On Measuring the Terms of the Turbulent Kinetic Energy Budget from an AUV

2006 ◽  
Vol 23 (7) ◽  
pp. 977-990 ◽  
Author(s):  
Louis Goodman ◽  
Edward R. Levine ◽  
Rolf G. Lueck
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Reynolds Stress ◽  
Vertical Velocity ◽  
Autonomous Underwater Vehicle ◽  
Temperature Fluctuations ◽  
Transverse Component ◽  
Vertical Flux ◽  
Vertical Shear ◽  
Statistical Uncertainty

Abstract The terms of the steady-state, homogeneous turbulent kinetic energy budgets are obtained from measurements of turbulence and fine structure from the small autonomous underwater vehicle (AUV) Remote Environmental Measuring Units (REMUS). The transverse component of Reynolds stress and the vertical flux of heat are obtained from the correlation of vertical and transverse horizontal velocity, and the correlation of vertical velocity and temperature fluctuations, respectively. The data were obtained using a turbulence package, with two shear probes, a fast-response thermistor, and three accelerometers. To obtain the vector horizontal Reynolds stress, a generalized eddy viscosity formulation is invoked. This allows the downstream component of the Reynolds stress to be related to the transverse component by the direction of the finescale vector vertical shear. The Reynolds stress and the vector vertical shear then allow an estimate of the rate of production of turbulent kinetic energy (TKE). Heat flux is obtained by correlating the vertical velocity with temperature fluctuations obtained from the FP-07 thermistor. The buoyancy flux term is estimated from the vertical flux of heat with the assumption of a constant temperature–salinity (T–S) relationship. Turbulent dissipation is obtained directly from the usage of shear probes. A multivariate correction procedure is developed to remove vehicle motion and vibration contamination from the estimates of the TKE terms. A technique is also developed to estimate the statistical uncertainty of using this estimation technique for the TKE budget terms. Within the statistical uncertainty of the estimates herein, the TKE budget on average closes for measurements taken in the weakly stratified waters at the entrance to Long Island Sound. In the strongly stratified waters of Narragansett Bay, the TKE budget closes when the buoyancy Reynolds number exceeds 20, an indicator and threshold for the initiation of turbulence in stratified conditions. A discussion is made regarding the role of the turbulent kinetic energy length scale relative to the length of the AUV in obtaining these estimates, and in the TKE budget closure.

scholarly journals Comment on “Using an ADCP to Estimate Turbulent Kinetic Energy Dissipation Rate in Sheltered Coastal Waters”

2017 ◽  
Vol 34 (6) ◽  
pp. 1387-1390 ◽  
Author(s):  
Ann E. Gargett
Keyword(s):  
Energy Dissipation ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Vertical Velocity ◽  
Dissipation Rate ◽  
Energy Dissipation Rate ◽  
Vertical Shear ◽  
Length Scale ◽  
Ocean Turbulence ◽  
Large Eddy

AbstractGreene et al. revisit the suggestion that the turbulent kinetic energy dissipation rate could be estimated through a “large-eddy estimate,” employing acoustic measurements of velocity fields associated with the largest energy-containing scales of ocean turbulence. While the large-eddy estimate as originally proposed used vertical velocity and a vertical eddy length scale, Greene et al. chose instead to substitute a horizontal length scale for the latter. This comment argues that combining a horizontal scale for length with a vertical velocity scale produces a large-eddy estimate of the dissipation rate that is accurate only if the energy-containing eddies are isotropic, and that this condition is highly unlikely in naturally occurring ocean turbulence, subject as it is to influences of stratification, vertical shear, and/or the presence of horizontal boundaries. The problem is documented using data from a large-eddy simulation of Langmuir supercells.

Coherent Velocity Structures in the Mixed Layer: Characteristics, Energetics, and Turbulent Kinetic Energy Budget

2021 ◽  
Author(s):  
Ewa Jarosz ◽  
Hemantha W. Wijesekera ◽  
David W. Wang
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Mixed Layer ◽  
Vertical Velocity ◽  
Mixed Layer Depth ◽  
Vertical Transport ◽  
Rate Of Change ◽  
Production Term ◽  
Forcing Mechanisms ◽  
Surface Buoyancy

