Non-Stationary Helical 3D Rivulet-Flows of Viscous-Plastic Incompressible Non-Newtonian Fluid

IF 2 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2026-08-09 Epub Date: 2026-05-13 DOI:10.1002/mma.70747

S. V. Ershkov, E. S. Baranovskii, A. V. Yudin

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引用次数: 0

Abstract

The novel case of nonstationary flows of helical type governed by gravity-driven viscous-plastic flow dynamics derived for incompressible non-Newtonian fluid is investigated here analytically in case of given (constant) value of Bernoulli-function. In such types of flow, the velocity is linearly and spatially dependent on curl field. Conditions for the existence of the exact solution for the aforementioned type of flows are obtained. Equations of momentum, continuity, and that one for the components of stress tensor are studied. The spatial and time-dependent structure of pressure field of the fluid flow should be determined via constant Bernoulli-function if components of the velocity of the flow are already obtained. It is remarkable that the case of non-stationary helical or Beltrami flow for incompressible gravity-driven viscous-plastic flow governed by three-dimensional equations has been investigated for the first time to the best of our knowledge.

MSC Classification: 35Q35, 76D17

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粘塑性不可压缩非牛顿流体的非平稳螺旋三维流

本文对不可压缩非牛顿流体在伯努利函数给定（常数）值的情况下，由重力驱动的非平稳螺旋型流动动力学进行了解析研究。在这种类型的流中，速度是线性和空间依赖于旋度场。得到了上述类型流的精确解存在的条件。研究了动量方程、连续性方程和应力张量分量方程。如果流体流动速度的分量已经确定，则应通过常数伯努利函数确定流体流动压力场的时空结构。值得注意的是，据我们所知，首次研究了三维方程控制的不可压缩重力驱动粘塑性流的非平稳螺旋流或贝尔特拉米流。MSC分类：35Q35, 76D17

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.