The structure of the head of an inertial gravity current determined by particle-tracking velocimetry

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1 The structure of the head of an inertial gravity current determined by particle-tracking velocimetry L.P. Thomas, S.B. Dalziel, B.M. Marino Experiments in Fluids 34 (2003) DOI /s Abstract Digital particle-tracking velocimetry is used to obtain the two-dimensional structure of the head of inertial gravity currents propagating along a no-slip boundary. The early stage of development of lock-release gravity current experiments is recorded in the laboratory frame of reference and subsequently transformed by software to a frame moving with the current head. Time averages of these statistically stationary flows are computed, with the technique providing not only the mean two-dimensional velocity field but also the vorticity, shear stress and divergence fields, and streamlines of the flows. The distributions of the magnitude of the fluid velocity fluctuation and Reynolds stress complete the picture of the flow. Key features of the flow are broadly in line with earlier qualitative and quantitative investigations, and the detailed measurements presented here confirm some of the most recent findings from numerical simulations. 1 Introduction Buoyancy-driven flows take place in many natural and man-made situations. They occur in the ocean where the flow is driven by salinity and/or temperature inhomogeneities, or as turbidity currents on the ocean floor, the density difference being supplied by suspended particles. In the atmosphere, sea-breeze fronts and thunderstorms outflows are gravity currents of relatively cold dense air, Received: 31 August 2000 / Accepted: 14 February 2003 Published online: 14 May 2003 Ó Springer-Verlag 2003 L.P. Thomas (&), B.M. Marino Instituto de Física Arroyo Seco, Facultad de Ciencias Exactas, Universidad Nacional del Centro de la Provincia de Buenos Aires, Pinto 399, B7000GHG Tandil, Argentina Lthomas@exa.unicen.edu.ar S.B. Dalziel Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge, CB3 9EW, UK Experiments were performed in the Laboratory of Fluid Dynamics, Department of Applied Mathematics and Theoretical Physics (DAMTP), University of Cambridge, UK. LPT thanks Universidad Nacional del Centro de la Provincia de Buenos Aires and Consejo Nacional de Investigaciones Científicas y Técnicas de la República Argentina for grants to support his visit to DAMTP. SBD acknowledges the support of Yorkshire Water plc while atmospheric-suspension gravity currents include avalanches of airborne snow particles, as well as fiery avalanches and base surges formed from gases and solids issuing from volcanic eruptions. Oil spillage on the sea surface, spreading of hot water discharged from power stations and the accidental release of dense industrial gases are a few of many industrial problems in which gravity currents are important. A review of these flows and of their applications is given by Simpson (1997). Even though real flows are invariably three-dimensional, the close agreement in the description of the gross features of gravity currents between earlier experiments and the analytical and numerical two-dimensional results indicates clearly that the large-scale dynamics is fundamentally of a two-dimensional character. Hartel et al. (1997, 2000) performed full three-dimensional calculations at moderately high Reynolds numbers and confirmed that most quantities integrated over the width of the flow fit well the results of two-dimensional numerical simulations and experimental observations. This agreement takes place despite the presence of significant three-dimensional structures such as lobes and clefts. Experimental studies have also focused on a two-dimensional view of the current, where visualisations and quantities integrated across the width of the experimental channel are often employed (see Simpson 1997 and references cited therein). Most previous experimental studies (Simpson 1972; Britter and Simpson 1978; Britter and Linden 1980; Huppert and Simpson 1980; Rottman and Simpson 1983; Parsons and Garcia 1998) determined the relationships characterising the frontal zone of a gravity current (usually named the head ) as functions of several parameters of the flow. Among them, the densimetric Froude number, which describes the speed of the front in terms of the depth of the head and the reduced gravity of the fluid, has been of central interest and a wide range of mechanisms affecting it was considered. Therefore, the understanding of the dynamics of the head is important to set the necessary boundary conditions on the following flow. Simpson and Britter (1979) suggested the pattern of the flow within the head based on experiments where the current was brought to rest by using an opposing flow and a moving floor. The direct numerical simulations performed by Hartel et al. (2000) presented a more complete picture of structure of the flow at the gravity-current head. However, although numerical simulations can provide important information and can be applied to large-scale flows, a careful validation of the main findings is necessary.

