...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Journal of physics, A. Mathematical and theoretical >Submodels of the generalization of the Leith model of the phenomenological theory of turbulence and of the model of nonlinear diffusion in the inhomogeneous media without absorption
【24h】

Submodels of the generalization of the Leith model of the phenomenological theory of turbulence and of the model of nonlinear diffusion in the inhomogeneous media without absorption

机译：湍流现象学理论的Leith模型和不吸收的非均匀介质中非线性扩散模型的推广的子模型

获取原文
获取原文并翻译 | 示例
   

获取外文期刊封面封底 >>

       
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

We study a nonlinear equation which is equivalent to an equation of generalization of the Leith model of turbulence and to the equation of the model of nonlinear diffusion in an inhomogeneous media without absorption. Using this equation, all submodels admitting continuous Lie transformation groups, acting on the set of solutions of the equations of these submodels are obtained. For obtained submodels, all invariant submodels are found. All essentially distinct invariant solutions describing these invariant submodels are found explicitly, or their finding is reduced to solving nonlinear integral equations. The integral equations defining these solutions reveal new possibilities for analytical and numerical studies. The presence of arbitrary constants in these equations allows one to apply them to the study of different boundary value problems. We have proved the existence and uniqueness of the solution for some boundary value problems. We have investigated the following boundary value problems: (1) a distribution of front-density turbulent kinetic energy in a framework of the generalizion of the Leith model of wave turbulence for which either the spectrum and its wavenumber derivative or the spectrum and its time derivative are given at the initial moment of time at a fixed wavenumber; (2) a nonlinear diffusion process in an inhomogeneous media without absorption, for which either the concentration and its gradient or the concentration and its rate of change are given at the initial moment of time at a fixed point. Under certain additional conditions we have established the existence and uniqueness of the solutions to boundary value problems describing these processes.
机译：我们研究了一个非线性方程，该方程等效于湍流Leith模型的推广方程和在没有吸收的非均匀介质中的非线性扩散模型的方程。使用该方程式，获得所有允许连续Lie变换组的子模型，这些子模型都作用于这些子模型的方程组的解。对于获得的子模型，找到所有不变的子模型。明确找到了描述这些不变子模型的所有本质上不同的不变解，或者将它们的发现简化为求解非线性积分方程。定义这些解决方案的积分方程式为分析和数值研究揭示了新的可能性。这些方程中任意常数的存在使人们可以将它们应用于研究不同的边值问题。我们已经证明了某些边值问题解的存在性和唯一性。我们研究了以下边值问题：（1）在波湍流的Leith模型的泛化框架下，前密度湍流动能的分布，其谱或波数导数或谱及其时间导数在初始时刻以固定的波数给出; （2）在不吸收的非均质介质中的非线性扩散过程，在初始时间的固定点给出浓度及其梯度或浓度及其变化率。在某些附加条件下，我们已经建立了描述这些过程的边值问题解的存在性和唯一性。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号