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Wake Interactions of a Small Uncrewed Aerial System with a Moving Vehicle 小型无人机系统与移动飞行器的尾流相互作用
IF 2.3 3区 工程技术 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-12-09 DOI: 10.1007/s00348-024-03930-w
David Lee, John Hrynuk

This study presents an experimental investigation of the aerodynamics relevant to the landing of a small Uncrewed Aerial System on a fast-moving ground vehicle. A Representative Ground Vehicle and small Uncrewed Aerial System have been constructed for experimental measurements of the wake interactions in a low-speed, recirculating wind tunnel. Quantitative flow image techniques are employed to probe how the sUAS interacts with the wake structures shed by the ground vehicle when the two are in close proximity. Tools are developed for quantitative comparisons of flow fields and turbulence spectra. Using this tool, it is possible to identify regions of the flow and relative positions of the two vehicles where wake interactions are mostly linear in nature. This near-linear wake interaction was observed to extend to the wake spectra in regions where the time-averaged flow fields were also near-linear. Finally, it is shown that these observations of a near-linear wake interaction do not hold when the sUAS interacts with highly decelerated regions of the ground vehicle wake.

本研究提出了一项空气动力学的实验研究相关的一个小型无人空中系统降落在一个快速移动的地面车辆。建立了具有代表性的地面飞行器和小型无人机系统,用于低速循环风洞中尾流相互作用的实验测量。采用定量流动图像技术,研究了当地面飞行器与sUAS近距离接触时,sUAS与尾迹结构的相互作用。开发了流场和湍流谱定量比较的工具。使用这个工具,可以识别流动区域和两个飞行器的相对位置,其中尾迹相互作用在本质上大多是线性的。观察到这种近似线性的尾迹相互作用扩展到时间平均流场近似线性的区域的尾迹谱。最后,研究表明,当sUAS与地面车辆尾流的高度减速区域相互作用时,这些近线性尾流相互作用的观测结果并不成立。
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引用次数: 0
On formation and breakup of jets during droplet impact on oscillating substrates 液滴撞击振荡基底时射流的形成与破裂
IF 2.3 3区 工程技术 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-12-06 DOI: 10.1007/s00348-024-03911-z
Aditya Potnis, Abhishek Saha

Droplet impact on substrates is the cornerstone of several processes relevant to many industrial applications. Imposing substrate oscillation modifies the impact dynamics and can, therefore, be used to control the ensuing heat, mass, and energy transfer between the substrate and the impacting droplet. Previous research has shown that substrate oscillation strongly influences the spreading behavior of the droplet. In this study, we extend this understanding to examine how substrate oscillations can further modulate the retraction dynamics of the droplet, consequently affecting its long-term behavior, with a particular focus on induced jetting and subsequent breakup. We systematically examine the breakup of jets formed by the recoiling droplet through experimental investigations across a range of oscillation frequencies and amplitudes. Our findings reveal two distinct jet breakup modes: early and late, each governed by different time scales. Subsequently, we present a mechanistic description of the jetting process. Furthermore, we derive a simple scaling analysis based on energy balance to identify the critical condition required for jet breakup. Finally, we compare the experimental data with the scaling analyses to show its efficacy.

液滴对基材的影响是与许多工业应用相关的几个过程的基石。施加基材振荡可以改变冲击动力学,因此可以用来控制基材和冲击液滴之间的热、质量和能量传递。以往的研究表明,衬底振荡强烈影响液滴的扩散行为。在这项研究中,我们扩展了这一理解,以研究基底振荡如何进一步调节液滴的收缩动力学,从而影响其长期行为,特别关注诱导喷射和随后的破裂。通过一系列振荡频率和振幅的实验研究,我们系统地研究了由反冲液滴形成的射流的破裂。我们的研究结果揭示了两种不同的射流分裂模式:早期和晚期,每种模式都受不同的时间尺度支配。随后,我们提出了喷射过程的机械描述。此外,我们推导了一个基于能量平衡的简单标度分析,以确定射流破碎所需的临界条件。最后,将实验数据与标度分析结果进行对比,验证了该方法的有效性。
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引用次数: 0
Using unmanned aerial systems for observations of water wave characteristics 利用无人机系统观测水波特性
IF 2.3 3区 工程技术 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-12-04 DOI: 10.1007/s00348-024-03922-w
Vivek Bheeroo, Soo Bum Bae, Mu-Jung Lee, Scott A. Socolofsky, Kuang-An Chang