2 To our knowledge, there are few experimental measurements of the velocity structure within the head previously reported in the literature. Alahyari and Longmire (1996) studied the evolving microburst during the initial stages of an axisymmetric release of a fixed volume of a solution of potassium phosphate in water into fresh water. Both fluids were seeded with titanium dioxide (TiO 2 ) particles of size small enough that the density difference with respect to the fluids (q p 3.5q 0, where q p is the density of the particles and q 0 is the density of water) was irrelevant to the characteristic time of the diagnostic used. Thin planar layers of the flow were illuminated by two Nd:YAG lasers fired in rapid succession. Images were captured with a 35-mm camera together with a rotating mirror placed between the camera and the object plane. The film negatives were digitised with a high-resolution scanner, and image data were processed to obtain displacement vectors from two-dimensional self-correlations. Hence, the authors provided instantaneous velocity fields averaged on an ensemble of experiments that depicted the evolution of the vortices within the current. Later, Kneller et al. (1999) determined the velocity structure of a gravity current from a series of nearly identical lock-release experiments carried out in a tank of rectangular cross section where horizontal brine underflows were originated with the same initial conditions. In each experiment, the instantaneous flow velocity at a point was carefully measured by laser-doppler velocimetry. The measurement points were located at 15 heights above the floor, in a vertical line at 2.35 lock lengths from the rear end of the tank. The instantaneous velocity as a function of time was expressed as the sum of its fluctuating part and the mean value obtained by averaging the data during 0.1 s. Results from different runs were used to construct a mean velocity profile in the flow of dense fluid behind the head in a situation in which the front ran at almost constant velocity. The horizontal velocity maximum was reported to be over 50% greater than the forward velocity of the head and to have occurred at a height equal to 0.2 times the thickness of the dense fluid. The complete profile corresponding to the dense fluid could be divided into two regions one near the floor, and the other extending to the top of the current in which the vertical velocity profiles had opposite gradients. In a subsequent process, the time evolution of the data for this profile was transformed into the spatial domain utilising the front velocity to generate the two-dimensional velocity structure of the head represented by a vector map. Grey-scale graphs representing the two-dimensional distribution of the magnitudes of downstream velocity, turbulent fluctuation and Reynolds stress were also reported. The aim of this paper is to introduce the use of digital particle-tracking velocimetry to extract the main features of the turbulent flow in and around the head of gravity currents running over a no-slip boundary. These currents are in the regime known as the slumping phase, or sometimes as the constant velocity phase (Huppert and Simpson 1980; Simpson 1997), during which the front propagates at essentially constant speed after the current becomes established. As in the earlier studies summarised above, the currents described here are high-reynolds number turbulent flows propagating over horizontal solid bottoms, and generating some mixing between the current and the ambient fluids. The underlying twodimensional flow field is extracted by averaging each experiment during a given time in the frame of reference moving with the front rather than considering an ensemble of experiments with the same initial conditions. The technique provides the velocity, vorticity, shear stress and divergence fields of the flow both within and around the head of gravity currents, as well as the magnitude of velocity fluctuations and Reynolds stresses in each run. Average and fluctuation fields are thus obtained by considering the temporal evolution of the velocity field during a long time (12 s for Re4000 case reported here) in each point of the head. Self-consistency is assured since all the information is extracted from the same experiment. The location at which the current is measured is sufficiently close to the position the current is released to ensure the head is within the slumping phase, but sufficiently far (about three times the fluid depth) that the current has become fully developed. The present technique is simpler and more cost-effective than the PIV method employed by Alahyari and Longmire (1996) to study an evolving microburst. Small particles with density very close to that of the fluid are used to ensure they move with the surrounding fluid during a time long enough to properly carry out the averaging process. As in Alahyari and Longmire (1996), both the gravity current and the ambient fluids are seeded with these particles to give a complete picture of the flow into and near the head of the current. However, a standard halogen lamp is sufficient to illuminate the particles. Images of