THEORETICAL METHOD OF THE OPTIMUM DESIGN OF A SUPERCAVITATING PROPELLER BLADE WITH SPOILER MOUNTED ON THE TRAILING EDGE

This paper presents theoretical design method to obtain 2-D optimum section with spoiler mounted on the trailing edge of a supercavitating propeller blade. Matched Asymptotic Expansions (MAE) is applied to determine the geometry of profile and cavity shape in the framework of potential flow theory. The blade section is of wedge-like shape and the opened cavity closure scheme is adopted. A typical section, on which the optimum blade design will be based, is singled out among the best individual sections from root to tip. The spoiler length of each hydrofoil section resulting from MAE method are finalized with CFD method so as to consider viscous effect under the same lift condition, others hydrofoil geometries being kept constant. The hydrodynamic performances of all blade sections being designed on the basis of the resulting typical section from linearized method are finally predicted with CFD method.

Multi-temperature generalized Zhdanov closure for scrape-off layer/edge applications

The derivation of the multi-temperature generalized Zhdanov closure is provided starting from the most general form of the left hand side of the moment averaged kinetic equation with the Sonine-Hermite polynomial ansatz for an arbitrary number of moments. The process of arriving at the reduced higher-order moment equations, with its assumptions and approximations, is explicitly outlined. The generalized multi-species, multi-temperature coefficients from the authors' previous article are used to compute values of higher order moments such as heat flux in terms of the lower order moments. Transport coefficients and the friction and thermal forces for magnetic confinement fusion relevant cases with the generalized coefficients are compared to the scheme with the single-temperature coefficients previously provided by Zhdanov et al. It is found that the 21N-moment multi-temperature coefficients are adequate for most cases relevant to fusion. Furthermore, the 21N-moment scheme is also tested against the trace approximation to determine the range of validity of the trace approximation with respect to fusion relevant plasmas. Possible refinements to the closure scheme are illustrated as well, in order to account for quantities which might be significant in certain schemes such as the drift approximation.

A Constitutive Equation of Turbulence

Even though applications of direct numerical simulations are on the rise, today the most usual method to solve turbulence problems is still to apply a closure scheme of a defined order. It is not the case that a rising order of a turbulence model is always related to a quality improvement. Even more, a conceptual advantage of applying a lowest order turbulence model is that it represents the analogous method to the procedure of introducing a constitutive equation which has brought success to many other areas of physics. First order turbulence models were developed in the 1920s and today seem to be outdated by newer and more sophisticated mathematical-physical closure schemes. However, with the new knowledge of fractal geometry and fractional dynamics, it is worthwhile to step back and reinvestigate these lowest order models. As a result of this and simultaneously introducing generalizations by multiscale analysis, the first order, nonlinear, nonlocal, and fractional Difference-Quotient Turbulence Model (DQTM) was developed. In this partial review article of work performed by the authors, by theoretical considerations and its applications to turbulent flow problems, evidence is given that the DQTM is the missing (apparent) constitutive equation of turbulent shear flows.

Evaluation of boundary-layer and urban-canopy parameterizations for simulating wind in Miami during Hurricane Irma (2017)

The simulated winds within the urban canopy of landfalling tropical cyclones are sensitive to the representation of the planetary-boundary and urban-canopy layers in numerical weather prediction models. In order to assess the sub-grid-scale parameterizations of these layers, mesoscale model simulations were executed and evaluated against near-surface observations as the outer wind field of Hurricane Irma (2017) interacted with the built-up region from downtown Miami northward to West Palm Beach. Four model simulations were examined, comprised of two different planetary boundary layer (PBL) parameterizations (a local closure scheme with turbulent kinetic energy prediction and a nonlocal closure scheme) and two different urban canopy models (UCMs) [a zeroth order bulk scheme and a multilayer Building Effect Parameterization (BEP) that mimics the three-dimensionality of buildings]. Overall, the simulated urban canopy winds were weakly sensitive to the PBL scheme and strongly sensitive to the UCM. The bulk simulations compared most favorably to an analyzed wind swath in the urban environment, while the BEP simulations had larger negative biases in the same region. There is uncertainty in magnitude of the urban environment biases due to the lack of many urban sheltered measurements in the wind swath analysis. Biases in the rural environment were similar among the bulk and BEP simulations. An improved comparison with the analyzed wind swath in the urban region was obtained by reducing the drag coefficient in BEP in one of the PBL schemes. The usefulness of BEP was demonstrated in its ability to predict realistic heterogeneous near-surface velocity patterns in urban regions.

