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首页> 外文期刊>EPJ Web of Conferences >Advection of a passive scalar field by turbulent compressible fluid: renormalization group analysis near d = 4
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Advection of a passive scalar field by turbulent compressible fluid: renormalization group analysis near d = 4

机译：湍流可压缩流体对被动标量场的平流：d = 4附近的重归一化组分析

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The field theoretic renormalization group (RG) and the operator product expansion (OPE) are applied to the model of a density field advected by a random turbulent velocity field. The latter is governed by the stochastic Navier-Stokes equation for a compressible fluid. The model is considered near the special space dimension d = 4. It is shown that various correlation functions of the scalar field exhibit anomalous scaling behaviour in the inertial-convective range. The scaling properties in the RG+OPE approach are related to fixed points of the renormalization group equations. In comparison with physically interesting case d = 3, at d = 4 additional Green function has divergences which affect the existence and stability of fixed points. From calculations it follows that a new regime arises there and then by continuity moves into d = 3. The corresponding anomalous exponents are identified with scaling dimensions of certain composite fields and can be systematically calculated as series in y (the exponent, connected with random force) and ε = 4 ? d. All calculations are performed in the leading one-loop approximation.
机译：将场理论重归一化组（RG）和算子乘积展开（OPE）应用于由随机湍流速度场平移的密度场模型。后者由可压缩流体的随机Navier-Stokes方程控制。该模型在特殊空间维数d = 4附近被考虑。结果表明，标量场的各种相关函数在惯性对流范围内表现出异常的标度行为。 RG + OPE方法中的缩放属性与重归一化组方程的固定点有关。与物理上有趣的情况d = 3相比，在d = 4时，附加的格林函数具有发散性，这会影响不动点的存在和稳定性。从计算中可以得出，在那里出现了一个新的状态，然后通过连续性进入d =3。相应的异常指数可以用某些复合场的缩放尺寸来标识，并且可以系统地以y的序列计算（该指数与随机力有关） ）和ε= 4？ d。所有计算均以超前单循环逼近法执行。

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