# Large Eddy Simulation and Dynamic Mode Decomposition of Turbulent Mixing Layers
## 1 Introduction  
Turbulent mixing layers are among the most important fundamental turbulent flows in nature and engineering [1; 2; 3]. In recent years, with the rapid development of computational technologies, large eddy simulation (LES) and direct numerical simulation (DNS) have become the widely used methods to study turbulent mixing layers. For example, [PERSON] and [PERSON] [4] implemented LES to investigate the influence of inlet disturbance on the large-scale spanwise and streamwise structure of turbulent mixing layers; [PERSON] et al. [5] used LES to study the influence of splitter plate cavity on the dynamic development of turbulent mixing layer; [PERSON] et al. [6] investigated the effect of multiple ring-like vortices on mixing in highly compressible turbulent mixing layer via DNS; [PERSON] and [PERSON] [7] studied the asymmetry of two different density fluids in turbulent mixing layers by DNS; [PERSON] et al. [8] analyzed the interactions of vortex, shock-wave and reaction in droplet laden supersonic turbulent mixing layer with DNS; [PERSON] and [PERSON] [9] found the effects of combustion mode on growth of reacting supersonic turbulent mixing layers through DNS. In these studies, high-precision numerical simulations have revealed many characteristics of turbulent mixing layers, thus continuously advancing the research frontier of turbulent mixing layers. In the process of high-precision numerical simulation, massive spatial and temporal flow field data will be generated. Extracting valuable information from these flow field data has become a research hotspot in fluid mechanics [10]. Existing methods of extracting flow information include proper orthogonal decomposition (POD) [11], dynamic mode decomposition (DMD) [12] and many others. Among these methods, DMD is a relatively new one. It obtains the main characteristics of unsteady flow by analyzing the flow field data acquired from numerical simulation or experimental measurement. DMD is only based onthe snapshot of the flow field and is not limited by the type of flow. DMD not only extracts the coherent structure, but also provides time evolution information of the flow field. These features indicate the excellent potential of the DMD. Taking this into consideration, the general performance of DMD as a method of extracting valuable information has been tested in various situations [13; 14; 15]. According to the results of these tests, standard DMD has been improved to be optimized DMD [16], sparsity-promoting DMD [17], streaming DMD [18], total DMD [19], recursive DMD [20], parametrized DMD [21], multi-resolution DMD [22], non-uniform DMD [23], extending DMD [24] as well as many others. Accompanied by the development of the method, DMD has been continuously applied to the studies in fluid dynamics, such as the investigations on turbulent mixing layers [25; 26], turbulent jet [27; 28; 29; 30; 31; 32; 33; 34; 35], turbulent wake [36; 37; 38; 20; 39; 40], turbulent boundary layers [41; 42; 43; 44; 45; 46], turbulent channel flow [47; 48; 49] and turbulent pipe flow [50; 51; 52]. The DMD method has already shown the applicability in the studies on turbulent mixing layers: [PERSON] et al. [25] carried out DNS on the spatially developing mixing layer issuing from two turbulent streams past a splitter plate, conducted modal analysis on the results by using DMD, obtained the dynamically relevant features of the mixing layer development, and found that it can single out the coherent eddies responsible for the development of the mixing layer. [PERSON] et al. [26] simulated the subsonic-supersonic mixing layer with three convective Mach numbers by using high-order scheme DNS and carried out modal analysis on the results using DMD. It was found that there was a certain dominant frequency in the flow structure, which can provide a reference for the design of active mixing enhancement method. Since the DMD method has only been proposed for about 10 years, its application in the study of turbulent mixing layers is still scarce.