Flamelet connection to turbulence kinetic energy dissipation rate

DNS of swirling hydrogen–air premixed flames

Turbulence within the upper ocean mixed layer plays a key role in various physical, biological, and chemical processes. Between September and November 2011, a dataset of 570 vertical profiles of the turbulent kinetic energy (TKE) dissipation rate, as well as conventional hydrological and meteorological data, were collected in the upper layer of the tropical Indian Ocean. These data were used to statistically analyze the vertical distribution of the TKE dissipation rate in the mixed layer. The arithmetic-mean method made the statistical TKE dissipation rate profile more scattered than the median and geometric-mean methods. The statistical TKE dissipation rate were respectively scaled by the surface buoyancy flux and the TKE dissipation rate at the mixed-layer base. It was found that the TKE dissipation rate scaled by that at the mixed-layer base exhibited better similarity characteristics than that scaled by the surface buoyancy flux, whether the stability parameter D/|LMO| was greater or less than 10, indicating that the TKE dissipation rate at the mixed-layer base is a better characteristic scaling parameter for reflecting the intrinsic structure of the TKE dissipation rate in the mixed layer, where D and LMO are respectively the mixed-layer thickness and the Monin-Obukhov length scale. The parameterization of the TKE dissipation rate at the mixed-layer base on the shear-driven dissipation rate and the surface buoyancy flux was further explored. It was found that the TKE dissipation rate at the mixed-layer base could be well fitted by a linear combination of three terms: the wind-shear-driven dissipation rate, the surface buoyancy flux, and a simple nonlinear coupling term of these two .

On the development of a subgrid scale clutter model

Turbulent structures, integral length scale and turbulent kinetic energy (TKE) dissipation rate in compound channel flow

The characteristics of the spatially averaged (SA) turbulent kinetic energy (TKE) dissipation rate are studied experimentally in flows over water-worked gravel beds (WGBs) and a screeded gravel bed (SGB) measuring the instantaneous velocity field by the Particle Image Velocimetry system. To study the response of water work roughness to the TKE related parameters, the flow Froude numbers in both the WGB and SGB were maintained identical in the experiments. Owing to the action of water work, the surface gravels in the WGB are more spatially organized than those of the SGB, where they are randomly oriented, resulting in a higher roughness in the WGB than in the SGB. Examination of the second- and the third-order velocity structure functions reveals the evidence of an inertial subrange in both the WGB and SGB. Kolmogorov’s two-thirds and four-fifths laws are preserved within the inertial subrange, providing an accurate estimation of the TKE dissipation rate in both the beds. However, owing to the higher roughness in the WGB than in the SGB, the TKE and the scaling law parameters are greater in the former than in the latter case. Furthermore, to examine the effects of the shear Reynolds number on the TKE dissipation rate and the scaling law parameters, two additional experiments with different shear Reynolds numbers were conducted with the WGBs. The comparative results suggest that the SA TKE dissipation rates estimated from Kolmogorov’s two-thirds and four-fifths laws increase with an increase in the shear Reynolds number in the WGBs.The characteristics of the spatially averaged (SA) turbulent kinetic energy (TKE) dissipation rate are studied experimentally in flows over water-worked gravel beds (WGBs) and a screeded gravel bed (SGB) measuring the instantaneous velocity field by the Particle Image Velocimetry system. To study the response of water work roughness to the TKE related parameters, the flow Froude numbers in both the WGB and SGB were maintained identical in the experiments. Owing to the action of water work, the surface gravels in the WGB are more spatially organized than those of the SGB, where they are randomly oriented, resulting in a higher roughness in the WGB than in the SGB. Examination of the second- and the third-order velocity structure functions reveals the evidence of an inertial subrange in both the WGB and SGB. Kolmogorov’s two-thirds and four-fifths laws are preserved within the inertial subrange, providing an accurate estimation of the TKE dissipation rate in both the beds. However, owing to the higher rough...

Abstract. In this paper we propose two approaches to estimating the turbulent kinetic energy (TKE) dissipation rate, based on the zero-crossing method by Sreenivasan et al. (1983). The original formulation requires a fine resolution of the measured signal, down to the smallest dissipative scales. However, due to finite sampling frequency, as well as measurement errors, velocity time series obtained from airborne experiments are characterized by the presence of effective spectral cutoffs. In contrast to the original formulation the new approaches are suitable for use with signals originating from airborne experiments. The suitability of the new approaches is tested using measurement data obtained during the Physics of Stratocumulus Top (POST) airborne research campaign as well as synthetic turbulence data. They appear useful and complementary to existing methods. We show the number-of-crossings-based approaches respond differently to errors due to finite sampling and finite averaging than the classical power spectral method. Hence, their application for the case of short signals and small sampling frequencies is particularly interesting, as it can increase the robustness of turbulent kinetic energy dissipation rate retrieval.