AbstractVelocity, hydrographic, and microstructure observations collected under moderate to high winds, large surface waves, and significant ocean-surface heat losses were utilized to examine coherent velocity structures (CVS) and turbulent kinetic energy (TKE) budget in the mixed layer on the outer shelf in the northern Gulf of Mexico in February 2017. The CVS exhibited larger downward velocities in downweling regions and weaker upward velocities in broader upwelling regions, elevated vertical velocity variance, vertical velocity maxima in the upper part of the mixed layer, and phasing of crosswind velocities relative to vertical velocities near the base of the mixed layer. Temporal scales ranged from 10 min to 40 min and estimated lateral scales ranged from 90 m to 430 m, which were 1.5 – 6 times larger than the mixed layer depth. Nondimensional parameters, Langmuir and Hoenikker numbers, indicated that plausible forcing mechanisms were surface-wave driven Langmuir vortex and destabilizing surface buoyancy flux. The rate of change of TKE, shear production, Stokes production, buoyancy production, vertical transport of TKE, and dissipation in the TKE budget were evaluated. The shear and Stokes productions, dissipation, and vertical transport of TKE were the dominant terms. The buoyancy production term was important at the sea surface, but it decreased rapidly in the interior. A large imbalance term was found under the unstable, high wind, and high-sea state conditions. The cause of this imbalance cannot be determined with certainty through analyses of the available observations; however, our speculation is that the pressure transport is significant under these conditions.

A revisit of the equilibrium assumption for predicting near-wall turbulence

2014 ◽  
Vol 760 ◽  
pp. 304-312 ◽  
Author(s):  
Farid Karimpour ◽  
Subhas K. Venayagamoorthy
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Reynolds Stress ◽  
Turbulent Viscosity ◽  
Wall Turbulence ◽  
Wall Region ◽  
Turbulence Decay ◽  
Prime 2 ◽  
Near Wall Turbulence ◽  
Near Wall

AbstractIn this study, we revisit the consequence of assuming equilibrium between the rates of production ($P$) and dissipation $({\it\epsilon})$ of the turbulent kinetic energy $(k)$ in the highly anisotropic and inhomogeneous near-wall region. Analytical and dimensional arguments are made to determine the relevant scales inherent in the turbulent viscosity (${\it\nu}_{t}$) formulation of the standard $k{-}{\it\epsilon}$ model, which is one of the most widely used turbulence closure schemes. This turbulent viscosity formulation is developed by assuming equilibrium and use of the turbulent kinetic energy $(k)$ to infer the relevant velocity scale. We show that such turbulent viscosity formulations are not suitable for modelling near-wall turbulence. Furthermore, we use the turbulent viscosity $({\it\nu}_{t})$ formulation suggested by Durbin (Theor. Comput. Fluid Dyn., vol. 3, 1991, pp. 1–13) to highlight the appropriate scales that correctly capture the characteristic scales and behaviour of $P/{\it\epsilon}$ in the near-wall region. We also show that the anisotropic Reynolds stress ($\overline{u^{\prime }v^{\prime }}$) is correlated with the wall-normal, isotropic Reynolds stress ($\overline{v^{\prime 2}}$) as $-\overline{u^{\prime }v^{\prime }}=c_{{\it\mu}}^{\prime }(ST_{L})(\overline{v^{\prime 2}})$, where $S$ is the mean shear rate, $T_{L}=k/{\it\epsilon}$ is the turbulence (decay) time scale and $c_{{\it\mu}}^{\prime }$ is a universal constant. ‘A priori’ tests are performed to assess the validity of the propositions using the direct numerical simulation (DNS) data of unstratified channel flow of Hoyas & Jiménez (Phys. Fluids, vol. 18, 2006, 011702). The comparisons with the data are excellent and confirm our findings.

Two-equation turbulence modeling of an oscillatory boundary layer under steep pressure gradient

2010 ◽  
Vol 37 (4) ◽  
pp. 648-656 ◽  
Author(s):  
Ahmad Sana ◽  
Hitoshi Tanaka
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Pressure Gradient ◽  
Turbulent Kinetic Energy ◽  
Reynolds Stress ◽  
Turbulence Modeling ◽  
Turbulence Models ◽  
Detailed Comparison ◽  
Stream Velocity ◽  
Oscillatory Boundary Layer

A total of seven versions of two-equation turbulence models (four versions of low Reynolds number k–ε model, one k–ω model and two versions of k–ε / k–ω blended models) are tested against the direct numerical simulation (DNS) data of a one-dimensional oscillatory boundary layer with flat crested free-stream velocity that results from a steep pressure gradient. A detailed comparison has been made for cross-stream velocity, turbulent kinetic energy (TKE), Reynolds stress, and ratio of Reynolds stress and turbulent kinetic energy. It is observed that the newer versions of k–ε model perform very well in predicting the velocity, turbulent kinetic energy, and Reynolds stress. The k–ω model and blended models underestimate the peak value of turbulent kinetic energy that may be explained by the Reynolds stress to TKE ratio in the logarithmic zone. The maximum bottom shear stress is well predicted by the k–ε model proposed by Sana et al. and the original k–ω model.