the flow are acquired using a fixed monochrome CCD video camera and recorded as the luminescence signal on an SVHS video recorder. The video sequences are subsequently digitised, and the particles tracked to supply velocity information of the advancing current. Finally, the information is averaged by software in the frame of reference moving with the head, providing similar but more easily obtained results than the ensemble averaging technique used by Kneller et al. (1999) and Alahyari and Longmire (1996). Although the technique is the main subject of this work, the results obtained are also interesting. The structure of the flow within the head is found to be different from that reported by Kneller et al. (1999). In particular, it is found that the slow flow of dense fluid from the centre of the head towards the leading edge forms two counter-rotating cells whose intensities and positions depend on the Reynolds number. This picture is consistent with the central flux that supplies the fluid to the bottom boundary layer, as in the classical conception indicated by Simpson (1997) and the results of direct numerical simulation performed by Hartel et al. (2000). In Sect. 2 the experimental set-up and the procedure employed are described. Section 3 shows the results for the case of plane gravity currents running over a horizontal solid bottom for a moderate value of the Reynolds number. Finally, a summary and some concluding remarks are given. 709

3 710 Fig. 1. Schematic of experimental set-up 2 Experimental set-up and procedure Gravity currents were produced in a Perspex tank (200-cm long, 20.3-cm wide and 25-cm deep) by means of the lockrelease system depicted in Fig. 1. The inside of the tank was lined on the back wall with black book-covering film to produce a dark background and keep out any stray light. The tank was filled with fresh water to a depth H=20 cm and a known amount of salt was dissolved into the water to have a fluid density q close to the mean density (q p 1.02) of the particles suspended in the water and used for PTV. These were particles of Pliolite VT (a granular resin used in the manufacture of modern solvent-based paints) sieved to obtain sizes in the range lm. A vertical gate was then inserted to define a lock of length x 0, dividing the tank into two parts. An extra quantity of salt was added to the fluid behind the lock to increase the density by Dq, which varied from 0.007% to 0.7% of the water density q 0. More particles of Pliolite and a small quantity of sodium fluorescein were also added to the fluid behind the lock to provide flow visualisation and determine the position (and hence velocity) of the head of the gravity current. The fluids were allowed to settle for about 30 min before starting the experiment by withdrawing the gate. To ensure the Pliolite particles were thoroughly wetted by salt water, they were soaked briefly in a solution containing a high concentration of wetting agent (dishwasher rinse aid), and later carefully washed with fresh water many times before adding them to the tank. This washing process removed both any remaining fine dust and the bulk of the wetting agent. To closely match the particle density on both sides of the lock gate, the initial value of the fluid density was chosen as qq p ±1/2Dq. Itwas observed that the velocity of the rising or settling of the particles remained smaller than 1% of the velocity of the current front. Indeed, the settling velocity was small enough for the particles to remain stationary and well distributed through the entire depth of the tank during the initial 30-min settling time. The experiment was illuminated by a 1-kW photographic halogen lamp with a linear filament that was focused by a spherical lens into a vertical light sheet, approximately 0.6-cm thick, entering through the floor and cutting along the central part of the tank (Fig. 1). A monochrome CCD video camera (COHU 4912, Synoptics, UK) fitted with a zoom lens was placed 4.30 m from the tank and focused on the vertical plane where the particles were illuminated. This camera was configured for frame integration (overlapping 1/25 s integration periods for the two interlace fields) and fitted with a 1/100 s mechanical shutter running at 25 Hz to achieve the maximum vertical resolution and ensure the two interlaced fields were exposed at the same time. The camera output was recorded using Super VHS video (Panasonic AG7350). A reference coordinate system was obtained by recording images of vertical and horizontal scales on the plane defined by the light sheet before the gate was inserted. During the experiments the field of view of the camera also contained a set of fixed reference points that were used subsequently to ensure correct registration of the images and to eliminate any electronic or mechanical vibration introduced by the video recorder. After completion of an experiment and digitisation of images, a horizontal row of pixels at the mean height of the foremost point of the current front (usually called the nose, Simpson 1997) was extracted from the image sequences to form the time series image shown by Fig. 2. This time series provides the