Analytical estimation of mixing coefficient induced by surface wave-generated turbulence based on the equilibrium solution of the second-order turbulence closure model

Based on the equations of motion and the assumption that ocean turbulence is of isotropy or quasi-isotropy, we derived the closure equations of the second-order moments and the variation equations for characteristic quantities, which describe the mechanisms of advection transport and shear instability by the sum of wave-like and eddy-like motions and circulation. Given that ocean turbulence generated by wave breaking is dominant at the ocean surface, we presented the boundary conditions of the turbulence kinetic energy and its dissipation rate, which are determined by energy loss from wave breaking and entrainment depth respectively. According to the equilibrium solution of the variation equations and available data of the dissipation rate, we obtained an analytical estimation of the characteristic quantities of surface-wave-generated turbulence in the upper ocean and its related mixing coefficient. The derived kinetic dissipation rate was validated by field measurements qualitatively and quantitatively, and the mixing coefficient had fairly good consistency with previous results based on the Prandtl mixing length theory.

ON THE CLOSURE PROBLEM OF TURBULENCE MODEL THEORY

It is a wrong viewpoint that the turbulence closure problem is due to thenon-linearity, of N-S equation, because if we omit the non-linear terms in N-Sequation,many, physical quantities can not be obtained other than the mean-values. Inthis paper, we proof that the closure problem of turbulence be induced by lack ofstatistical disiribution in present turbulence theory. And the restriction of turbulencemodel theory and shortcoming of direct numerical simulation of N-S to solve theturbulence have been pointed out.

Numerical simulation of the flow within and over an intersection model with Reynolds-averaged Navier-Stokes method

In this study, the Reynolds-averaged Navier-Stokes （RANS） method is employed to simulate the flow within and over an intersection model with three kinds of k-ε turbulence closure schemes, namely, standard model, renormalization group （RNG） model and realizable k-ε model. The comparison between the simulated and observed flow fields shows that the RANS simulation with all the three turbulence models cannot completely and accurately reproduce the observed flow field in all details. A detailed comparison between the predicted profiles of wind velocities and the measured data shows that the realizble k-ε model is the best one among the three turbulence closure models in general. However, the extent to which the improvement is achieved by the realizable k-ε model is still not enough to completely and accurately describe the turbulent flow in a relatively complex environment.

A STUDY OF 1.5-ORDER CLOSURE TURBULENCE MODEL

Based on turbulence theory,a 1.5-order closure turbulence model is established.The model incorporating with the ground surface energy budget equation is constructed by means of a vertical one-dimensional(1-D)40-level grid-mesh.The numerical results reveal the 24-h evolution of the clear planetary boundary layer comparing with the Wangara boundary layer data of days 33—34.The model also takes into account some physical processes of radiative transfer and baroclinicity,revealing some important characteristics observed in the boundary layer,especially for the evolution of the mixed layer and low-level jet.The calculated results are in good agreement with the observational data. On the other hand,we also run the high-resolution model of the planetary boundary layer in the Mesoscale Model Ver- sion 4(MM4)with the same physical processes and initial conditions.The results show that the high-resolution model can not reveal those important characteristics as the 1.5-order closure model did.In general,it is shown that the 1.5-or- der closure turbulence model based on turbulence theory is better in rationality and reality.

Turbulence and mixing in a freshwater-influenced tidal bay: Observations and numerical modeling

In situ observations and numerical simulations of turbulence are essential to understanding vertical mixing processes and their dynamical controls on both physical and biogeochemical processes in coastal embayments. Using in situ data collected by bottom-mounted acoustic Doppler current profilers(ADCPs) and a free-falling microstructure profiler, as well as numerical simulations with a second-moment turbulence closure model, we studied turbulence and mixing in the Xiamen Bay, a freshwater-influenced tidal bay located at the west coast of the Taiwan Strait. Dynamically, the bay is driven predominantly by the M2 tide, and it is under a significant influence of the freshwater discharged from the Jiulong River. It is found that turbulence quantities such as the production and dissipation rates of the turbulent kinetic energy(TKE) were all subject to significant tidal variations, with a pronounced ebb-flood asymmetry. Turbulence was stronger during flood than ebb. During the flooding period, the whole water column was nearly well mixed with the depth-averaged TKE production rate and vertical eddy viscosity being up to 5?10?6 W kg?1 and 2?10?2 m2 s?1, respectively. In contrast, during the ebb strong turbulence was confined only to a 5?8 m thick bottom boundary layer, where turbulence intensity generally decreases with distance from the seafloor. Diagnosis of the potential energy anomaly showed that the ebb-flood asymmetry in turbulent dissipation and mixing was due mainly to tidal straining process as a result of the interaction between vertically shared tidal currents and horizontal density gradients. The role of vertical mixing in generating the asymmetry was secondary. A direct comparison of the modeled and observed turbulence quantities confirmed the applicability of the second-moment turbulence closure scheme in modeling turbulent processes in this weakly stratified tidally energetic environment, but also pointed out the necessity of further refinements of the model.

Large Eddy Simulation and Study of the Urban Boundary Layer

Based on a pseudo-spectral large eddy simulation (LES) model, an LES model with an anisotropy turbulent kinetic energy (TKE) closure model and an explicit multi-stage third-order Runge-Kutta scheme is established. The modeling and analysis show that the LES model can simulate the planetary boundary layer (PBL) with a uniform underlying surface under various stratifications very well. Then, similar to the description of a forest canopy, the drag term on momentum and the production term of TKE by subgrid city buildings are introduced into the LES equations to account for the area-averaged effect of the subgrid urban canopy elements and to simulate the meteorological fields of the urban boundary layer (UBL). Numerical experiments and comparison analysis show that: (1) the result from the LES of the UBL with a proposed formula for the drag coefficient is consistent and comparable with that from wind tunnel experiments and an urban subdomain scale model; (2) due to the effect of urban buildings, the wind velocity near the canopy is decreased, turbulence is intensified, TKE, variance, and momentum flux are increased, the momentum and heat flux at the top of the PBL are increased, and the development of the PBL is quickened; (3) the height of the roughness sublayer (RS) of the actual city buildings is the maximum building height (1.5-3 times the mean building height), and a constant flux layer (CFL) exists in the lower part of the UBL.

A NEW DEPTH-AVERAGED TWO-EQUATION (K-) TURBULENT CLOSURE MODEL AND ITS APPLICATION TO NUMERICAL SIMULATION FOR A RIVER

The paper mainly focuses on describing the modification made to a new depth-averaged two-equation turbulent closure model based on the revised κ-ω model recently. In the case of side discharged jets with tempera- ture difference and transverse current, the new model has been investigated numerically in detail. As a practical example of application to use the new model, the side discharge of the cooling water from three outlets into a natu- ral river on one bank has been simulated, and the geomorphic variation under water has been treated suitably. Two depth-averaged models, and have been used, the later was the unique one up to the present. Emphasis is placed on the comparative research with different models under the same computational conditions. It has been verified that if the discharged flow rates are relatively small, when the pollutant plume in the near and transitional zons is predicted, the agreement with experimental and field data simulated by the model is better than by the model or other methods commonly used in engineering.

A NEW DEPTH-AVERAGED TWO-EQUATION(?) TURBULENT CLOSURE MODEL

Based on the revised turbulent k-w model, a new depth-averaged two-equation closure model is offered in this paper. Through numerical investigation, it is shown that the - model has the same order of accuracy as the - model in predicting the eddy regions produced by side temprature jets with transverse currents, but the newly developed model is better than the - model in predicting the jet width,