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Monthly Weather Review James E DEPARTMENT OF COMMERCE WEATHERBUREAU SINCLAIR WEEKS, Secretary F. W. REICHELDERFER, Chief MONTHLY WEATHER REVIEW JAMES E. CASKEY, JR., Editor Volume 83 Cloeed Febru 15, 1956 Number 12 DECEMBER 1955 Issued Mm% 15, 1956 A SIMULTANEOUS LAGRANGIAN-EULERIAN TURBULENCE EXPERIMENT F'RA.NK GIFFORD, R. U. S. Weather Bureau The Pennsylvania State University * [Manuscript received October 28, 1955; revised January 9, 1956J ABSTRACT Simultaneous measurements of turbulent vertical velocity fluctuationsat a height of 300 ft. measured by means of a fixed anemometer, small floating balloons, and airplane gust equipment at Brookhaven are presented. The re- sulting Eulerian (fixed anemometer) turbulence energy mectra are similar to the Lagrangian (balloon) spectra but " - with a displacement toward higher frequencies. 1. THE NATURE OF THEPROBLEM function, and the closely related autocorrelation function. This paper reports an attempt to make measurements of The term Eulerian, in turbulence study, impliescon- both Lagrangian and Eulerianturbulence fluctuations sideration of velocity fluctuations at a point or points simultaneously. This problem owes its importance largely fixed in space, as measured for example by one or more to the fact that experimenters usually measure the Eu- fixed anemometers or wind vanes. The term Lagrangian lerian-time form of the turbulence spectrumor correlation, implies study of the fluctuations of individual fluid par- which all 6xed measuring devices of turbulence record; cels; these are very difficult to measure. In a sense, these but theoretical developments as well as practical applica- two points of view of the turbulence phenomenon are tionsinevitably require the Eulerian-space, or the La- closely related tothe two most palpable physical manifesta- grangian form. Consequently, both experimental vesca- tions of turbulence, first the irregular or random nature of tion of theoretical developments and theapplication of the theturbulent fluctuations and second the remarkable theories to many practicalproblems require some consider ability of fluid in a state of t,urbulence to disperse proper- ation of the Eulerian and Lagrangian interrelationships. ties. Such problems of turbulence in the atmosphere as the effect of gusts on structures (towers, buildings, air- frames) lead to the Eulerian kind of analysis, whereas the 2. OBSERVATIONALTECHNIQUES Lagrangian form arises naturally in the highly important A comparatively wide variety of instruments is available field of atmospheric diffusion. for direct Eulerian-time observation of the natural wind The irregular nature of turbulence early suggested, in at low elevations, the only requirement being that the fact imposed, a statistical rather than a deterministic ap- device should respond to fluctuations in both the vertical proach to its study. Certain important quantities have and horizontal directions as rapidly as is required by the emerged, with the development of this theory, that serve frequencies of fluctuations that are to be studied. Hot to characterize turbulence, chiefly the energy spectrum wire and thermopile anemometers 161, and bidirectional wind vanes of several types [SI, [13], have all been used,, 1 TMsresearch was conducted under an agreement between the U. 8. Weather Bureau as well as more unusual devices like the anemoclinometer and the U. 8. Atomic Energy Oommission. a Present address: Weather Bureau Offlce, Oak Ridge, Tenn. 1121, and tethered balloons [7]. Presumably any of these, 372903-"-1 293 Unauthenticated | Downloaded 09/26/21 01:20 PM UTC 294 MONTHLYREVIEW WEATHER DECEMBER1955 if available in quantities of at least two, could be used for wind, andthe Aerovanes provide the windspeed and Eulerian-space observations. Few such analyses have horizontal direction. Instrumental characteristics of the been reported; t,he observation6 of Shiotani 1241, with hot Brookhaven bivanes were described in a study by Mazza- wire anemometers arranged in thevertical, areone example. rella [13]; and the manner of their use in wind fluctuation Sakagami hasrecently, in two fascinating papers [22], measurement, in connection with the Aerovanes, is 1231, reported on some spatial wind fluctuation measure- covered in several papers of Panofsky [17], [18], Panofsky ments of very small-scale turbulence, obtained by using and McCormick [ 191, and McCormick [ 111. The tech- an array of tiny wind vanes, each only a centimeter long. nique may now be considered to be a tested, reliable one Airplane gusts measurements, for example those reported for obtaining low-level wind fluctuation data, possessing by Bunker and McCasland [2] orPress and Mazelsky well understood properties and limitations. [20], provide a kind of Eulerian-space information. Al- It