Pseudo-turbulent gas-phase velocity fluctuations in homogeneous gas–solid flow: fixed particle assemblies and freely evolving suspensions

2015 ◽  
Vol 770 ◽  
pp. 210-246 ◽  
Author(s):  
M. Mehrabadi ◽  
S. Tenneti ◽  
R. Garg ◽  
S. Subramaniam
Keyword(s):  
Kinetic Energy ◽  
Phase Velocity ◽  
Turbulent Kinetic Energy ◽  
Gas Phase ◽  
Reynolds Stress ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Velocity Fluctuations ◽  
The Mean ◽  
Particle Assemblies

Gas-phase velocity fluctuations due to mean slip velocity between the gas and solid phases are quantified using particle-resolved direct numerical simulation. These fluctuations are termed pseudo-turbulent because they arise from the interaction of particles with the mean slip even in ‘laminar’ gas–solid flows. The contribution of turbulent and pseudo-turbulent fluctuations to the level of gas-phase velocity fluctuations is quantified in initially ‘laminar’ and turbulent flow past fixed random particle assemblies of monodisperse spheres. The pseudo-turbulent kinetic energy $k^{(f)}$ in steady flow is then characterized as a function of solid volume fraction ${\it\phi}$ and the Reynolds number based on the mean slip velocity $\mathit{Re}_{m}$. Anisotropy in the Reynolds stress is quantified by decomposing it into isotropic and deviatoric parts, and its dependence on ${\it\phi}$ and $Re_{m}$ is explained. An algebraic stress model is proposed that captures the dependence of the Reynolds stress on ${\it\phi}$ and $Re_{m}$. Gas-phase velocity fluctuations in freely evolving suspensions undergoing elastic and inelastic particle collisions are also quantified. The flow corresponds to homogeneous gas–solid systems, with high solid-to-gas density ratio and particle diameter greater than dissipative length scales. It is found that for the parameter values considered here, the level of pseudo-turbulence differs by only 15 % from the values for equivalent fixed beds. The principle of conservation of interphase turbulent kinetic energy transfer is validated by quantifying the interphase transfer terms in the evolution equations of kinetic energy for the gas-phase and solid-phase fluctuating velocity. It is found that the collisional dissipation is negligible compared with the viscous dissipation for the cases considered in this study where the freely evolving suspensions attain a steady state starting from an initial condition where the particles are at rest.

scholarly journals Wind–Wave Misalignment Effects on Langmuir Turbulence in Tropical Cyclone Conditions

2019 ◽  
Vol 49 (12) ◽  
pp. 3109-3126 ◽  
Author(s):  
Dong Wang ◽  
Tobias Kukulka ◽  
Brandon G. Reichl ◽  
Tetsu Hara ◽  
Isaac Ginis
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Reynolds Stress ◽  
Wind Wave ◽  
Stokes Drift ◽  
Scaling Analysis ◽  
Surface Boundary ◽  
Langmuir Turbulence ◽  
Near Surface ◽  
Momentum Budget

AbstractThis study utilizes a large-eddy simulation (LES) approach to systematically assess the directional variability of wave-driven Langmuir turbulence (LT) in the ocean surface boundary layer (OSBL) under tropical cyclones (TCs). The Stokes drift vector, which drives LT through the Craik–Leibovich vortex force, is obtained through spectral wave simulations. LT’s direction is identified by horizontally elongated turbulent structures and objectively determined from horizontal autocorrelations of vertical velocities. In spite of a TC’s complex forcing with great wind and wave misalignments, this study finds that LT is approximately aligned with the wind. This is because the Reynolds stress and the depth-averaged Lagrangian shear (Eulerian plus Stokes drift shear) that are key in determining the LT intensity (determined by normalized depth-averaged vertical velocity variances) and direction are also approximately aligned with the wind relatively close to the surface. A scaling analysis of the momentum budget suggests that the Reynolds stress is approximately constant over a near-surface layer with predominant production of turbulent kinetic energy by Stokes drift shear, which is confirmed from the LES results. In this layer, Stokes drift shear, which dominates the Lagrangian shear, is aligned with the wind because of relatively short, wind-driven waves. On the contrary, Stokes drift exhibits considerable amount of misalignments with the wind. This wind–wave misalignment reduces LT intensity, consistent with a simple turbulent kinetic energy model. Our analysis shows that both the Reynolds stress and LT are aligned with the wind for different reasons: the former is dictated by the momentum budget, while the latter is controlled by wind-forced waves.

An Improved Model for the Return to Isotropy of Homogeneous Turbulence

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Hari Warrior ◽  
Sajo Mathews ◽  
Subhendu Maity ◽  
Kaushik Sasmal
Keyword(s):  
Kinetic Energy ◽  
Strain Rate ◽  
Turbulent Kinetic Energy ◽  
Reynolds Stress ◽  
Experimental Results ◽  
Homogeneous Turbulence ◽  
Cfd Modeling ◽  
Present Formulation ◽  
Improved Model ◽  
Stress Models

In CFD modeling, the most widely used Reynolds stress models is the Speziale, Sarkar, Gatski (SSG) model. The present formulation, though similar in structure to the SSG model, is a mathematical variation assuming homogeneity of turbulence and is an improved model for the slow pressure strain of turbulence. The basic thrust is that anisotropy of dissipation tensor is not negligible when compared to the anisotropy of turbulent kinetic energy and affects the slow pressure strain rate. After an exhaustive survey of the available experimental results on return to isotropy, graphical plots reveal that the model performs as good as the SSG model.

