The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface
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...VI. Figure 2, reproduced from Huppert (1982b), presents various patterns that emerge when a fluid sheet is released on an inclined plane....
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...In geology, they appear as gravity currents under water or as lava flows (Huppert and Simpson, 1980; Huppert, 1982a)....
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...The comparison between our theoretical results and the experimental ones presented by Didden & Maxworthy (1982) for the axisymmetric spreading of salt water into fresh water is also very good....
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...The current is thus identical with one propagating with a free surface beneath fluid of negligible inertia. The resulting nonlinear partial differential equations have similarity solutions which yield the shape and rate of propagation of the current. For a = 1, the only case considered by Didden & Maxworthy, the calculated functional forms of the position of the front of the current as a function of time are the same as evaluated by them. Further, our calculated value for the constant of proportionality is in excellent agreement with those presented for axisymmetric currents by Britter (1979) and by Didden & Maxworthy, but 10 % higher than that presented by Didden & Maxworthy for two-dimensional currents....
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...They also determined for t + t , dimensional relationships between the position of the front as a function of time and the external parameters. In a series of experiments they verified the functional forms of the position-versus-time relationships and evaluated the constants of proportionality from their experimental measurements. Previous studies of low-Reynolds-number gravity currents include those by Fay (1969) and Hoult (1972), who analysed the release of a fixed volume of relatively light fluid flowing under a free surface....
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...These values were determined by dropping a series of different size ball bearings in the oil contained in a measuring cylinder and recording the terminal velocities. This approach led to errors of less than 1 Yo in determining the coefficients of viscosity. The experiments were designed to examine a new theory for the spreading of volcanic lava domes by Huppert et al. (1982) and further details of the experiments and geological applications can be found in that paper....
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...(The relationships (2.15) and (2.27), used to commence the integration of the differential equations, are obtained from them and are not an externally imposed condition.) This lack of influence of the front will be true only if the Reynolds number is low and the Bond number is high. High-Reynolds-number gravity currents are totally controlled by conditions at the front, and many theoretical and experimental studies have been devoted almost entirely to determining the controlling condition, or Froude number, at the front (see, e.g. Benjamin 1968; Britter t Simpson 1978; Huppert & Simpson 1980). The front of a surface-tension-dominated (low-Bond-number) gravity current also plays an essential role in determining its spreading rate, as documented for example by Greenspan (1978) and Hocking (1981). However, while our approach has been successful in predicting the overall shape - as evidenced by the experimental measurements of height presented in $3 - it should not be thought that the vertical front common to all the solutions is realistic....
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