تحليل تراز برخورد معادله بنجامين -بونا-ماهوني-برگرزدر (1+1) بعد

Level Crossing Analysis Of The Benjamin-Bona-Mahony-Burgers Equation in (1+1) Dimension

Introduction: In this paper we are planing to study the mean positive slopes which produced when the fluctuations of the velocity of a turbluent fluid is crossed by the level ux - ux =a in the Benjamin-Bona-Mahony-Burgers (BBM-B) equation. Here we just consentrate to the high Reynolde number limit and do the level crossing analysis where a ^ 0, p ^ 0 . (before the appearance of the schocks) Over aim in this paper is to show how the quantity v+a counts the fluctuations of the velocity in the Benjamin-Bona-Mahony-Burgers tutbulence. Aim: we calculated the mean positive slopes in the Benjamin-Bona-Mahony-Burgers equation in (1+1) dimensions using stochastic process methods. Materials and Method: In the Benjamin-Bona-Mahony-Burgers equation in (1+1) dimensions with stochastic force when the fluctuation of the velocity of a turbulent fluid is crossed by the level ux - ux =a we calculated the mean positive slopes crossing by the level ux - ux =a Results: In this paper we study of Benjamin-Bona-Mahony-Burgers equation in (1+1) dimensions with Gaussian correlated in space also we determined the average frequency of a positive slope when a certain level crosses the velocity in the BBM-B equation. The integral representation of v+a was given for BBM-B equation in the zero dispersion limit before the creation of shocks and it was shown that the velocity dependence of the v+a is Gaussian after all we have found that the total creation number of positive slopes for the BBM-b equation in the zero dispersion limit and before the creation of shocks scale 1 as 12. Conclusion: In this paper we study of Benjamin-Bona-Mahony-Burgers equation in (1+1) dimensions with Gaussian correlated in space also we determined the average frequency of a positive slope when a certain level crosses the velocity in the BBM-B equation . The integral representation of v+a was given for BBM-B equation in the zero dispersion limit before the creation of shocks and it was shown that the velocity dependence of the v+a is Gaussian after all we have found that the total creation number of positive slopes for the BBM-b equation in the zero dispersion limit and before the creation of shocks scale as