Steady flamelet modelling of a turbulent non-premixed flame considering scalar dissipation rate fluctuations

Abstract. Current turbulence parameterizations in numerical weather prediction models at the mesoscale assume a local equilibrium between production and dissipation of turbulence. As this assumption does not hold at fine horizontal resolutions, improved ways to represent turbulent kinetic energy (TKE) dissipation rate (ϵ) are needed. Here, we use a 6-week data set of turbulence measurements from 184 sonic anemometers in complex terrain at the Perdigão field campaign to suggest improved representations of dissipation rate. First, we demonstrate that the widely used Mellor, Yamada, Nakanishi, and Niino (MYNN) parameterization of TKE dissipation rate leads to a large inaccuracy and bias in the representation of ϵ. Next, we assess the potential of machine-learning techniques to predict TKE dissipation rate from a set of atmospheric and terrain-related features. We train and test several machine-learning algorithms using the data at Perdigão, and we find that the models eliminate the bias MYNN currently shows in representing ϵ, while also reducing the average error by up to almost 40 %. Of all the variables included in the algorithms, TKE is the variable responsible for most of the variability of ϵ, and a strong positive correlation exists between the two. These results suggest further consideration of machine-learning techniques to enhance parameterizations of turbulence in numerical weather prediction models.

A structure function approach is applied to estimate the turbulent kinetic energy (TKE) dissipation rate in the bottom boundary layer of the Pearl River Estuary (PRE). Simultaneous measurements with an acoustic Doppler velocimeter (ADV) supplied independent data for the verification of the structure function method. The results show that, 1) the structure function approach is reliable and successfully applied method to estimate the TKE dissipation rate. The observed dissipation rates range between 8.3×10−4 W/kg and 4.9×10−6 W/kg in YM01 and between 3.4×10−4 W/kg and 4.8×10−7 W/kg in YM03, respectively, while exhibiting a strong quarter-diurnal variation. 2) The balance between the shear production and viscous dissipation is better achieved in the straight river. This first-order balance is significantly broken in the estuary by non-shear production/dissipation due to wave-induced fluctuations.

The turbulent kinetic energy and energy dissipation rate in the wake of a circular cylinder are examined at a Reynolds number of 1000. The turbulence characteristics are quantified using direct numerical simulation, which provides a comprehensive dataset that is almost impossible to acquire from physical experiments. The energy dissipation rate is decomposed into the components due to the mean flow, the coherent primary vortices and the remainder. It is found that the remainder component, which develops only in a three-dimensional turbulent wake and resides mainly in the regions of vortices, accounts for 95 % and 97 % of the total dissipation rate for 10 and 20 cylinder diameters downstream of the cylinder, respectively (while the remainder accounts for 62 % and 83 % of the total turbulent kinetic energy). Based on the remainder component, the validity of local isotropy, local axisymmetry, local homogeneity and homogeneity in they–zplane for the turbulent dissipation in the wake is examined. The analysis reveals that the turbulent dissipation is largely locally homogeneous, but not locally isotropic or axisymmetric, even after the annihilation of the primary vortex street. In addition, the performances of the four corresponding surrogates to the true dissipation rate are evaluated. Owing to the general validity of local homogeneity, the surrogates of local homogeneity and homogeneity in they–zplane perform well. Although local axisymmetry does not hold, the corresponding surrogate performs well, because errors from different terms largely cancel out. However, the surrogate of local isotropy generally underestimates the true dissipation rate.

It has been recognized that modulated wave groups trigger wave breaking and generate energy dissipation events on the ocean surface. Quantitative examination of wave-breaking events and associated turbulent kinetic energy (TKE) dissipation rates within a modulated wave group in the open ocean is not a trivial task. To address this challenging topic, a set of laboratory experiments was carried out in an outdoor facility, the Oil and Hazardous Material Simulated Environment Test Tank (203 m long, 20 m wide, 3.5 m deep). TKE dissipation rates at multiple depths were estimated directly while moving the sensor platform at a speed of about 0.53 m s−1 toward incoming wave groups generated by the wave maker. The largest TKE dissipation rates and significant whitecaps were found at or near the center of wave groups where steepening waves approached the geometric limit of waves. The TKE dissipation rate was O(10−2) W kg−1 during wave breaking, which is two to three orders of magnitude larger than before and after wave breaking. The enhanced TKE dissipation rate was limited to a layer of half the wave height in depth. Observations indicate that the impact of wave breaking was not significant at depths deeper than one wave height from the surface. The TKE dissipation rate of breaking waves within wave groups can be parameterized by local wave phase speed with a proportionality breaking strength coefficient dependent on local steepness. The characterization of energy dissipation in wave groups from local wave properties will enable a better determination of near-surface TKE dissipation of breaking waves.

