The rhythm of fountains: the length and time scales of rise height fluctuations at low and high Froude numbers

被引:38
作者
Burridge, H. C. [1 ]
Hunt, G. R. [2 ]
机构
[1] Univ London Imperial Coll Sci Technol & Med, Dept Civil & Environm Engn, London SW7 2AZ, England
[2] Univ Cambridge, Dept Engn, Cambridge CB2 1PZ, England
基金
英国工程与自然科学研究理事会;
关键词
jets; plumes/thermals; turbulent convection; TURBULENT FOUNTAINS; WEAK FOUNTAINS; BUOYANCY; JETS; TRANSITION; BEHAVIOR; CHAMBER; FLUID;
D O I
10.1017/jfm.2013.263
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
The magnitude and frequency of vertical fluctuations of the top of an axisymmetric miscible Boussinesq fountain forms the focus of this work. We present measurements of these quantities for saline-aqueous fountains in uniform quiescent surroundings. Our results span source Froude numbers 0.3 <= Fr-0 <= 40 and, thereby, encompass very weak, weak, intermediate and forced classes of fountain. We identify distinct scalings, based on known quantities at the fountain source, for the frequency of fountain height fluctuations which collapse our data within bands of Fr-0. Notably, our scalings reveal that the (dimensionless) frequency takes a constant value within each band. These results highlight characteristic time scales for the fluctuations which we decompose into a single, physically apparent, length scale and velocity scale within each band. Moreover, within one particular band, spanning source Froude numbers towards the lower end of the full range considered, we identify unexpectedly long-period fluctuations indicating a near balance of inertia and (opposing) buoyancy at the source. Our analysis identifies four distinct classes of fluctuation behaviour (four bands of Fr-0) and this classification matches well with existing classifications of fountains based on rise heights. As such, we show that an analysis of the behaviour of the fountain top alone, rather than the entire fountain, provides an alternative approach to classifying fountains. The similarity of classifications based on the two different methods confirms that the boundaries between classes mark tangible changes in the physics of fountains. For high Fr-0 we show that the dominant fluctuations occur at the scale of the largest eddies which can be contained within the fountain near its top. Extending this, we develop a Strouhal number, Str(top), based on experimental measures of the fountain top, defined such that Str(top) = 1 would suggest the dominant fluctuations are caused by a continual cycle of eddies forming and collapsing at this largest physical scale. For high-Fr-0 fountains we find Str(top) approximate to 0.9.
引用
收藏
页码:91 / 119
页数:29
相关论文
共 18 条
[1]   TURBULENT FOUNTAINS IN A CLOSED-CHAMBER [J].
BAINES, WD ;
CORRIVEAU, AF ;
REEDMAN, TJ .
JOURNAL OF FLUID MECHANICS, 1993, 255 :621-646
[2]   TURBULENT FOUNTAINS IN AN OPEN CHAMBER [J].
BAINES, WD ;
TURNER, JS ;
CAMPBELL, IH .
JOURNAL OF FLUID MECHANICS, 1990, 212 :557-592
[3]   A theoretical model of a turbulent fountain [J].
Bloomfield, LJ ;
Kerr, RC .
JOURNAL OF FLUID MECHANICS, 2000, 424 :197-216
[4]  
Brooks N. H., 1979, MIXING INLAND COASTA, P483
[5]   The rise heights of low- and high-Froude-number turbulent axisymmetric fountains [J].
Burridge, H. C. ;
Hunt, G. R. .
JOURNAL OF FLUID MECHANICS, 2012, 691 :392-416
[6]   On large-amplitude pulsating fountains [J].
Clanet, C .
JOURNAL OF FLUID MECHANICS, 1998, 366 :333-350
[7]   Oscillation in height of a negatively buoyant jet [J].
Friedman, P. D. .
JOURNAL OF FLUIDS ENGINEERING-TRANSACTIONS OF THE ASME, 2006, 128 (04) :880-882
[8]   Turbulent entrainment in jets with arbitrary buoyancy [J].
Kaminski, E ;
Tait, S ;
Carazzo, G .
JOURNAL OF FLUID MECHANICS, 2005, 526 :361-376
[9]   Weak fountains [J].
Kaye, N. B. ;
Hunt, G. R. .
JOURNAL OF FLUID MECHANICS, 2006, 558 (319-328) :319-328
[10]   Very weak fountains in a homogeneous fluid [J].
Lin, WX ;
Armfield, SW .
NUMERICAL HEAT TRANSFER PART A-APPLICATIONS, 2000, 38 (04) :377-396