8 results
Bottom wall shear stress fluctuations in shallow-water Langmuir turbulence
- Bing-Qing Deng, Zixuan Yang, Lian Shen
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- Journal:
- Journal of Fluid Mechanics / Volume 942 / 10 July 2022
- Published online by Cambridge University Press:
- 13 May 2022, A6
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In neutrally stratified shallow water, full-depth Langmuir cells (LCs) can interact with the turbulent benthic boundary layer and, thus, influence bottom wall shear stresses. In this paper the impacts of full-depth LCs on the streamwise and spanwise wall shear stresses are systematically studied using the database obtained from wall-resolved large-eddy simulation of shallow-water Langmuir turbulence. Analyses focus on the instantaneous wall shear stress fluctuations and the joint probability density functions between the stress fluctuations and the LCs parts of the velocity fluctuations, which show that the linear superimposition effect and nonlinear modulation effect of LCs are responsible for the spanwise organized distribution of wall shear stress fluctuations. Compared with the statistics in pure shear-driven turbulence without LCs, the mean square values of wall shear stress fluctuations in shallow-water Langmuir turbulence are enhanced by the strong linear superimposition effect of LCs, while the skewness and kurtosis are reduced by the combination of the linear superimposition effect and nonlinear modulation effect of LCs. Based on the scalings of these effects, a new predictive model of wall shear stress fluctuations is proposed for shallow-water Langmuir turbulence. The proposed model can predict the spatial distribution and statistics of wall shear stress fluctuations using the LCs parts of velocity fluctuations measured above the water bottom. Owing to the persistence of the spanwise inhomogeneity of wall shear stresses induced by full-depth LCs, the new predictive model will be useful for improving the wall-layer modelling for shallow-water Langmuir turbulent flows.
Using machine learning to detect the turbulent region in flow past a circular cylinder
- Binglin Li, Zixuan Yang, Xing Zhang, Guowei He, Bing-Qing Deng, Lian Shen
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- Journal:
- Journal of Fluid Mechanics / Volume 905 / 25 December 2020
- Published online by Cambridge University Press:
- 26 October 2020, A10
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Detecting the turbulent/non-turbulent interface is a challenging topic in turbulence research. In the present study, machine learning methods are used to train detectors for identifying turbulent regions in the flow past a circular cylinder. To ensure that the turbulent/non-turbulent interface is independent of the reference frame of coordinates and is physics-informed, we propose to use invariants of tensors appearing in the transport equations of velocity fluctuations, strain-rate tensor and vortical tensor as the input features to identify the flow state. The training samples are chosen from numerical simulation data at two Reynolds numbers, $Re=100$ and 3900. Extreme gradient boosting (XGBoost) is utilized to train the detector, and after training, the detector is applied to identify the flow state at each point of the flow field. The trained detector is found robust in various tests, including the applications to the entire fields at successive snapshots and at a higher Reynolds number $Re=5000$. The objectivity of the detector is verified by changing the input features and the flow region for choosing the turbulent training samples. Compared with the conventional methods, the proposed method based on machine learning shows its novelty in two aspects. First, no threshold value needs to be specified explicitly by the users. Second, machine learning can treat multiple input variables, which reflect different properties of turbulent flows, including the unsteadiness, vortex stretching and three-dimensionality. Owing to these advantages, XGBoost generates a detector that is more robust than those obtained from conventional methods.
