Network: Wave-flow interactions

在许多环境和工业应用中遇到的流体动力学是流动运动和波传播的复杂混合。水流和波浪可以以各种方式相互作用：水流可以产生波浪，正如我们熟悉的由连续性产生的噪音的例子所证明的那样，但波浪也会产生水流运动，就像海面波浪迫使沿岸水流运动一样。了解流体和波之间相互作用的性质是流体动力学中的一个重要问题，具有广泛的应用。这也是一个非常困难的问题：首先，什么是运动流体中的波的定义并不简单。波流相互作用的研究目前在英国蓬勃发展：几个小组致力于这个问题的不同方面，特别是在地球物理流动的背景下。他们考虑不同类型的流动和波，并使用不同的技术（分析，数值，实验）。然而，这些小组研究的问题背后的数学模型有许多共同点，如果小组之间能够开始合作，那将是非常有益的。这是拟议网络的目标。通过年度会议和小规模讲习班，它将促进具有互补专长的研究人员之间的互动，以便有效应对当前的挑战。首先是波和流之间的分离。在这里，我们要寻找的是合适的数学定义和实际方法，以确定流体运动的哪些分量可以被视为流动和波。第二个问题是关于流体自发产生波的问题。当考虑比非色散波更复杂的情况时，这在很大程度上仍然是开放的。第三个问题是由控制大气环流的某些部分的波产生鲁棒的平均流。这里的挑战将是超越目前的理论，往往局限于对称的平均流量，并模拟耗散和非耗散的相互作用。第四个问题是表面波和洋流之间的相互作用，并应用于反常波和海啸波传播的建模。这四个问题与网络成员互动中出现的其他问题相辅相成。

The dynamics of the fluids encountered in many environmental and industrial applications is a complicated mixture of flow motion and wave propagation. Flows and waves can interact in a variety of ways: flows can generate waves, as the familiar example of turbulence-generated noise demonstrates, but waves also generate flow motion, as in the case of along-shore currents forced by sea-surface waves. Understanding the nature of the interaction between flows and waves is a problem of central importance in fluid dynamics, with a broad range of applications. It is also a very difficult problem: for a start, the very definition of what is a wave in a moving fluid is not straighforward. Research on wave-flow interactions is currently buoyant in the UK: several groups work on different aspects of the problem, especially in the context of geophysical flows. They consider different types of flows and waves and use different techniques (analytical, numerical, experimental). However, there are many commonalities in the mathematical models underlying the problems these groups study, and it would be highly beneficial if collaborations between the groups could be initiated. This is the aim of the proposed Network. Through yearly meetings and small-scale workshops, it will stimulate interactions between researchers with complementary expertises, so that current challenges can be tackled efficiently.Four problems have been identified to start collaborative work. A first is the separation between waves and flow. Here what will be sought are both suitable mathematical definitions and practical means of identifying which components of fluid motion can be regarded as flow and as waves. A second problem concerns the spontaneous generation of waves by flow. This remains largely open when situations more complex than that of non-dispersive waves are considered. A third problem is the generation of robust mean flows by waves, of the type that controls some part of the atmospheric circulation. The challenge here will be to go beyong the current theory, often limited to symmetric mean flows, and to model both dissipative and non-dissipative interactions. A fourth problem is that of the interaction between surface waves and ocean currents, with applications to the modelling of freak waves and tsunami-wave propagation. These four problems with be complemented by others which will emerge from the interactions of the Network members.