The energy spectrum must be useful in describing the energy transfer not only in isotropic turbulence but also in inhomogeneous turbulence. A new expression for the energy density in the scale space was introduced on the basis of the filtered two-point velocity correlation in the physical space. In contrast to previous expressions, this expression is expected to be non-negative. The transport equation for the energy density was derived and direct numerical simulation data of channel flow was used to evaluate the energy transport in the physical and scale spaces. The energy flux from large to small scales was adequately observed.

Mean-field dynamo equations are addressed with the aid of the path-integral method. The evolution of magnetic field is treated as a three-dimensional Wiener random process, and the mean magnetic-field equations are obtained with the Winer integral over all the trajectories of fluid particle. The form of the equations is just the same as the conventional mean-field equations, but the present equations are derived with the velocity-field realization affected by the magnetic-field force. In this sense, the present ones are nonlinear dynamo equations.

In studying turbulence model, grid turbulence is the most fundamental flow field for the numerical prediction of turbulence. However, there seem to be not necessarily many experiments of thermally stratified grid turbulence and they seem to be not necessarily produce reliable data. Therefore, we need to pay attention to the results from the experiments when referring to them to verify turbulence models. In this study, we consider the model for the dissipation rate of temperature fluctuation and show the results.

It is known that kinetic energy is rapidly transferred in the direction of the rotation axis. Previous researches indicate that the rapid energy transport is closely related to the helicity of fluids. In this study, we discuss the relationship between the axial energy transport and the helicity using the statistical quantities of turbulence. It is suggested that the pressure related to the angular velocity of the system rotation plays a significant role in the energy flux. This point is confirmed by the numerical simulation, and the estimation for the energy flux in the axis direction is discussed.

Meteorological condition related to the lack of overturn was examined by numerical simulation of water current and density fields in Lake Biwa under 40 future scenarios of atmospheric temperature and solar radiation, and two condition for wind velocity. The overturn can be ceased by lower wind velocity in winter, and solar radiation in winter that is higher than solar radiation in the winter of the previous year. As future studies, the scenario of wind in addition to atmospheric temperature and solar radiation will be generated in order to examine the risk of the lack of overturn.

In order to increase an efficiency of thermo-fluids systems, enhancing heat transfer performance of heat exchangers in turbulent thermal convections is on huge demand. Shape optimization of heat transfer surfaces for convective heat transfer has been achieved with an adjoint-based shape optimization theory. Since linearization on the momentum equation is not applicable for turbulent flows due to strong nonlinearity, one main approach uses a steady RANS-based adjoint analysis with turbulent models. Existing turbulence models, however, may not always provide good estimates especially when flow separation and reattachment are present, so that the resultant optimal shape would not guarantee the performance enhancement. In this study, we propose a new adjoint-based approach which uses the eddy viscosity and the eddy diffusivity obtained from scale-resolved unsteady simulations such as DNS or LES.

We consider a turbulent channel flow, where a scalar point source with a time-harmonic intensity releases a substance that can be modeled as a passive scalar. Our objective is to estimate the time history of the source intensity based on the measurements obtained by a movable sensor which is restricted to move on a cross-wind plane downstream of the source. We have adopted an adjoint approach in order to optimize the sensor trajectory for a simplified case where the source location is known. It is shown that the proposed algorithm provides a good reconstruction of the original coherent sinusoidal wave of the scalar source accurately from the chaotic scalar signals measured by the moving sensor downstream. The proposed scheme can be easily extended to multiple sensors.

Almost all LES wall model assumes an assumption that the instantaneous velocity field follows some kind of empirical statistical laws, however by our preliminary study, the assumption does not necessarily hold in the flow field around the simplified geometries. Therefore, we develop an LES wall model which does not use any empirical statistical law, focusing on nonstationary feedback force to turbulent structure. In this study, as the first report, we report the effect of grid resolution on the behavior of the turbulent structure and the momentum transport process.

Wall-resolving LES flow solver based on Lattice Boltzmann Method (LBM） is being developed. The features of the flow solver are accurate prediction of turbulent phenomena and auto-meshing. A large scale flow computation with over two trillion grids is possible with the solver. Such a large scale computation enable wall-resolving LES of high Reynolds number flow. Auto-meshing tool implemented to the solver is feasible for flow computation with complex geometry. Mesh data for a complex geometry with approximately 50 billion grids can be generated within a minute. Several benchmark tests were performed to evaluate accuracy, performance and feasibility of meshing tools of a prototype solver. Cavity flow and homogeneous isotropic flow were computed to evaluate accuracy. Weak-scale benchmark test with mesh composed of up to 2.2 trillion grids were performed to evaluate performance and parallel efficiency. Flow around a dolphin model was computed with mesh composed of 50 billion grids to evaluate the meshing tool for a complex geometry. In this paper, we report the results of the above benchmark tests for a prototype of wall-resolving LES flow solver based on LBM.