Nonlinear dynamics of directed acoustic waves in stratified and homogeneous liquids and gases with~arbitrary equation of state
Abstract
A method of separating one-dimensional disturbances into components propagating upwards and downwards and the stationary one in a stratified medium was developed. The system of equations is split into three coupled nonlinear equations of interacting components. Weak nonlinear evolution formulae for the directed and stationary components of a medium with an arbitrary equation of state were obtained. The wave components treated by the numerical calculations keep their propagation direction, even for quite large initial amplitudes. The results of the numerical simulation are presented. The examples demonstrate a nonlinear evolution of the wave propagating downwards for both the models of the atmosphere: the exponentially stratified model and the homogeneous one.References
[1] A.S. Monin and A.M. Obukhov, The small oscillations of atmosphere and adaptation of meteorological fields [in Russian], Izv. AN SSSR, Geophysics, 41, 1360–1373 (1958).
[
2] V.A. Gordin, Mathematical problems of hydrodynamic weather prediction. The analytical aspects [in Russian], Gydrometeoizdat, Leningrad 1987, p. 256.
[3] L.M. Brekhovskich and A.O. Godin, Acoustics of layered media, Springer-Verlag, Berlin 1990, p. 141.
[4] S.B. Leble, Nonlinear waves in waveguides with stratification, Springer-Verlag, Berlin 1990, p. 163.
[5] A.A. Perelomova, Construction of directed disturbances in one-dimensional isothermal atmosphere model, Izv. RAN, Physics of Atm. Ocean, 29, 1, 47–50 (1993).
[6] A.A. Perelomova, Generation conditions and nonlinear sound directed propagation in inhomogeneous medium, EAA Symposium, Gdansk–Jurata, 189–194 (1997).
[7] Yu.V. Brezhnev, S.B. Leble and A.A. Perelomova, Nonlinear effects and one-dimensional sound propagation in inhomogeneous gas media, Physical Express, 41, 29–37 (1993).
[8] A.A. Perelomova, Nonlinear dynamics of vertically propagating acoustic waves in a stratified atmosphere, Acta Acustica, 84, 6, 1002–1006 (1998).
[9] M.B. Vinogradova, O.V. Rudenko and A.P. Sukhorukov, Theory of waves [in Russian], Nauka, Moscow 1979, p. 383.
[10] O.V. Rudenko and S.I. Soluyan, Theoretical foundations of nonlinear acoustics, Consultants Bureau, Plenum, 1977, p. 287.
[
2] V.A. Gordin, Mathematical problems of hydrodynamic weather prediction. The analytical aspects [in Russian], Gydrometeoizdat, Leningrad 1987, p. 256.
[3] L.M. Brekhovskich and A.O. Godin, Acoustics of layered media, Springer-Verlag, Berlin 1990, p. 141.
[4] S.B. Leble, Nonlinear waves in waveguides with stratification, Springer-Verlag, Berlin 1990, p. 163.
[5] A.A. Perelomova, Construction of directed disturbances in one-dimensional isothermal atmosphere model, Izv. RAN, Physics of Atm. Ocean, 29, 1, 47–50 (1993).
[6] A.A. Perelomova, Generation conditions and nonlinear sound directed propagation in inhomogeneous medium, EAA Symposium, Gdansk–Jurata, 189–194 (1997).
[7] Yu.V. Brezhnev, S.B. Leble and A.A. Perelomova, Nonlinear effects and one-dimensional sound propagation in inhomogeneous gas media, Physical Express, 41, 29–37 (1993).
[8] A.A. Perelomova, Nonlinear dynamics of vertically propagating acoustic waves in a stratified atmosphere, Acta Acustica, 84, 6, 1002–1006 (1998).
[9] M.B. Vinogradova, O.V. Rudenko and A.P. Sukhorukov, Theory of waves [in Russian], Nauka, Moscow 1979, p. 383.
[10] O.V. Rudenko and S.I. Soluyan, Theoretical foundations of nonlinear acoustics, Consultants Bureau, Plenum, 1977, p. 287.