instantaneous location of the front as the contour between two zones with different grey levels. The mean front velocity U was then calculated using a least-squares fit to the front contour. In some experiments, small sloshing motions excited by the removal of the gate caused the front to deviate from a constant velocity. These oscillations were not significant in the experiments reported in this paper. Velocity information was obtained by tracking the Pliolite particles using DigImage (Dalziel 1992, 1993, 1995). Each frame was digitised to a resolution of pixels and 256 grey levels using a data translation frame grabber (DT2861). The individual particles were then identified and their relationships with particles found at earlier times were determined. Typically, about 1000 particles were visible in the illuminated region of the flow, and most of them were tracked in the two-dimensional projection of this region. During the post-processing stage, the data were shifted into the frame of reference moving with the head of the current by subtracting the

4 711 Fig. 2. Typical image representing the front position evolution. The abscissa is proportional to the horizontal position, while the (downward) vertical axis is proportional to time. The two zones clearly distinguished indicate the current fluid (grey) and the ambient fluid (black). Bright lines elsewhere depict particle paths instantaneous location of the front from the particle positions at each time step. As the speed of propagation of the front was constant to a good approximation, the transformed frame of reference remained inertial. The velocity for each particle path in the transformed Lagrangian coordinate system was calculated by a local least-squares fitting of a function quadratic in time. These velocity vectors corresponding to randomly located particles could be analysed in many ways. However, for the purposes of this paper, the velocity data were mapped onto a regular grid using a weighted least-squares approach. In particular, the velocity on each grid point was calculated by fitting the velocity of the neighbouring particles with a bilinear function using a weighting that decayed with the distance from that grid point. This process could be undertaken over short time intervals to yield the instantaneous time-varying velocity field of the current. Alternatively, the entire sequence could be used to determine the mean velocity field. The latter approach provides direct access to the temporal mean velocity field without mapping the instantaneous data first. The results presented in Sect. 3 are based mainly on such temporal means determined on a grid averaged over about 100 frames. The use of bilinear functions in the gridding process allows direct access to the velocity gradients used to construct the vorticity, stress, shear and divergence fields. The approximate stream function w was computed by iteratively inverting uñ w from the gridded velocity field. A series of experiments was carried out in which only the images corresponding to gravity currents running on the solid bottom of the tank were recorded. The lock extended from x=0 (the rear wall) up to x=x 0 =50 cm, and the camera was held fixed looking at the region placed between x130 cm and x160 cm. Comparisons with test experiments confirmed that the gravity current was in the slumping phase when the head passed through the recorded window. The current in the observed region was not affected by the initial transient flow after release, the bore coming from the rear end of the lock, or the other end of the tank (see Rottman and Simpson 1983; Hartel et al. 2000). In contrast, tests with a much shorter lock, Fig. 3a,b. Profile of a bottom current with Dq=0.7%, U=4.96 cm/s and Reynolds number about Re4000: a Time-averaged image. b Virtual streak photograph constructed from particle-tracking data showing the particle positions over a 0.32-s period that is, x 0 15 cm, showed unsteady conditions related to the transition between the slumping and the self-similar phases. Thus the fields reported here correspond to the flow near the head under quasi-steady state conditions. The experiments were performed for Reynolds numbers Re=Uh/m, varying in the range from 120 to Here U is the front velocity, h the maximum depth of the head, and m the kinematic viscosity of water. Over this range of Re, the currents were reproducible from one experiment to the next, and the Froude number of the front Fr=U/Ög h, where g (Dq/q)g is the reduced gravity, was found to increase with Reynolds number from 0.5 to 0.7. These Froude numbers agree well with the values found by previous authors (taking into account the definition of h used here). In this paper we concentrate on an experiment with Re=4000 in order to aid comparison with Kneller et al. (1999). 3 Results Figure 3a indicates the time-average shape of the gravity current. This image was constructed by averaging the intensity of 11 images, separated by 0.32 s, where each image was first shifted to the frame of reference of the head. This resulting image suggests the shape of the region that may be identified as the head of the gravity current. Figure 3b shows a virtual streak photograph in the frame of reference of the head calculated from the particle-tracking data. The final position of each particle is indicated by the

