The forced Burgers equation is linearized and investigated in the case when the forcing is the product of a distribution (a derivative of a dirac delta function) multiplied by an arbitrary function of time: G(x,t) = δ′(x)F(t). In the case when F(t) is a deterministic function of time, explicit solutions are obtained and the asymptotic behaviour is analyzed for different choices of F(t). The case when F(t) is random Gaussian noise and weakly correlated, is also analyzed. Explicit expressions are obtained for the statistical average of the solution and for some relevant correlation functions. In the large time and long wavelength limit, the two-time correlation function of the system, exhibits a scaling behaviour of diffusive type.
The Burgers equation under deterministic and stochastic forcing
DE LILLO, Silvana
1996
Abstract
The forced Burgers equation is linearized and investigated in the case when the forcing is the product of a distribution (a derivative of a dirac delta function) multiplied by an arbitrary function of time: G(x,t) = δ′(x)F(t). In the case when F(t) is a deterministic function of time, explicit solutions are obtained and the asymptotic behaviour is analyzed for different choices of F(t). The case when F(t) is random Gaussian noise and weakly correlated, is also analyzed. Explicit expressions are obtained for the statistical average of the solution and for some relevant correlation functions. In the large time and long wavelength limit, the two-time correlation function of the system, exhibits a scaling behaviour of diffusive type.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