was accordingly proposed tomake simultaneous though the sampling time of such measurements is finite, observations of turbulentfluctuations in the ,lower it is short enough that a relatively large space is sampled atmosphere, withboth the fixed bivane-Aerovane ap- quite rapidly. Such measurements represent a fairly paratus on the Brookhaven tower and visual double close approach to true Eulerian-space observations. theodolite observations of neutral balloons, released from The method invariably employed in Lagrangian obser- the tower. The cooperation of Mr. Andrew Bunker, vations of atmospheric turbulence has been to introduce Woods Hole Oceanographic Institution, was alsoob- some tracer into the air and follow its motion. The list tained; his group agreed toat,tempt airplane measure- of tracers that have been employed (most of them were ments of vertical accelerations at the tower level during first tried by L. F. Richardson [21]) is, as Edinger [4] the same period. In this way, all three of the spa.ce, remarked, ent,ertaining, including as it does Edinger’s time, and Lagrangian fluctuations could be estimated at soap bubbles, Miller’s Kleenex lint experiments [15], and the same time. the work done by Badgley [l] using dandelion seed. Standard practice with the bivane data, because of the Balloons of various sizes have of course been used, also; instrument’s resonant period, is to work with 5- or 10- and some work has been done by following smoke puffs, second averages of the velocity fluctuations, depending on using a camera obscura [3]. The difficulty is to find a the prevailing wind speed. Resulting spectra often show tracer that has negligible mass, zero terminal velocity or two peaks, or at least two more or less distinct high energy net buoyancy, is small enough torepresent, faithfully, regions, one at a frequency of about 200 c. p. h., attributed the smallest significant scale of air motions, and that can to mechanical turbulence, and anotherat about 40 c. p. h., be traced by some reasonably convenient system. Cer- due presumably to convection. Since visual triangulation tain of the abovetracers satisfy one or more of these on small balloons any more oftten than every 10 seconds criteria, but no one satisfies all. seemed an impossible prospect, it was thought best to Considering this great diversity of measuring systems, choose a period for the experiment when the convective it is clear that some care must be exercised in intercompar- turbulence would be reasonably well developed. Based ing various results. Different devicespossess entirely on the climatological expectancy of clear days, the period different response properties, and size alone introduces a June 14 to 18,1954, waschosen. This choicewas also strong selective effect upon the fluctuations that can be influenced bythe requirement that all three of the measured. Bunker’s PBY airplane is certainly indifferent different systems for measuring turbulence should provide to a range of small turbulentfluctuations that,say, comparable information. All threesystems have a Edinger’s soap bubbles will detect easily. Considerations limited ability to respond to high-frequency fluctuations, of this kind have been an important factor in the design and so it was thought best to concentrate on the lower, of the following experiment. convective frequencies. 3. SIMULTANEOUSA EULERIAN-TIME,EULERIAN- 4. OBSERVATIONALTECHNIQUE OF SPACE,AND LAGRANGIAN TURBULENCE NEUTRAL BALLOONS EXPERIMENT Bivane-Aerovane turbulence observations are a standard The Brookhaven National Laboratory, on eastern Long technique at Brookhaven andhave been described in Island,maintains a permanent micrometeorological in- several papers referred to previously. The airplane gust stallation including a completely instrumented, 410-ft. measuring system used byBunker is described in 121. high meteorological tower. A general description of this The technique of making neutral balloon runs, although site has been given by Smith and Singer [25]. For wind familiar, was modified suflticiently in the present experi- fluctuation measurements, there are available at Brook- ment to deserve some additional comment. haven permanently mounted bidirectional wind vanes, or The basic double theodolite procedure is described in a bimnes, at three levels on the tower, and Bendix-Friez WeatherBureau Circular [28], andby Lange [lo] or Aerouane anemometers at these three as well as several Mildner, Hansch,and Griessbach [14], for example. A other levels. The bivanes give the inclination of the number of standard precautions concerning orientation of Unauthenticated | Downloaded 09/26/21 01:20 PM UTC DECEMBER1955 REVIEWWEATHER MONTHLY 295 the baseline, collimation of the theodolites, and so on, gained, the longer flights being
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