Interfacial turbulence in falling liquid films

降膜是一种对流不稳定的开流流体动力系统，具有丰富多样的时空结构和一系列的波动不稳定性和过渡，这是一大批流体动力系统和其他非线性系统的共性。入口的白噪声，线性不稳定的滤波机制，将初级波场转变为二维（2D - 1+1维）孤立脉冲并最终将二维脉冲转变为完全发展的三维（3D - 2+1维）波态的二次调制。这一演化阶段通常被称为“界面湍流”。这是一种低维时空混沌，或者说是“弱/耗散湍流”：事实上，尽管系统看起来很复杂，但人们仍然可以在看似随机扰动的表面上识别出3D孤立脉冲。三维脉冲随后成为基本过程，因此薄膜的动力学可以被描述为这些脉冲的叠加。因此，下降的液膜可以作为研究弱/耗散湍流的典型参考系统。除了纯粹的理论兴趣之外，降液膜在各种工程和技术应用中，如蒸发器、热交换器、吸收器、洗涤器、精馏塔、结晶器和降膜反应器等，在高效传热和传质手段的发展中起着核心作用。这主要是由于在相对小的流速下，下降膜的传热传质阻力小。在前面提到的薄膜的自由表面存在2D/3D孤立脉冲，这通常会导致传热和传质的显着增强，从而进一步降低这种阻力。因此，几十年来，下落的液体薄膜一直是基础研究和应用研究的主题，这并不奇怪。然而，尽管在下降膜上的波演化已经得到了一些发展和相当大的关注，但大量的问题和问题尚未得到解决，特别是三维孤立脉冲的相互作用和最终过渡到界面湍流，仍然使我们无法解决。为了回答这些问题，本项目将在其任期内进行的研究领域涉及在下降膜上的三维孤立脉冲的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.