Niven Robert K
School of Engineering and Technology, The University of New South Wales, Canberra, ACT 2600, Australia.
Entropy (Basel). 2023 Nov 11;25(11):1538. doi: 10.3390/e25111538.
The aim of this study is to explore the insights of the information-theoretic definition of similarity for a multitude of flow systems with wave propagation. This provides dimensionless groups of the form Πinfo=U/c, where is a characteristic flow velocity and is a signal velocity or wave celerity, to distinguish different information-theoretic flow regimes. Traditionally, dimensionless groups in science and engineering are defined by based on ratios of length scales; based on ratios of velocities or accelerations; and based on ratios of forces. In Part I, an additional category of was proposed based on ratios of (i) entropy production terms; (ii) entropy flow rates or fluxes; or (iii) information flow rates or fluxes. In this Part II, the information-theoretic definition is applied to a number of flow systems with wave phenomena, including acoustic waves, blast waves, pressure waves, surface or internal gravity waves, capillary waves, inertial waves and electromagnetic waves. These are used to define the appropriate Mach, Euler, Froude, Rossby or other dimensionless number(s)-including new groups for internal gravity, inertial and electromagnetic waves-to classify their flow regimes. For flows with wave dispersion, the coexistence of different celerities for individual waves and wave groups-each with a distinct information-theoretic group-is shown to imply the existence of more than two information-theoretic flow regimes, including for some acoustic wave systems (subsonic/mesosonic/supersonic flow) and most systems with gravity, capillary or inertial waves (subcritical/mesocritical/supercritical flow). For electromagnetic wave systems, the additional vacuum celerity implies the existence of four regimes (subluminal/mesoluminal/transluminal/superluminal flow). In addition, entropic analyses are shown to provide a more complete understanding of frictional behavior and sharp transitions in compressible and open channel flows, as well as the transport of entropy by electromagnetic radiation. The analyses significantly extend the applications of entropic similarity for the analysis of flow systems with wave propagation.
本研究的目的是探讨信息论中相似性定义对众多具有波传播的流动系统的见解。这给出了形式为Πinfo = U/c的无量纲组，其中U是特征流速，c是信号速度或波速，用于区分不同的信息论流动状态。传统上，科学和工程中的无量纲组是基于长度尺度的比值定义的；基于速度或加速度的比值定义的；以及基于力的比值定义的。在第一部分中，基于（i）熵产生项的比值；（ii）熵流率或通量；或（iii）信息流率或通量，提出了另一类无量纲组。在本第二部分中，信息论定义被应用于一些具有波动现象的流动系统，包括声波、冲击波、压力波、表面或内重力波、毛细波、惯性波和电磁波。这些被用于定义适当的马赫数、欧拉数、弗劳德数、罗斯比数或其他无量纲数——包括用于内重力波、惯性波和电磁波的新组——以对其流动状态进行分类。对于具有波色散的流动，单个波和波群存在不同的波速——每个都有一个独特的信息论组——这表明存在不止两种信息论流动状态，包括一些声波系统（亚声速/中声速/超声速流动）以及大多数具有重力、毛细或惯性波的系统（亚临界/中临界/超临界流动）。对于电磁波系统，额外的真空波速意味着存在四种状态（亚光速/中光速/跨光速/超光速流动）。此外，熵分析表明能更全面地理解可压缩和明渠流动中的摩擦行为和急剧转变，以及电磁辐射的熵传输。这些分析显著扩展了熵相似性在具有波传播的流动系统分析中的应用。