Dominant wave components within a wavefield play key hydrodynamic and morphodynamic processes. Herein, we present a method to detect and measure the parameters of these waves, such as their wavelength, propagation angle and period. Image sequences of the free surface are captured with the use of a commercial unmanned aerial system. A snapshot proper orthogonal decomposition analysis is then applied to the image sequence, and a 2D autocorrelation is performed on the resulting modes. By extracting the mode that is representative of the dominant wave signal, it is then possible to infer the wave properties of the dominant wave. The outlined procedure is applied to ocean swells, wind waves, free surface undulations along a river and propagating ship wakes. Our results demonstrate an improvement in the signal-to-noise ratio of the peak wave signal to ambient noise over the more widely used fast Fourier transform approach.

波场中的主要波分量起着关键的水动力和形态动力作用。在此,我们提出了一种检测和测量这些波的波长、传播角和周期等参数的方法。使用商用无人机系统捕获自由表面的图像序列。然后对图像序列进行快照适当的正交分解分析,并对所得模式进行二维自相关。通过提取代表主导波信号的模态,就可以推断主导波的波动特性。概述的程序适用于海浪,风浪,沿河流的自由表面波动和传播的船舶尾迹。我们的结果表明,与更广泛使用的快速傅立叶变换方法相比,峰值波信号与环境噪声的信噪比有所改善。
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引用次数: 0
Experimental investigation on boundary-layer streaks induced by grid-generated free-stream turbulence in a water channel 水道网格自由湍流边界层条纹的实验研究
IF 2.3 3区 工程技术 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-12-03 DOI: 10.1007/s00348-024-03917-7
Tristan M. Römer, Markus J. Kloker, Ulrich Rist, Christoph Wenzel

In this study, the influence of various turbulence-grid configurations is analysed on both the induced free-stream turbulence (FST) and the resulting Klebanoff modes/streaks developing in a laminar flat-plate boundary layer downstream in a laminar water channel. All results are based on hot-film and particle image velocimetry measurements as well as visualizations. The grid design and installation has been done according to common grid installation recommendations to ensure homogeneous FST causing meandering Klebanoff modes inside the boundary layer. But it was found that (i) the Klebanoff modes do not meander for all grid configurations, (ii) not all configurations cause Klebanoff modes with the expected temporal and spatial behaviour, and (iii) for some configurations, the spanwise streak spacing is strictly locked to the grid spacing (mesh width). As these observations are unreported in the literature, this study is aimed at a thorough description of the influence of key grid parameters on the FST and the resulting streaks within the boundary layer. The investigation includes the grid parameters typically reported, such as the grid-bar diameters, the associated Reynolds numbers, or the streamwise placement of the grid, but now also the grid-orientation order (horizontal/vertical or vertical/horizontal order of grid bars of the dual-plane grid), the wall-normal position of the horizontal bars relative to the leading edge of the flat plate, and the existence of palpable imperfections in the manufactured grids. The Reynolds-number range covered lies well in the lower band of wind-tunnel experiments. Thus, this study suggests that the reliability and reproducibility of future experimental studies on FST would be greatly improved if they demonstrated homogeneity in the free-stream in both spanwise and wall-normal directions, documented the ongoing meandering and wavelengths of the generated Klebanoff modes and thus (implicitly) documented the spanwise independence of the results in the temporal mean. The latter is a prerequisite for the reliable investigation of FST/isolated-roughness interactions.