Numerical study of effect of wave phase on Reynolds stresses and turbulent kinetic energy in Langmuir turbulence
- Anqing Xuan, Bing-Qing Deng, Lian Shen
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- Journal:
- Journal of Fluid Mechanics / Volume 904 / 10 December 2020
- Published online by Cambridge University Press:
- 07 October 2020, A17
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The dynamics of Reynolds stresses and turbulent kinetic energy (TKE) in Langmuir turbulence are analysed using data of large-eddy simulations with the wave phase resolved. It is found that the streamwise and spanwise Reynolds normal stresses and the Reynolds shear stress vary appreciably with the wave phase, while the vertical normal stress is only weakly dependent on the wave phase. Budget analyses indicate that the production due to wave straining and the effects associated with turbulence pressure are the dominant mechanisms for the wave-phase variation of Reynolds stresses. The accumulative effect of wave–turbulence interactions on TKE is then investigated using the Lagrangian average. It is discovered that the energy transfer from wave to turbulence is contributed by two mechanisms. The first mechanism is the turbulence production by the Lagrangian mean wave shearing and the mean shear stress, which is consistent with the traditional wave-phase-averaged model. The second mechanism, which is not accounted for in previous studies, is the correlation between the wave-phase variation of the Reynolds shear stress and the wave orbital shearing. A model is proposed for the second mechanism. Comparison of the frequency spectrum with Craik–Leibovich simulation results shows that the correlation effect can affect the turbulence fluctuations at time scales around the wave period, indicating the importance of this effect on Reynolds stresses and TKE.
A simulation-based mechanistic study of turbulent wind blowing over opposing water waves
- Tao Cao, Bing-Qing Deng, Lian Shen
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- Journal:
- Journal of Fluid Mechanics / Volume 901 / 25 October 2020
- Published online by Cambridge University Press:
- 27 August 2020, A27
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We perform large-eddy simulation (LES) and theoretical analysis to investigate the effects of opposing waves on overlying turbulent wind. The LES results show that opposing waves induce nearly antisymmetric vertical velocity $\tilde {w}$ in the wind on the two sides of the wave crest, while the streamwise velocity $\tilde {u}$ away from the surface and the air pressure $\tilde {p}$ seem symmetric. To study the mechanisms for the wave-induced airflow, we develop a viscous model by linearising the phase-averaged Navier–Stokes equations in the mapped computational curvilinear coordinate. To illustrate the flow dynamics, we split $\tilde {w}$ into an antisymmetric component and a symmetric component. The solution of the antisymmetric component of $\tilde {w}$ from the viscous curvilinear model agrees well with the LES results for different opposing wave conditions. According to the viscous curvilinear model, the large-magnitude antisymmetric component of $\tilde {w}$ is driven by the wave kinematics at the surface and amplified by the mean shear and viscous stress in the air, and it causes the strong symmetric components of $\tilde {u}$ and $\tilde {p}$. In contrast, the small-magnitude symmetric component of $\tilde {w}$ is forced by the antisymmetric $\tilde {w}$ through viscous and turbulent stresses near the surface, and it can be described by a further simplified inviscid curvilinear model away from the surface. It is discovered that the weak symmetric $\tilde {w}$ causes a slight asymmetry in $\tilde {u}$ and $\tilde {p}$, and generates a mean wave-coherent stress and the form drag on the wave surface. The wave attenuation rates quantified using the form drag agree with the published experiments.
Localizing effect of Langmuir circulations on small-scale turbulence in shallow water
- Bing-Qing Deng, Zixuan Yang, Anqing Xuan, Lian Shen
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- Journal:
- Journal of Fluid Mechanics / Volume 893 / 25 June 2020
- Published online by Cambridge University Press:
- 17 April 2020, A6
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Wall-resolved and wall-modelled large-eddy simulations are performed to study the localizing effect of Langmuir cells (LCs) on small-scale background turbulence in shallow water. The total velocity fluctuations are decomposed into an LC content extracted by streamwise averaging and a background turbulence part. Based on the large-scale motions of LCs, the spanwise domain is divided into three regions dominated by the upwelling, spanwise and downwelling flows of LCs, respectively. The localized Reynolds stresses $\langle u_{i}^{T}u_{j}^{T}\rangle _{xt}$ in different spanwise regions are compared to show the localizing effects of the LCs on the background turbulence quantitatively, where $u_{1}^{T}$ (or $u^{T}$), $u_{2}^{T}$ (or $v^{T}$) and $u_{3}^{T}$ (or $w^{T}$) represent the streamwise, vertical and spanwise components of the background turbulence velocity, respectively, and $\langle \cdot \rangle _{xt}$ denotes time and streamwise averaging. It is shown that the magnitudes of the localized Reynolds stresses in different spanwise regions vary significantly. The transport equations of the localized Reynolds stresses are then analysed to investigate the mechanisms underlying the localizing effects. It is discovered that the difference in the energy production correlated to the shear of the LC content among different regions is the key factor that leads to the localization of background turbulence. In addition, the energy production correlated to the shear of the mean flow, the energy redistribution due to the pressure–strain correlation, and the interaction between the localized Reynolds stresses and the shear of the Stokes drift also play important roles. Based on the results obtained from the analysis of the transport equations, predictive models are proposed for the localizing effects, which assess the spatial dependence of the Boussinesq model for background turbulence in coastal Langmuir turbulence. These models show good scaling performance of $\langle u^{T}u^{T}\rangle _{xt}$ near the water bottom and of $\langle -u^{T}v^{T}\rangle _{xt}$, $\langle -u^{T}w^{T}\rangle _{xt}$ and $\langle -v^{T}w^{T}\rangle _{xt}$ in the central region of the water column under various flow conditions with different values of the Reynolds number, turbulent Langmuir number and wavenumber.
