Interfacial turbulence in falling liquid films

降膜是一个对流不稳定的开流流体动力学系统，具有丰富的时空结构和一系列的波动不稳定性和相变序列，这些都是一大类流体动力学和其他非线性系统的共性：入口处的白噪声，线性不稳定性的滤波机制，将一次波场转换为二维(2D-1+1维)孤立脉冲的二次调制，最终将2D脉冲转变为完全发展的三维(3D-2+1维)波系。这一演变阶段通常被称为“界面湍流”。这是一种低维时空混沌或另一种“弱/耗散湍流”：事实上，尽管系统表面上很复杂，人们仍然可以在看起来是随机扰动的表面上识别3D孤立脉冲。然后，3D脉冲成为基本过程，使得胶片的动力学可以被描述为这些脉冲的叠加。因此，下降液膜可以作为研究弱/耗散湍流的典型参照系。除了纯粹的理论兴趣外，下降液膜在开发各种工程和技术应用中的高效传热和传质手段方面发挥着核心作用，如蒸发器、热交换器、吸收塔、洗涤器、精馏塔、结晶器和降膜反应器。这主要是由于在相对较小的流速下，降膜的传热和传质阻力很小。在薄膜的自由表面施加2D/3D孤立脉冲可以进一步降低这种阻力，这通常会显著增强传热和传质。因此，几十年来，液膜的下降一直是基础和应用研究的主题，这并不令人惊讶。然而，尽管降膜上的波动演化已经得到了一些进展和相当大的关注，但仍然有大量的问题和问题没有得到解决，特别是三维孤立脉冲的相互作用和最终过渡到界面湍流的问题，仍然没有得到我们的解决。为了回答这些问题，本项目的主要研究领域是关于降膜上三维孤立脉冲相干结构理论的理论发展，其主要目的是促进我们对界面湍流的理解。

A falling film is a convectively unstable open-flow hydrodynamic system with a rich variety of spatial/temporal structures and a sequence of wave instabilities and transitions which are generic to a large class of hydrodynamic and other nonlinear systems: white noise at the inlet, filtering mechanism of linear instability, secondary modulation that transforms the primary wave field into two-dimensional (2D -- 1+1 dimensions) solitary pulses and eventually transition of the 2D pulses into a fully developed three-dimensional (3D -- 2+1 dimensions) wave regime. This stage of the evolution is frequently referred to as `interfacial turbulence'. This is low-dimensional spatio-temporal chaos or alternatively `weak/dissipative turbulence': indeed, despite the apparent complexity of the system one can still identify 3D solitary pulses in what appears to be a randomly disturbed surface. 3D pulses then become elementary processes so that the dynamics of the film can be described as a superposition of these pulses. Hence, a falling liquid film can serve as a canonical reference system for the study of weak/dissipative turbulence.In addition to the purely theoretical interest, falling liquid films play a central role in the development of efficient means of heat and mass transfer in a wide variety of engineering and technological applications, such as evaporators, heat exchangers, absorbers, scrubbers, rectification columns, crystallizers and falling film reactors. This is mainly due to the small heat and mass transfer resistance of a falling film at relatively small flow rates. This resistance is further decreased by the presence of 2D/3D solitary pulses at the free surface of the film mentioned earlier which typically lead to a significant enhancement of heat and mass transfer.Not surprisingly, therefore, falling liquid films have been a topic of fundamental and applied research for several decades. However,despite the several developments and considerable attention that wave evolution on a falling film has received, a large number of issues and problems have not been resolved, and in particular, the interaction of 3D solitary pulses and eventual transition to interfacial turbulence, still elude us. In an attempt to answer these questions, the field of research to be pursued during the tenure of this project concerns the theoretical development of a coherent structures theory of 3D solitary pulses on a falling film with the principal aim to advance our understanding of interfacial turbulence.