Fisher equation with turbulence in one dimension
نویسندگان
چکیده
We investigate the dynamics of the Fisher equation for the spreading of micro-organisms in one dimenison subject to both turbulent convection and diffusion. We show that for strong enough turbulence, bacteria , for example, track in a quasilocalized fashion (with remakably long persistance times) sinks in the turbulent field. An important consequence is a large reduction in the carrying capacity of the fluid medium. We determine analytically the regimes where this quasi-localized behavior occurs and test our predictions by numerical simulations.
منابع مشابه
The comparison of optimal homotopy asymptotic method and homotopy perturbation method to solve Fisher equation
In recent years, numerous approaches have been applied for finding the solutions of functional equations. One of them is the optimal homotopy asymptotic method. In current paper, this method has been applied for obtaining the approximate solution of Fisher equation. The reliability of the method will be shown by solving some examples of various kinds and comparing the obtained outcomes with the ...
متن کاملThe one - dimensional complex Ginzburg - Landau equation in the low dissipation limit
Turbulent solutions of the one-dimensional complex Ginzburg-Landau equation when the dissipation is very small aie considered. It is found that probability distributions are strictly Gaussian, implying hard turbulence does not occur. Also. no inertial range is observed in ule wavenumber spect”. As expected a linear relation between the atuacfor dimension and the domain length exists, but the re...
متن کاملOn the exact and numerical solution of the time-delayed Burgers equation
A number of nonlinear phenomena in many branches of sciences such as physical [6], chemical, economical [20] and biological processes [15,14] are described by the interplay of reaction and diffusion or by the interaction between convection and diffusion. One of the well-known partial differential equations (PDEs) which governs a wide variety of them is Burgers equation, which provides the simpl...
متن کاملProbability Density, Diagrammatic Technique, and Epsilon Expansion in the Theory of Wave Turbulence
We apply the methods of Field Theory to study the turbulent regimes of statistical systems. First we show how one can find their probability densities. For the case of the theory of wave turbulence with four-wave interaction we calculate them explicitly and study their properties. Using those densities we show how one can in principle calculate any correlation function in this theory by means o...
متن کاملA fractal model for large eddy simulation of turbulent flow
A new class of subgrid closures for large eddy simulation (LES) of turbulence is developed, based on the construction of synthetic, fractal subgrid-scale fields. The relevant mathematical tool, fractal interpolation, allows to interpolate the resolved velocity with fields that have fluctuations down to much smaller scales and to compute the required stresses explicitly. In one dimension, the ap...
متن کامل