617
0.35	0.40017521	155.37479081
0.35	0.44986139	175.13603111
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0.35	0.55012901	205.98124370
0.35	0.59981519	216.61605624
0.35	0.64994900	250.69171866
0.35	0.70008281	376.83814414
0.35	0.75021661	509.71914567
0.35	0.79990280	605.59645453
0.35	0.85003660	636.60826947
0.35	0.90017041	595.40761629
0.35	0.94985659	503.43787158
0.35	0.99999040	387.75426053
0.40	0.00000000	1.00000000
0.40	0.05013381	10.99473135
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0.40	0.20008761	79.72537266
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0.40	0.29990760	126.00019354
0.40	0.35004140	147.71750076
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0.40	0.90017041	968.13152951
0.40	0.94985659	745.27165068
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0.45	0.00000000	1.00000000
0.45	0.05013381	11.22130309
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0.45	0.20008761	93.52532066
0.45	0.25022141	116.64284001
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0.45	0.40017521	187.36202811
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0.45	0.79990280	1589.08813131
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0.45	0.94985659	736.03262060
0.45	0.99999040	486.70141789
0.50	0.00000000	1.00000000
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0.50	0.09981999	42.80031569
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0.50	0.20008761	110.68679048
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0.50	0.35004140	198.11284538
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0.50	0.64994900	1723.94044672
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0.50	0.90017041	799.84398929
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0.50	0.99999040	335.14922849
0.55	0.00000000	1.00000000
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0.55	0.29990760	190.36871196
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0.80	0.25022141	203.13381667
0.80	0.29990760	274.63509404
0.80	0.35004140	324.08636870
0.80	0.40017521	339.50947536
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0.80	0.55012901	221.18240233
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0.80	0.70008281	205.99008311
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0.80	0.85003660	227.35771638
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0.80	0.94985659	238.31392031
0.80	0.99999040	241.13309057
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0.85	0.09981999	26.33129738
0.85	0.14995380	64.48905979
0.85	0.20008761	117.42341392
0.85	0.25022141	175.97290287
0.85	0.29990760	220.18889026
0.85	0.35004140	239.85151622
0.85	0.40017521	232.63859610
0.85	0.44986139	205.93462749
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0.85	0.55012901	180.19669571
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0.85	0.70008281	200.16752309
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0.85	0.85003660	228.90602771
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0.85	0.99999040	241.34787743
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0.90	0.09981999	24.88385297
0.90	0.14995380	59.83735000
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0.90	0.29990760	167.23349757
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0.90	0.44986139	152.91244813
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0.90	0.59981519	181.11689847
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1.00	0.05013381	6.21354423
1.00	0.09981999	21.99962527
1.00	0.14995380	48.03750192
1.00	0.20008761	70.74003121
1.00	0.25022141	89.43918579
1.00	0.29990760	98.08571137
1.00	0.35004140	109.96071258
1.00	0.40017521	123.48357859
1.00	0.44986139	136.76798706
1.00	0.49999520	153.24868547
1.00	0.55012901	168.00657094
1.00	0.59981519	184.33047947
1.00	0.64994900	199.12816852
1.00	0.70008281	211.95530196
1.00	0.75021661	222.62734073
1.00	0.79990280	231.00641114
1.00	0.85003660	237.27741827
1.00	0.90017041	241.48144625
1.00	0.94985659	243.80420925
1.00	0.99999040	244.53339544