5 712 highest intensity, while the comet-like tail of decreasing intensity indicates the particle position at earlier times. The depth of the head is close to 10 cm or half the channel depth, as found by previous authors (see Simpson 1997 and references quoted) and predicted by the theory of Benjamin (1968). The small departure from h/h=1/2 is consistent with the fact that the upper and lower boundary conditions are different. The characteristic raised nose and enlarged head of the gravity current are clearly visible, as are the billows at the back of the head. In this particular case, the average elevation of the nose is observed to vary between g0.9 cm and g1.4 cm during the passage of the head through the recording window. At the same time, we see that a small amount of ambient fluid overrun by the head mixes inside, indicating that the lower value of the elevation corresponds to a lobe in the illuminated slice, while the upper value corresponds to a cleft. The lower elevation of the nose is in agreement with the results reported by Simpson and Britter (1979) and Simpson (1997), and with Simpson s law (1972), g=0.6hre )0.23, which predicts g0.89 cm in the present case. Figure 4 exhibits the flow field in the frame of reference of the head for the same gravity current shown in Fig. 3. The time-averaged velocity field (vectors) is superimposed on a grey-scale representation of the time-averaged fields of the speed (in-plane magnitude of velocity, Fig. 4a), vorticity (Fig. 4b) and shear strain (Fig. 4c). As expected, Fig. 4a shows that the ambient fluid, with uniform velocity far from the gravity current, is decelerated immediately ahead of (and at the same level as) the current and accelerated as it passes over the head of the current. Farther downstream, the velocity of the ambient fluid tends towards a constant value that is uniform with depth. A careful analysis shows a small flux of fluid towards the nose within the current, balancing the flux associated with the generation of fluid of intermediate density, which is then swept downstream of the head. The gradual reduction in the inner flux closer to the nose of the current indicates that this mixing process takes place (in the time-average sense) over a significant length of the gravity current head. Figure 4b demonstrates that the vorticity in the ambient fluid remains close to zero everywhere, as may be expected from an inviscid flow at the passage of the current. The generation of vorticity is confined to the boundary between the fluids and the bottom of the channel. Positive vorticity arises from the shear between the current and the ambient fluid, carried towards the left by the mean flow. Even though an instantaneous view of the current (not reported here) shows that the flow is unsteady with distinct vortex structures, the time-average pictures indicate that these structures are largely confined to a relatively narrow upper band near the nose that broadens downstream as the flow separates towards the rear of the head. At the same time, negative vorticity is generated by the passage of the current over the floor of the tank as a result of the no-slip boundary condition there. The structure of the shear strain field (Fig. 4c) is similar to that of the vorticity field (Fig. 4b). The main differences between these two fields are around the top of the nose of the current, where a negative shear strain is generated in the ambient fluid but relatively little strain is generated within the current. Although weak, the shear strain in the ambient flow indicates the existence of a region of viscous dissipation in the ambient fluid above the nose of the current. The low strain at the nose suggests the velocity of the recirculation flow approximately matches that of the ambient flow there. This observation is consistent with the absence of vortices in that zone. Downstream of the nose, the shear strain increases with the acceleration of the ambient fluid as it squeezes past the head. Kelvin Helmholtz instabilities grow in this strongly sheared region, disrupting the structure of the flow and leading to relatively high levels of dissipation. The irreversible mixing that occurs within these billows represents an additional loss of energy and is the source of most of the mixed fluid left in the wake of the current. We estimate the Richardson number Ri=g l/du 2, where l and Du are the thickness and the velocity variation in the layer, respectively, to be of the order of 0.01 at the front up to about 0.1 downstream. These values of Ri are consistent with the results of Britter and Simpson (1978). The instantaneous two-dimensional divergence (not shown here) in the vertical fluid slice shows zones of significant convergence/divergence, indicating lateral fluxes generated by the turbulence at the level of the billows. In contrast, the time-average divergence field is close to zero everywhere, indicating the mean flow is truly two-dimensional. In such a case, the two components of the velocity