Generation of equations for shell models of turbulence in the Maple system

The paper describes a technology for the automated compilation of equations for shell models of turbulence in the computer algebra system Maple. A general form of equations for the coefficients of nonlinear interactions is given, which will ensure that the required combination of quadratic invariants and power-law solutions is fulfilled in the model. Described the codes for the Maple system allowing to generate and solve systems of equations for the coefficients. The proposed technology allows you to quickly and accurately generate classes of shell models with the desired properties.

Construction of complex shell models of MHD turbulence in computer algebra systems

The paper describes the developed by authors technique for construct-ing complex shell models of turbulence. The compilation of the equa-tions of this model and its exactly solution are implemented using by computer algebra system. The technique allows one to vary the sizes of nonlocality of nonlinear interaction in the space of scales, expressions for shell analogues of conservation laws, and the nature of stationary solutions with different power distribution.

Application of computer algebra for the construction of shell models of turbulence

The technique for automatic constructing of shell models of turbulence has been developed. The compilation of a model equations and its exactly solution is implemented using computer algebra (symbolic calculation) systems. The technique allows one to vary the scaling nonlocality of nonlinear interaction, form of expressions for conservation laws in models, and the form of stationary solutions with power distributions to scales.