Quantitative schlieren measurements of coherent structures in a cavity shear layer S. Garg, L. N. Cattafesta III Abstract Quantitative ¯ow-®eld data were obtained in a planar shear layer spanning an open cavity with an ex- tension of the schlieren method. The technique is based on the measurement of light-intensity ¯uctuations in a real- time schlieren image. Data were collected using a ®ber- optic sensor embedded in the imaging screen coupled to a photodetector. Time-resolved measurements of the in- stantaneous density gradient at a point in the two di- mensional ¯ow cross section were thus obtained. Detailed surveys were carried out with both the optical instrument as well as a hot wire at a Mach number of 0.25 and with the optical instrument alone at a Mach number of 0.6. A comparison of the results shows that the non-intrusive technique can accurately measure the growth rates of in- stability waves in the initial ``linear'' region of the shear layer. The density-gradient ¯uctuations measured at dif- ferent locations and times) were synchronized by using a microphone inside the cavity as a reference and integrated to yield pro®les of the density ¯uctuations associated with the dominant large-scale structures in the shear layer. Such quantitative visualization is expected to clarify the mechanism of sound generation by shear-layer impinge- ment at the cavity trailing edge and elucidate the nature of this sound source. List of symbols c convection velocity, acoustic velocity, m/s f focal length, m; frequency, Hz k Gladstone±Dale constant,  2.259 ´ 10 )4 m 3 /kg M Mach number p pressure, Pa x streamwise direction, m y cross-stream direction, m t time, s u, U, v velocity, m/s a streamwise wavenumber, m )1 b cross-stream decay rate of disturbances, m )1 D displacement of light source image in the plane of the knife edge, m e angular de¯ection of light rays, rad q density, kg/m 3 x radian frequency  2pf, rad/s Superscripts ) long-time average, mean 0 ¯uctuating or time-varying quantity, deviation from mean Subscripts 0 basic undisturbed) state 1 freestream 1 Introduction The experimental determination of the ¯uctuating prop- erties of turbulent ¯ows is usually accomplished using either hot-wire anemometry HWA) or laser-Doppler velocimetry LDV). These techniques have undergone signi®cant re®nement since their inception, yet their application to any given ¯ow situation is often far from routine, especially for high-speed ¯ows. In many such situations, HWA is constrained by sensor fragility, inad- equate frequency response and the intrusive nature in- herent to the technique. LDV, while not intrusive, depends upon the presence of seed particles. For a successful measurement, these particles have to be large and nu- merous enough to produce a measurable signal without producing a signi®cant disturbance, yet small enough to faithfully ``follow'' the ¯ow. These requirements are often dif®cult to satisfy in high-speed ¯ows. In addition, the high cost of research-grade LDV systems precludes their use in laboratories of modest size and resources. The development of accurate, simple and inexpensive turbulence measurement techniques as a supplement to HWA and LDV is therefore desirable. Optical techniques, especially those not requiring ¯ow seeding, are desirable, since they do not involve the insertion of probes into the ¯ow. Further, the frequency response of photodetector- based measurement systems both solid-state and surface- emission type) can easily be many orders of magnitude higher than that of hot wires. Two traditional optical methods for investigating compressible ¯ows are schlieren Experiments in Fluids 30 2001) 123±134 Ó Springer-Verlag 2001 Received: 28 December 1999/Accepted: 15 March 2000 S. Garg &) 1 , L. N. Cattafesta III High Technology Corporation, 28 Research Drive Hampton, VA 23666, USA Present address: 1 Hypertherm, Inc., Etna Road, Hanover, NH 03755, USA The authors wish to acknowledge the assistance of Stephen B. Jones of NASA Langley in the optical set-up and that of Gregory S. Jones, also of NASA Langley, with the preparations for the experiments. The assistance of Michael A. Kegerise of Syracuse University in the dynamic calibration of the photodiode is also gratefully acknowledged. 123