Towards a potential vorticity based mesoscale closure scheme

<p>With the advent of high-performance computing, we are now capable of simulating the ocean and climate system on decadal to centennial timescales. However, global and basin-scale simulations still lack the spatial resolution necessary to resolve the mesoscales (hereon referred to as mesoscale-permitting simulations), a scale roughly on the order of O(100 km). Here, we provide a first step towards a potential vorticity (PV) based mesoscale closure scheme in order to improve the representation of mesoscale eddies in such simulations by taking advantage of the thickness-weighted averaged (TWA) framework. In the TWA framework the total eddy feedback can be encapsulated in the Eliassen-Palm (E-P) flux divergence. This implies that mesoscale closure schemes aimed at representing the total eddy feedback should therefore be representing the E-P flux divergence. The TWA framework further elucidates that its divergence is equivalent to the eddy Ertel PV flux. In other words, if one is to parametrize the eddy Ertel PV flux, one has parametrized the total eddy feedback onto the mean flow. Using a 1/12° North Atlantic ensemble simulation with 24 members, which allows us to decompose the mesoscale variability from the forced dynamics, we show that the eddy Ertel PV flux can be related to the local-gradient of mean Ertel PV as an active tracer via an anisotropic eddy diffusivity tensor. What follows is that not only does the tensor bring together the isopycnal thickness skew diffusivity and isopycnic tracer diffusivity, the former known as the Gent-McWilliams (GM) parametrization and latter the Redi parametrization, but also incorporates the eddy momentum fluxes. Although the Redi parametrization has existed longer than GM, there has been much more development in the latter, leaving the Redi diffusivity poorly constrained. Being able to treat GM and Redi simultaneously is another strength of our framework.</p>

Scaling Behavior of a Turbulent Kinetic Energy Closure Scheme for the Stably Stratified Atmosphere: A Steady-State Analysis

We present a turbulent kinetic energy (TKE) closure scheme for the stably stratified atmosphere in which the mixing lengths for momentum and heat are not parameterized in the same manner. The key difference is that, while the mixing length for heat tends toward the stability independent mixing length for momentum in neutrally stratified conditions, it tends toward one based on the Brunt–Väisälä time scale and square root of the TKE in the limit of large stability. This enables a unique steady-state solution for TKE to be obtained, which we demonstrate would otherwise be impossible if the mixing lengths were the same. Despite the model’s relative simplicity, it is shown to perform reasonably well with observational data from the 1999 Cooperative Atmosphere–Surface Exchange Study (CASES-99) using commonly employed model constants. Analyzing the scaling behavior of the nondimensional velocity and potential temperature gradients, or of the stability (correction) functions, reveals that for large stability the present model scales in the same manner as the first-order operational scheme of Viterbo et al. Alternatively, it appears as a blend of two cases of the TKE closure scheme of Baas et al. Critically, because a unique steady-state TKE can be obtained, the present model avoids the nonphysical behavior identified in one of the cases of Baas et al.

Development of a two-way-coupled ocean–wave model: assessment on a global NEMO(v3.6)–WW3(v6.02) coupled configuration

This paper describes the implementation of a coupling between a three-dimensional ocean general circulation model (NEMO) and a wave model (WW3) to represent the interactions of upper-oceanic flow dynamics with surface waves. The focus is on the impact of such coupling on upper-ocean properties (temperature and currents) and mixed layer depth (MLD) at global eddying scales. A generic coupling interface has been developed, and the NEMO governing equations and boundary conditions have been adapted to include wave-induced terms following the approach of McWilliams et al. (2004) and Ardhuin et al. (2008). In particular, the contributions of Stokes–Coriolis, vortex, and surface pressure forces have been implemented on top of the necessary modifications of the tracer–continuity equation and turbulent closure scheme (a one-equation turbulent kinetic energy – TKE – closure here). To assess the new developments, we perform a set of sensitivity experiments with a global oceanic configuration at 1/4∘ resolution coupled with a wave model configured at 1/2∘ resolution. Numerical simulations show a global increase in wind stress due to the interaction with waves (via the Charnock coefficient), particularly at high latitudes, resulting in increased surface currents. The modifications brought to the TKE closure scheme and the inclusion of a parameterization for Langmuir turbulence lead to a significant increase in the mixing, thus helping to deepen the MLD. This deepening is mainly located in the Southern Hemisphere and results in reduced sea surface currents and temperatures.