Graphical abstract

在本研究中,分析了不同的湍流网格结构对层流水道下游层流平板边界层中诱导自由流湍流(FST)和由此产生的克莱巴诺夫模态/条纹的影响。所有结果都是基于热膜和粒子图像测速测量以及可视化。根据常用的网格安装建议进行网格设计和安装,以确保边界层内FST均匀,导致弯曲的k黎巴嫩夫模式。但研究发现:(1)并非所有栅格构型的k黎巴嫩诺夫模式都具有弯曲;(2)并非所有栅格构型的k黎巴嫩诺夫模式都具有预期的时空行为;(3)对于某些构型,沿展向的条纹间距严格锁定于栅格间距(网格宽度)。由于这些观测结果未在文献中报道,因此本研究旨在全面描述关键网格参数对FST的影响以及边界层内产生的条纹。调查包括通常报告的网格参数,如网格条直径、相关雷诺数或网格的流向位置,但现在也包括网格方向顺序(双平面网格网格条的水平/垂直或垂直/水平顺序)、水平条相对于平板前缘的墙法向位置,以及制造网格中明显缺陷的存在。所覆盖的雷诺数范围处于风洞实验的较低范围。因此,本研究表明,如果能够证明自由流在展向和壁法向上的均匀性,记录所产生的kbanoff模的持续弯曲和波长,从而(隐含地)记录结果在时间平均值上的展向独立性,那么未来FST实验研究的可靠性和可重复性将大大提高。后者是可靠地研究FST/隔离-粗糙度相互作用的先决条件。图形抽象
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引用次数: 0
Impact of spanwise extent of transverse grooves on drag reduction in boat-tailed bluff bodies: an experimental study 横槽展向范围对船尾钝体减阻影响的实验研究
IF 2.3 3区 工程技术 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-12-02 DOI: 10.1007/s00348-024-03924-8
Alessandro Mariotti, Gianmarco Lunghi, Elena Pasqualetto, Maria Vittoria Salvetti

The paper describes the first experimental study on the application of small contoured grooves in boat-tailed bodies characterized by vortex shedding. In particular, we experimentally investigate the flow-separation delay and drag-reducing performance of spanwise-extruded and spanwise-discontinuous grooves. For this purpose, we consider groove geometries similar to those proposed and numerically investigated by Mariotti et al. (Eur J Mech B/Fluids 74:351–362, 2019) and Pasqualetto et al. (Fluids 7:121, 2022a). The Reynolds number, based on the freestream velocity and the model crossflow dimension, is (mathrm Re=9.6cdot 10^4). In addition to serving as an experimental confirmation of previous numerical studies, an important difference is that the present experiments were conducted with a freestream turbulence intensity of 0.9%, whereas the simulations were carried out with a freestream without turbulence. This extends the applicability of this flow control device to a situation closer to real-world or industrial applications. In the experiments, we measure pressure-drag variations for different configurations and flow correlations in the spanwise direction through pressure and hot-wire measurements. The results confirm the good performance of the grooves as passive flow-control devices and the capability of grooves to delay flow separation even in a turbulent freestream. The experiments elucidate the physical mechanism leading to the enhanced performance, specifically the reduction of friction losses due to the local recirculation embedded in the groove region. However, the experiments reveal a different behavior in terms of vortex shedding correlation in the spanwise direction with the introduction of grooves of different spanwise extents. Interestingly, the spanwise-extruded grooves exhibit a weaker increase in spanwise correlation of vortex shedding in experiments compared to simulations. This difference is likely due to the presence of freestream turbulence in the wind tunnel, which is absent in simulations. As expected, the introduction of the spanwise-discontinuous groove reduces vortex shedding correlation. Consequently, in experiments the adoption of spanwise-discontinuous grooves yields fewer benefits than those previously found numerically.

本文首次对小轮廓槽在具有涡落特性的船尾体中的应用进行了实验研究。特别地,我们实验研究了跨向挤压和跨向不连续凹槽的流动分离延迟和减阻性能。为此,我们考虑了类似于Mariotti等人(Eur J Mech B/Fluids 74:351-362, 2019)和Pasqualetto等人(fluid 7:21 1,2022 a)提出和数值研究的沟槽几何形状。基于自由流速度和模型横流尺寸的雷诺数为(mathrm Re=9.6cdot 10^4)。除了作为以往数值研究的实验证实外,一个重要的区别是,本实验是在自由流湍流强度为0.9的情况下进行的%, whereas the simulations were carried out with a freestream without turbulence. This extends the applicability of this flow control device to a situation closer to real-world or industrial applications. In the experiments, we measure pressure-drag variations for different configurations and flow correlations in the spanwise direction through pressure and hot-wire measurements. The results confirm the good performance of the grooves as passive flow-control devices and the capability of grooves to delay flow separation even in a turbulent freestream. The experiments elucidate the physical mechanism leading to the enhanced performance, specifically the reduction of friction losses due to the local recirculation embedded in the groove region. However, the experiments reveal a different behavior in terms of vortex shedding correlation in the spanwise direction with the introduction of grooves of different spanwise extents. Interestingly, the spanwise-extruded grooves exhibit a weaker increase in spanwise correlation of vortex shedding in experiments compared to simulations. This difference is likely due to the presence of freestream turbulence in the wind tunnel, which is absent in simulations. As expected, the introduction of the spanwise-discontinuous groove reduces vortex shedding correlation. Consequently, in experiments the adoption of spanwise-discontinuous grooves yields fewer benefits than those previously found numerically.
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引用次数: 0
Estimation of local Mach number in compressible flows of dense organic vapors using Gabor filters and Radon transforms for the post-processing of schlieren images 利用 Gabor 滤波器和 Radon 变换估算高密度有机蒸汽可压缩流动中的局部马赫数,用于雪莲花图像的后处理
IF 2.3 3区 工程技术 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-11-28 DOI: 10.1007/s00348-024-03925-7
Theodoros Michelis, Adam Head, Piero Colonna