Study of wave effect on vorticity in Langmuir turbulence using wave-phase-resolved large-eddy simulation
- Anqing Xuan, Bing-Qing Deng, Lian Shen
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- Journal:
- Journal of Fluid Mechanics / Volume 875 / 25 September 2019
- Published online by Cambridge University Press:
- 18 July 2019, pp. 173-224
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The effects of a water surface wave on the vorticity in the turbulence underneath are studied for Langmuir turbulence using wave-phase-resolved large-eddy simulation. The simulations are performed on a dynamically evolving wave-surface-fitted grid such that the phase-resolved wave motions and their effects on the turbulence are explicitly captured. This study focuses on the vorticity structures and dynamics in Langmuir turbulence driven by a steady and co-aligned progressive wave and surface shear stress. For the first time, the detailed vorticity dynamics of the wave–turbulence interaction in Langmuir turbulence in a wave-phase-resolved frame is revealed. The wave-phase-resolved simulation provides detailed descriptions of many characteristic features of Langmuir turbulence, such as elongated quasi-streamwise vortices. The simulation also reveals the variation of the strength and the inclination angles of the vortices with the wave phase. The variation is found to be caused by the periodic stretching and tilting of the wave orbital straining motions. The cumulative effect of the wave on the wave-phase-averaged vorticity is analysed using the Lagrangian average. It is discovered that, in addition to the tilting effect induced by the Lagrangian mean shear gradient of the wave, the phase correlation between the vorticity fluctuations and the wave orbital straining is also important to the cumulative vorticity evolution. Both the fluctuation correlation effect and the mean tilting effect are found to amplify the streamwise vorticity. On the other hand, for the vertical vorticity, the fluctuation correlation effect cancels the mean tilting effect, and the net change of the vertical vorticity by the wave straining is negligible. As a result, the wave straining enhances only the streamwise vorticity and cumulatively tilts vertical vortices towards the streamwise direction. The above processes are further quantified analytically. The role of the fluctuation correlation effect in the wave-phase-averaged vorticity dynamics provides a deeper understanding of the physical processes underlying the wave–turbulence interaction in Langmuir turbulence.