define the usual stream function (Batchelor 1974, p. 76) that provides a valuable picture of the flow field. However, when interpreting the approximate stream function, it is important to remember that the real flow is turbulent and three-dimensional, and that this twodimensional approximation is the result of the time averaging. As a consequence of the underlying turbulence, we might expect the transport across streamlines to be much greater than the molecular transport, with regions where Ñu and Ñw are aligned and large suffering the greatest dissipation. Contours of the approximate stream function w for Re4000 and 1200 are shown in Figs. 5a and 5b, respectively. As expected, the streamlines tend towards the horizontal at the top of the field of view located a few centimetres below the liquid free surface. The streamlines within the head confirm the existence of two circulation cells, corroborated by the analysis of the evolving particle paths in the movie of the streak image (an instantaneous picture is shown in Fig. 3b). For Re4000 the larger and stronger upper cell continually replenishes the fluid at the nose of the gravity current, ensuring the strong density gradients are maintained. The weak lower circulation cell is created by the boundary layer on the bottom dragging fluid back to the left. Note that Fig. 5a (Re4000) shows a stronger upper circulation cell than that found in Fig. 5b (Re1200). At higher Reynolds number this cell extends further forward and down, resulting in a reduced nose elevation and an increase in the shear strain in the upper boundary of the head. Another interesting feature visible in Fig. 5a is that the lower recirculation cell appears to be broken into several smaller cells. Careful study of the video sequences used to generate this figure shows bottom vortices slowly drifted towards the tail of

6 713 Fig. 4a c. Flow fields for a bottom current with Re4000. Vectors represent mean fluid velocities for selected points, which are superimposed to a grey-scale representation of the magnitude of: a In-plane speed. b Vorticity. c Shear strain the current in the frame of reference of the front. Therefore, the smallest cells at the floor depicted in Fig. 5a are remaining vortices that arise due to the finite time-averaging process carried out with the experimental data. These features qualitatively agree well with the results of Hartel et al. (2000). Of particular interest is the position of the ambient fluid stagnation streamline near the nose of the current.

7 714 Fig. 5. Streamlines for Re4000 (a) and Re1200 (b), represented for nonuniform distributed values of the stream function It was thought that this streamline intersected the top of the nose (Simpson and Britter 1979; Simpson 1997). However, the direct numerical simulations reported by Hartel et al. (2000) suggest that the stagnation point lies on the underside of the raised nose, although still forward of the point where the gravity current first makes contact with the ground. While the resolution of the present velocity measurements cannot determine the precise location of this stagnation point, the stagnation streamline appears to be under the nose before disappearing into the base of the current. This finding is reinforced by a careful analysis of the individual particle paths. Consequently, the current overruns less fluid than previously estimated due to some of this fluid being diverted back forward and around the current. In addition to the determination of the average velocity field of gravity currents, the velocity fluctuations describing the turbulence in the gravity current head are calculated. Although the turbulent fluctuations are always three-dimensional, the measurement technique only provides the in-plane component of the fluctuations. Nevertheless, this two-dimensional information provides a clear picture of the turbulent structure of the flow. Such an approach is frequently used in turbulent boundary layers, jets and wakes generated by two-dimensional boundary conditions. Figure 6a introduces the time-averaged square velocity fluctuations (u, v ) by means of vectors (i.e. magnitudes and orientation) and a grey scale (magnitude only), for the same gravity current advancing over a solid boundary for Re4000. Note that by definition both u and v are positive, hence all fluctuation vectors are oriented up and towards the right. The orientation of the vectors provides information about the relative magnitude of these two components. The magnitude of the fluctuation is directly related to the kinetic energy per unit volume associated with the turbulence. As expected, the maximum magnitude occurs in an upper band between the current and ambient fluids, in agreement with the vorticity and shear strain fields shown in Figs. 4b and 4c. There are also some fluctuations in the lower turbulent boundary layer adjacent to the bottom of the channel. At the left side of Fig. 6a, a band of small constant fluctuation within the current suggests that the small flux of fluid towards the nose is an outer region of both upper and lower turbulent boundary layers as mentioned in Kneller et al. (1999). The velocity fluctuations