Images of compressible flows can be post-processed with digital imaging techniques to obtain accurate quantitative information about variables characterizing the flow. For example, the local flow Mach number can be obtained from the angle of Mach lines visualized with the schlieren method. These techniques were recently applied to supersonic flows of dense organic vapors, with the objective of obtaining accurate data to validate theory and CFD codes. Non-ideal compressible fluid dynamics (NICFD) is concerned with these flows, for which therefore the thermodynamic properties of the fluid can be modeled only with equations that are more complex than the ideal gas relations. NICFD flows are relevant, e.g., for applications in the power and chemical industry. However, currently employed image post-processing techniques used to obtain the local Mach number or shock wave angle from schlieren images, like the Hough transform, suffer from few drawbacks, namely a long computational time to obtain the relevant quantities and improvable accuracy. The investigation reported here concerns the application of known digital image processing methods to schlieren images, in this case Gabor filters and Radon transforms, to obtain the local Mach number and the shockwave angle of flows in NICFD conditions. The selected test case is the supersonic expansion of the dense vapor of hexamethyldisiloxane flowing through the nozzle test section of the ORCHID facility in operation at the Propulsion and Power laboratory of Delft University of Technology. The investigated digital image processing techniques provide values of the local Mach number with comparable uncertainty (within (5%)) as the Hough transform approach. Moreover, Mach line orientations are computed for the whole field of view, together with Mach line wavelength. It was also proven that these methods are suitable for discerning Mach line orientation even in the case of very complex flow fields, with coexisting Mach waves and shock waves.

可压缩流的图像可通过数字成像技术进行后处理,以获得有关流动特征变量的精确定量信息。例如,可以从使用 Schlieren 方法可视化的马赫线角度中获得局部流动的马赫数。最近,这些技术被应用于高密度有机蒸汽的超音速流动,目的是获得准确的数据来验证理论和 CFD 代码。非理想可压缩流体动力学(NICFD)与这些流动有关,因此只能用比理想气体关系更为复杂的方程来模拟流体的热力学特性。NICFD 流体与电力和化工等行业的应用息息相关。然而,目前使用的图像后处理技术(如 Hough 变换)都存在一些缺点,即需要较长的计算时间才能获得相关数据,而且精度不高。本文所报告的研究涉及将已知的数字图像处理方法应用于离散图像,在本例中应用 Gabor 滤波器和 Radon 变换,以获得 NICFD 条件下流动的局部马赫数和冲击波角。所选测试案例是流经代尔夫特理工大学推进与动力实验室运行中的 ORCHID 设备喷嘴测试部分的六甲基二硅氧烷稠密蒸汽的超音速膨胀。所研究的数字图像处理技术提供的局部马赫数值与霍夫变换方法的不确定性相当(在(5%)之内)。此外,还计算了整个视场的马赫线方向以及马赫线波长。研究还证明,即使在马赫波和冲击波共存的非常复杂的流场中,这些方法也适用于辨别马赫线的方向。
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引用次数: 0
On-site aerodynamics using stereoscopic PIV and deep optical flow learning 利用立体 PIV 和深度光流学习进行现场空气动力学研究
IF 2.3 3区 工程技术 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-11-27 DOI: 10.1007/s00348-024-03914-w
Mohamed Elrefaie, Steffen Hüttig, Mariia Gladkova, Timo Gericke, Daniel Cremers, Christian Breitsamter