The accuracy of turbulent kinetic energy (TKE) dissipation rate measured by PIV is studied. The critical issue for PIV-based dissipation measurements is the strong dependency on the spatial resolution, Δx, as reported by Saarenrinne and Piirto (Exp Fluids Suppl:S300–S307, 2000). When the PIV spacing is larger than the Kolmogorov scale, η, the dissipation is underestimated because the small scale fluctuations are filtered. For the case of Δx smaller than the Kolmogorov scale, the error rapidly increases due to noise. We introduce a correction method to eliminate the dominant error for the small Δx case. The correction method is validated by using a novel PIV benchmark, random Oseen vortices synthetic image test (ROST), in which quasi-turbulence is generated by randomly superposing multiple Oseen vortices. The error of the measured dissipation can be more than 1,000% of the analytical dissipation for the small Δx case, while the dissipation rate is underestimated for the large Δx case. Though the correction method does not correct the underestimate due to the low resolution, the dissipation was accurately obtained within a few percent of the true value by using the correction method for the optimal resolution of η/10 < Δx < η/2.

A Kongsberg Seaglider with a microstructure package was deployed in the Faroe-Shetland Channel in 2017 as part of the 4th Marine Autonomous Systems in Support of Marine Observations (MASSMO4). Using the FP07 fast thermistor (512 Hz), the standard Seaglider thermistor (0.2 Hz) and potential density calculated from Seaglider conductivity-temperature sail (0.2 Hz) a comparison of the Thorpe Scale method has been made. Through this method turbulent kinetic energy (TKE) dissipation rates are inferred from the length-scale of a turbulent overturn. Comparison of the three physical quantities show that overturns with a comparable length-scale also have a comparable TKE dissipation rate. The range of estimated TKE dissipation rates from the 0.2 Hz data is also comparable to those inferred using the same method applied to potential density calculated from a ship mounted CTD.

In this paper, a two-phase flow model combined with the Realizable k–ε turbulence model was used to simulate hydraulic characteristics of two-type dissipaters: the stepped spillway combined with stilling pool and the stepped spillway combined with wide tailing pier and stilling pool. The distributions of physical parameters, such as velocity field, pressure field, turbulence kinetic energy and turbulence dissipation rate were obtained. The grid was generated by using the regional division method, the unstructured grids used for the irregular and complex parts and the structured grids for the regular and simple parts, and the grid density is arranged according to the flow gradient size. The finite volume method was adopted to discretized the control equations; and the VOF method was adopted to deal with the free water surface; and the PISO algorithm was used to solve the velocity and pressure coupling equations. A comparative analysis of the two energy-dissipators in the velocity field, pressure field, turbulence kinetic energy and turbulence kinetic energy dissipation rate shows that the dissipation of overflow for a stepped spillway together with wide tailing piers and a stilling pool jointing energy dissipator is better than that with pier situation.

Gadanki radar observations of the low‐latitude mesospheric echoes studied earlier have shown that while both occurrence rate and signal‐to‐noise ratio of the mesospheric echoes peak in the equinoxes turbulent kinetic energy (TKE) dissipation rate and eddy diffusivity, estimated using spectral width of these echoes, peak in the summer. This seasonal difference is apparently inconsistent with the understanding that the mesospheric echoes are generated by turbulence. In this paper, we analyze Gadanki radar observations of mesospheric echoes made during 2011 and 2012 and study seasonal variations in reflectivity and TKE dissipation rate in an attempt to address the aforementioned puzzle. We show that both reflectivity and TKE dissipation rate in the mesosphere show semiannual variations peaking in the equinoxes, which are vastly different from those reported earlier. We also show that seasonal variations in reflectivity and TKE dissipation rate have a close correspondence with gravity wave activity. These results are found to be consistent with the gravity wave breaking hypothesis generating turbulence and radar echoes in the low‐latitude mesosphere.