produce a stress on the mean flow (the Reynolds stress) because of correlations between u and v. High values of Reynolds stress indicate that the kinetic energy of the turbulence is increased due to a net deceleration on the average flow. In this case, the element of the Reynolds stress tensor is calculated from the correlation of the vertical and horizontal components of the velocity fluctuation at each point. In Fig. 6b a greyscale representation of the time-averaged magnitude of the in-plane Reynolds stress component is introduced. Note that the Reynolds stress is important especially in the region between the nose and the floor, and in some regions in the upper band. These high-stress regions are located on the band with high magnitude of fluctuation shown in Fig. 6a, but they do not fill the entire band, probably because the averaging interval is not long enough. The complete sequence of images shows how such high-stress patches that start somewhere in the leading part of the upper band are advected downstream in the wake. 4 Concluding remarks Particle-tracking velocimetry is used to study the structure of the head of inertial gravity currents under quasi-steady state conditions in a reference frame moving with the head. A time-averaging process made by software when the head passes through a fixed window extracts the twodimensional mean features of the flow. The particletracking method and the time-average process used give good results with a relatively lower-cost facility than those previously employed. The main fields and streamlines of the flow are determined and, consequently, the user is able to obtain results directly from experiments in addition to those suggested up to now only by analytical models and numerical simulations. Moreover, PTV even gives valuable qualitative information from the evolving streak images like those shown in Fig. 3b. When comparing the present results of the average structure with those reported by Kneller et al. (1999), a similar velocity map within the head is found. The vorticity and shear strain fields and the streamlines presented here complete the picture of the main flow. The high resolution offered by the technique introduced clearly indicates that dense fluid is supplied from the centre of the head to the leading edge by two main counter-rotating rolls whose intensities and positions depend on the Reynolds number.

8 715 Fig. 6. a Time-averaged square velocity fluctuations and b time-averaged Reynolds stress for a Re4000 gravity current This dense flux is very low and may be easily lost in the averaging for high Re because of turbulence. In addition to the time-average flow, the magnitude of the turbulent fluctuations and Reynolds stresses are calculated with the vertical and horizontal components of the fluid velocity. As expected, the upper boundary layer at the interface provides a viscous drag and Reynolds stress that reduces the Froude number. These distributions are consistent with the rest of the information presented here and with earlier experimental and numerical results. Models for predicting the sediment processes occurring in sediment gravity flows and in oceanic turbidity currents may be enhanced by the results reported. References Alahyari A, Longmire EK (1996) Development and structure of a gravity current head. Exp Fluids 20: Batchelor GK (1974) An introduction to fluid dynamics. Cambridge University Press, Cambridge Benjamin TB (1968) Gravity currents and related phenomena. J Fluid Mech 31: Britter RE, Linden PF (1980) The motion of the front of a gravity current travelling down an incline. J Fluid Mech 99: Britter RE, Simpson JE (1978) Experiments on the dynamics of a gravity current head. J Fluid Mech 88: Dalziel SB (1992) Decay of rotating turbulence: some particle tracking experiments. Appl Sci Res 49: Dalziel SB (1993) Rayleigh Taylor instability: experiments with image analysis. Dyn Atmos Oceans 20: Dalziel SB (1995) DigImage: system overview. Cambridge Environmental Research Consultants, Cambridge, UK Hartel C, Kleiser L, Michaud M, Stein CF (1997) A direct numerical simulation approach to the study of intrusion fronts. J Eng Math 32: Hartel C, Meiburg E, Necker F (2000) Analysis and direct numerical simulation of the flow at a gravity-current head. 1. Flow topology and front speed for slip and no- slip boundary. J Fluid Mech 418: Huppert HE, Simpson JE (1980) The slumping of gravity currents. J Fluid Mech 99: Kneller BC, Bennet SJ, McCaffrey WD (1999) Velocity structure, turbulence and fluid stresses in experimental gravity currents. J Geophys Res 104(C3):

9 Parsons JD, Garcia MH (1998) Similarity of gravity current fronts. Phys Fluids 10: Rottman JW, Simpson JE (1983) Gravity currents produced by instantaneous releases of a heavy fluid in a rectangular channel. J Fluid Mech 135: Simpson JE (1972) Effects of the lower boundary on the head of a gravity current. J Fluid Mech 53: Simpson JE (1997) Gravity currents: in the environment and the laboratory, 2nd edn. Cambridge University Press, Cambridge Simpson JE, Britter RE (1979) The dynamics of the head of a gravity current advancing over a horizontal surface. J Fluid Mech 94: