Abstract
We investigate the processes that arise when a wave front hits a natural obstacle in the form of a forest. The modeling is carried out in the framework of a single methodological approach that uses the Euler equation to describe the motion of the air mass both over an open area and inside the forest. In the latter case the equations include mass forces associated with the vegetation. The numerical solution is obtained by Godunov’s method using parallel programming techniques. Two types of incident wave front are investigated: a plane shockwave and a nonlinear acoustic impulse modeling a spherical explosion wave at a large distance from the source. The specific features of the interaction process, including penetration of the wave front into the forest, partial reflection from the near boundary, and diffraction above the top boundary, are investigated for different types of vegetation (coniferous and deciduous forests). The numerical results reveal the formation of a pair of ascending and descending currents in the upper part of the forest (inside the tree crowns). The existence of this structure is confirmed by experimental findings.
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References
D. Heimann, Influence of meteorological parameters on outdoor noise propagation, Euronoise Naples, 113-IP (2003).
D. Heimann, Meteorological aspects in modeling noise propagation outdoors, Euronoise Naples, 213-IP (2003).
V. P. Stulov, V. N. Mirskii, and A. N. Vislyi, Bolide Aerodynamics [in Russian], Nauka, Moscow (1995).
J. B. Keller, “A geometrical theory of diffraction,” in: Proc. Symp. App. Math., 8, Calculus of Variations and Its Applications, McGraw-Hill, New York (1958), pp. 27–52.
Z. Maekawa, “Noise reduction by screens,” Appl. Acoustics, 1, 157–173 (1968).
A. D. Pierce, “Diffraction of sound around corners and over wide barriers,” J. Acoust. Soc. Am., 55, 941–955 (1974).
D. J. Saunders and R. D. Ford, “A study of the reduction of explosive impulses by finite size barriers,” J. Acoust. Soc. Am., 94, 2859–2875 (1993).
C. F. Eyring, “Jungle acoustics,” J. Acoust. Soc. Am., 18, 267–277 (1946).
T. F. W. Embleton, “Sound propagation in homogeneous deciduous and evergreen woods,” J. Acoust. Soc. Am., 35, 1119–1125 (1963).
V. I. Kondratev and Yu. S. Kryukov, “Numerical computation of the diffraction of a nonlinear acoustic impulse signal on a rectangular ledge,” Akust. Zh., 46, No. 2, 220–227 (2000).
S. Courtier-Arnoux, “Modelisation parabolique tri-dimensionnelle de la propagation acoustique en milieu exterieur dun champ convecteur, dune topographie au sol dobtacle eventuels,” J. Physique, 51, 1209–1212 (1990).
M. A. Price, K. Attenborough, and N. W. Heap, “Sound attenuation through trees: measurements and models,” J. Acoust. Soc. Am., 84, 1836–1844 (1988).
A. Tunick, Coupling Meteorology to Acoustics in Forest, U.S. Army Research Laboratory, Adelphi, MD (2002).
S. H. Burns, “The absorption of sound by pine trees,” J. Acoust. Soc. Am., 65, 658–661 (1979).
A. S. Dubov, L. P. Bykova, and S. V. Marunich, Turbulence in Vegetative Cover [in Russian], Gidrometeoizdat, Leningrad (1978).
M. G. Boyarshinov, “Estimating the aftereffects of the transport of a gas cloud over a forest,” Izv. RAN, Fluid and Gas Mechanics, No. 4, 79–87 (2000).
A. M. Grishin, Mathematical Modeling of Forest Fires and New Fire-Fighting Methods [in Russian], Nauka, Moscow (1992).
D. Larom, M. Garstang, K. Payne, R. Raspet, and M. Lindeque, “The influence of surface atmospheric conditions on the range and area reached by animal vocalization,” J. Exp. Biology, 200, 421–431 (1997).
L. D. Landau and E. M. Lifshits, Theoretical Physics, Vol. 6, Hydrodynamics [in Russian], Nauka, Moscow (1986).
M. G. Lebedev and V. V. Sitnik, “Computing compressible gas flows with infinite velocity and pressure gradients,” Prikl. Mat. Informatika, No. 20, 40–57 (2005).
S. K. Godunov, A. V. Zabodin, M. Ya. Ivanov, A. N. Kraiko, and G. P. Prokopov, Numerical Solution of Multidimensional Problems in Fluid Dynamics [in Russian], Nauka, Moscow (1976).
A. N. Andrianov, S. K. Bazarov, and K. N. Efimkin, Solving Two-Dimensional Problems of Fluid Dynamics by Godunov’s Method on Parallel Computers Using the NORMA Language, IPM im. M. V. Keldysh RAN, Preprint No. 9 (1997).
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Translated from Prikladnaya Matematika i Informatika, No. 21, pp. 48–71, 2005.
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Lebedev, M.G., Sitnik, V.V. Modeling the interaction of a wave front with a forest. Comput Math Model 17, 226–242 (2006). https://doi.org/10.1007/s10598-006-0020-6
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DOI: https://doi.org/10.1007/s10598-006-0020-6