Measurements and Predictions of a Highly Turbulent Flowfield in a Turbine Vane Passage

2000 ◽  
Vol 122 (4) ◽  
pp. 666-676 ◽  
Author(s):  
R. W. Radomsky ◽  
K. A. Thole
Keyword(s):  
Kinetic Energy ◽  
Turbulent Flow ◽  
Gas Turbine ◽  
Turbulent Kinetic Energy ◽  
Reynolds Stress ◽  
Complex Geometry ◽  
Turbulence Models ◽  
Reynolds Stress Model ◽  
Stress Model ◽  
Mean Flow

As highly turbulent flow passes through downstream airfoil passages in a gas turbine engine, it is subjected to a complex geometry designed to accelerate and turn the flow. This acceleration and streamline curvature subject the turbulent flow to high mean flow strains. This paper presents both experimental measurements and computational predictions for highly turbulent flow as it progresses through a passage of a gas turbine stator vane. Three-component velocity fields at the vane midspan were measured for inlet turbulence levels of 0.6%, 10%, and 19.5%. The turbulent kinetic energy increased through the passage by 130% for the 10% inlet turbulence and, because the dissipation rate was higher for the 19.5% inlet turbulence, the turbulent kinetic energy increased by only 31%. With a mean flow acceleration of five through the passage, the exiting local turbulence levels were 3% and 6% for the respective 10% and 19.5% inlet turbulence levels. Computational RANS predictions were compared with the measurements using four different turbulence models including the k-ε, Renormalization Group (RNG) k-ε, realizable k-ε, and Reynolds stress model. The results indicate that the predictions using the Reynolds stress model most closely agreed with the measurements as compared with the other turbulence models with better agreement for the 10% case than the 19.5% case. [S0098-2202(00)00804-X]

scholarly journals Turbulence parameters measured by the Beijing Mesosphere–Stratosphere–Troposphere radar in the troposphere/lower stratosphere with three models: Comparison and analyses

2022 ◽  
Author(s):  
Ze Chen ◽  
Yufang Tian ◽  
Yinan Wang ◽  
Yongheng Bi ◽  
Xue Wu ◽  
...  
Keyword(s):  
Wind Speed ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Spectral Width ◽  
Vertical Shear ◽  
Horizontal Wind ◽  
Horizontal Wind Speed ◽  
Turbulence Parameters ◽  
2D Model ◽  
Calculation Models

Abstract. Based on the quality-controlled observational spectral width data of the Beijing Mesosphere–Stratosphere–Troposphere (MST) radar in the altitudinal range of 3–19.8 km from 2012 to 2014, this paper analyzes the relationship between the proportion of negative turbulent kinetic energy (N-TKE) and the horizontal wind speed/horizontal wind vertical shear domain, and gives the distributional characteristics of atmospheric turbulence parameters obtained by using different calculation models. Three calculation models of the spectral width method were used in this study—namely, the H model (Hocking, 1985), N-2D model (Nastrom, 1997) and D-H model (Dehghan and Hocking, 2011). The results showed that the proportion of N-TKE in the H model increases with the horizontal wind speed and/or the vertical shear of horizontal wind speed, up to 80 %. When the horizontal wind speed is greater than 40 m·s−1, the proportion of N-TKE in the H model is greater than 60 %, and thus the H model is not applicable. When the horizontal wind speed is greater than 20 m s−1, the proportion of N-TKE in the N-2D model and D-H model increases with the horizontal wind speed, independent of the vertical shear of the horizontal wind speed, and the maximum values are 2 % and 4 %, respectively. However, it is still necessary to consider the applicability of the N-2D model and D-H model in some weather processes with strong winds. The distributional characteristics with height of the turbulent kinetic energy dissipation rate 𝜀 and the vertical eddy diffusion coefficient Kz derived by the three models are consistent with previous studies. Still, there are differences in the values of turbulence parameters. Also, the range resolution of the radar has little effect on the differences in the range of turbulence parameters' values. The median values of 𝜀 in the H model, N-2D model and D-H model are 10−3.2–10−2.8 m2 s−3, 10−2.8–10−2.4 m2 s−3 and 10−3.0–10−2.5 m2 s−3, respectively. The median values of Kz in these three models are 100.18–100.67 m2 s−1, 100.57–100.90 m2 s−1 and 100.44–100.74 m2 s−1.

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