Influence of Langmuir circulations on turbulence in the bottom boundary layer of shallow water
- Bing-Qing Deng, Zixuan Yang, Anqing Xuan, Lian Shen
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- Journal:
- Journal of Fluid Mechanics / Volume 861 / 25 February 2019
- Published online by Cambridge University Press:
- 19 December 2018, pp. 275-308
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Langmuir circulations (LCs) generated by the interaction between wind-driven currents and surface waves can engulf the whole water column in neutrally stratified shallow water and interact with the turbulence in the bottom boundary layer. In this study, we perform a mechanistic study using wall-resolved large-eddy simulations (LES) based on the Craik–Leibovich equations to investigate the effects of LCs on turbulence statistics in the bottom half of shallow water. The highest Reynolds number considered in this paper, $Re_{\unicode[STIX]{x1D70F}}=1000$, is larger than the values considered in wall-resolved LES studies of shallow-water Langmuir turbulence reported in literature. The logarithmic layer is diagnosed based on a plateau region in the profile of a diagnostic function. It is found that the logarithmic layer disrupted at $Re_{\unicode[STIX]{x1D70F}}=395$ reappears at $Re_{\unicode[STIX]{x1D70F}}=1000$, but the von Kármán constant is slightly different from the traditional value $0.41$. To study the effects of LCs on turbulence statistics, LCs are extracted using streamwise averaging. The velocity fluctuations $u_{i}^{\prime }$ are decomposed into a LC-coherent part $u_{i}^{L}$ and a residual turbulence part $u_{i}^{T}$. It is found that the profiles of LC-coherent Reynolds shear stress $-\langle u^{L}v^{L}\rangle$ obtained at various Reynolds numbers are close to each other in the water-column coordinate $y/h$, with $h$ being the half-water depth. As the Reynolds number (or, by definition, the ratio between the outer and inner length scales) increases, the influence of LCs on the near-bottom momentum transfer is reduced, which is responsible for the reappearance of the logarithmic layer. At all of the Reynolds numbers under investigation, the peaks of $\langle u^{L}u^{L}\rangle$ are collocated in the water-column coordinate $y/h$, while those of $\langle u^{T}u^{T}\rangle$ are collocated in the inner-scale coordinate $y/(\unicode[STIX]{x1D708}/u_{\unicode[STIX]{x1D70F}})$. Due to the increase in the distance between the peaks of $\langle u^{L}u^{L}\rangle$ and $\langle u^{T}u^{T}\rangle$ with the Reynolds number, the profile of $\langle u^{\prime }u^{\prime }\rangle$ forms a bimodal shape at $Re_{\unicode[STIX]{x1D70F}}=700$ and $1000$.
Direct numerical simulation of wind turbulence over breaking waves
- Zixuan Yang, Bing-Qing Deng, Lian Shen
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- Journal:
- Journal of Fluid Mechanics / Volume 850 / 10 September 2018
- Published online by Cambridge University Press:
- 04 July 2018, pp. 120-155
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We study wind turbulence over breaking waves based on direct numerical simulation (DNS) of two-fluid flows. In the DNS, the air and water are simulated as a coherent system, with the interface captured using the coupled level-set and volume-of-fluid method. Because the wave breaking is an unsteady process, we use ensemble averaging over 100 runs to define turbulence statistics. We focus on analysing the turbulence statistics of the airflow over breaking waves. The effects of wave age and wave steepness are investigated. It is found that before wave breaking, the turbulence statistics are largely influenced by the wave age. The vertical gradient of mean streamwise velocity is positive at small and intermediate wave ages, but it becomes negative near the wave surface at large wave age as the pressure force changes from drag to thrust. Furthermore, wave-coherent motions make increasingly important contributions to the momentum flux and kinetic energy of velocity fluctuations (KE-F) as the wave age increases. During the wave breaking process, spilling breakers do not influence the wind field significantly; in contrast, plunging breakers alter the structures of wind turbulence near the wave surface drastically. It is observed from the DNS results that during wave plunging, a high pressure region occurs ahead of the wave front, which further accelerates the wind in the downstream direction. Meanwhile, a large spanwise vortex is generated, which greatly disturbs the airflow around it, resulting in large magnitudes of Reynolds stress and turbulence kinetic energy (TKE) below the wave crest. Above the crest, the magnitude of KE-F is enhanced during wave plunging at small and large wave ages, but at intermediate wave age, the transient enhancement of KE-F is absent. The effect of wave breaking on the magnitude of KE-F is further investigated through the analysis of the KE-F production. It is discovered that at small wave age, the transient enhancement of KE-F is caused by the appearance of a local maximum in the profile of total momentum flux; but at large wave age, it results from the change in the sign of the KE-F production from negative to positive, due to the sign change in the wave-coherent momentum flux. At intermediate wave age, neither of these two processes is present, and the transient growth of KE-F does not take place.