We introduce recurrent all-pairs field transforms for stereoscopic particle image velocimetry (RAFT-StereoPIV). Our approach leverages deep optical flow learning to analyze time-resolved and double-frame particle images from on-site measurements, particularly from the ‘Ring of Fire,’ as well as from wind tunnel measurements for fast aerodynamic analysis. A multi-fidelity dataset comprising both Reynolds-averaged Navier–Stokes (RANS) and direct numerical simulation (DNS) was used to train our model. RAFT-StereoPIV outperforms all PIV state-of-the-art deep learning models on benchmark datasets, with a 68 % error reduction on the validation dataset, Problem Class 2, and a 47 % error reduction on the unseen test dataset, Problem Class 1, demonstrating its robustness and generalizability. In comparison with the most recent works in the field of deep learning for PIV, where the main focus was the methodology development and the application was limited to either 2D flow cases or simple experimental data, we extend deep learning-based PIV for industrial applications and three-component two-dimensional (3C2D) velocity estimation. We believe that this study brings the field of experimental fluid dynamics one step closer to the long-term goal of having experimental measurement systems that can be used for fast flow field estimation.

我们为立体粒子图像测速(RAFT-StereoPIV)引入了循环全对场变换。我们的方法利用深度光流学习来分析来自现场测量(尤其是 "火环 "测量)以及风洞测量的时间分辨和双帧粒子图像,以进行快速空气动力学分析。为了训练我们的模型,我们使用了由雷诺平均纳维-斯托克斯(RANS)和直接数值模拟(DNS)组成的多保真度数据集。在基准数据集上,RAFT-StereoPIV 的表现优于所有 PIV 最新深度学习模型,在验证数据集 "问题类 2 "上减少了 68% 的误差,在未见测试数据集 "问题类 1 "上减少了 47% 的误差,这证明了它的鲁棒性和通用性。与最近在深度学习 PIV 领域的工作相比,这些工作的主要重点是方法论的开发,应用仅限于二维流动情况或简单的实验数据,而我们将基于深度学习的 PIV 扩展到了工业应用和三分量二维(3C2D)速度估计。我们相信,这项研究将使实验流体动力学领域离拥有可用于快速流场估算的实验测量系统这一长期目标更近一步。
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引用次数: 0
Exploring droplet oscillation dynamics in surface tension measurements 探索表面张力测量中的液滴振荡动力学
IF 2.3 3区 工程技术 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-11-27 DOI: 10.1007/s00348-024-03926-6
Kiana Fahimi, Lutz Mädler, Nils Ellendt

This study builds upon prior research by exploring droplet oscillation dynamics for surface tension determination using a drop-on-demand high-temperature droplet generator. Computational fluid dynamics (CFD) simulations were conducted to analyse frequency shifts over time, comparing two different materials with consistent results. The findings suggest potential for developing correction factors for oscillations with larger initial deformations. Additionally, frequency shifts relative to evolving aspect ratios of droplets starting with higher initial deformations were compared. Corrective measures can be applied, particularly beneficial for short-term measurements based on image analysis with minimal overall frequency shift. Slight asymmetry in oscillation with increasing aspect ratio could be accredited to droplet cross-sectional geometry or energy availability for returning prolate droplets to a spherical state. Experimental results indicated minimal frequency shift within a measurement duration of up to 40 ms, affirming the adequacy of using a fitted sine function without a time-dependent frequency term for overall frequency determination. A dimensionless criterion can be used to filter out unsuitable droplets. A temperature-dependent surface tension trend for AlCu10 alloy consistent with literature findings is introduced.

本研究在先前研究的基础上,利用按需滴高温液滴发生器探索液滴振荡动力学,以确定表面张力。研究人员进行了计算流体动力学(CFD)模拟,以分析随时间变化的频率偏移,并对两种不同材料进行了比较,结果一致。研究结果表明,有可能为初始变形较大的振荡开发校正因子。此外,还比较了与初始变形较大的液滴的长宽比变化有关的频率偏移。可以采用校正措施,尤其有利于基于图像分析的短期测量,使整体频率偏移最小。随着长宽比的增加,振荡略有不对称,这可能与液滴横截面的几何形状有关,也可能与液滴的能量可用性有关,因为能量可用性可使凸形液滴恢复到球形状态。实验结果表明,在长达 40 毫秒的测量持续时间内,频率偏移极小,这证明使用拟合正弦函数而不使用随时间变化的频率项来确定总体频率是合适的。无量纲标准可用于过滤不合适的液滴。介绍了 AlCu10 合金随温度变化的表面张力趋势,与文献结论一致。
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引用次数: 0
Robust detection and characterization of a bifurcated bi-phasic interface propagating through a granular medium: physically and morphologically 在颗粒介质中传播的分叉双相界面的稳健检测和特征描述:物理和形态学方法
IF 2.3 3区 工程技术 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-11-26 DOI: 10.1007/s00348-024-03919-5
Rana Al Nemer, Julien Réthoré, Giulio Sciarra

The detection of an interface separating two zones of low contrast and evolving in a deformable medium is very challenging. The low-contrasted images describing a partially saturated granular medium are replaced by high contrasted images generated from the correlation error maps issued from a standard digital image correlation (DIC) calculation. A robust algorithm has been developed to capture automatically the sought interface evolving in 2D space through time. Capable of detecting all morphological reliefs, this approach is completed by a sequence of steps to remove aberrant contours and track the main advancing interface. Consequently, adequate algorithms have been developed to determine physical and morphological properties that will give insights on the factors that monitor the interface propagation.

在可变形介质中检测分隔两个低对比度区域的界面是一项非常具有挑战性的工作。描述部分饱和颗粒介质的低对比度图像被由标准数字图像相关性(DIC)计算产生的相关性误差图生成的高对比度图像所取代。我们开发了一种稳健的算法,可自动捕捉二维空间中随时间演变的所需界面。这种方法能够检测所有形态浮雕,并通过一系列步骤去除异常轮廓并跟踪主要的前进界面。因此,已开发出适当的算法来确定物理和形态属性,从而深入了解监测界面传播的因素。
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引用次数: 0
Internal wave field generated by oscillating rough topography 振荡粗糙地形产生的内波场
IF 2.3 3区 工程技术 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-11-25 DOI: 10.1007/s00348-024-03928-4
Natasha Wilson, Julie Crockett

Internal waves generated by oscillating topography with a series of ridges in a stratified medium are experimentally explored. Experiments represent oscillating tidal flow in the ocean where small-scale roughness on topography cannot be fully resolved in global circulation models, but the generated internal wave field can impact global mixing and ocean dynamics. Here, the influence of topography roughness is evaluated by including different numbers of ridges, with slopes equivalent to the edge slope of the full topography, on top of the original topography. Specifically, the internal wave field generated by a wide plateau shape is compared with the same shape except with three to six Gaussian ridges overlain on the plateau. In all scenarios, a complex pattern of internal waves generated by each ridge is observed. However, the results show as the number or width of ridges increases, the waves generated by the ridges near the center of the plateau decay very quickly and in the far field the internal wave field is indistinguishable from that generated by a smooth plateau. A non-dimensional number is suggested that accounts for both the number of ridges and overall topography width while defining a limit for which plateau-like internal wave generation is expected and this form of surface roughness may be neglected.

通过实验探索了在分层介质中具有一系列海脊的振荡地形所产生的内波。实验代表了海洋中的振荡潮汐流,全球环流模型无法完全解析地形上的小尺度粗糙度,但产生的内波场会影响全球混合和海洋动力学。在这里,通过在原始地形上加入不同数量的脊,其斜率相当于完整地形的边缘斜率,来评估地形粗糙度的影响。具体来说,将宽阔高原形状产生的内波场与在高原上覆盖三至六条高斯山脊的相同形状进行比较。在所有情况下,都能观察到每个山脊产生的复杂内波模式。然而,结果表明,随着脊的数量或宽度增加,靠近高原中心的脊产生的波衰减得非常快,在远场,内波场与光滑高原产生的内波场没有区别。我们提出了一个非维数,它既考虑了脊的数量和整体地形宽度,又定义了一个极限,在这个极限上,预计会产生类似高原的内波,这种形式的表面粗糙度可以忽略不计。
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引用次数: 0
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