Search

Motivated by wind blowing over water, we use asymptotic methods to study the evolution of short wavelength interfacial waves driven by the combined action of these flows. We solve the Rayleigh equation for the stability of the shear flow, and construct a uniformly valid approximation for the perturbed streamfunction, or eigenfunction. We then expand the real part of the eigenvalue, the phase speed, in a power series of the inverse wavenumber and show that the imaginary part is exponentially small. We give expressions for the growth rates of the Miles (J. Fluid Mech., vol. 3, 1957, pp. 185-204) and rippling (e.g. Young & Wolfe, J. Fluid Mech., vol. 739,2014, pp. 276-307) instabilities that are valid for an arbitrary shear flow. The accuracy of the results is demonstrated by a comparison with the exact solution of the eigenvalue problem in the case when both the wind and the current have an exponential profile. [ABSTRACT FROM AUTHOR]

When wind blows over water, ripples are generated on the water surface. These ripples can be regarded as perturbations of the wind field, which is modelled as a parallel inviscid flow. For a given wavenumber k, the perturbed streamfunction of the wind field and the complex phase speed are the eigenfunction and the eigenvalue of the so-called Rayleigh equation in a semi-infinite domain. Because of the small air--water density ratio, ρa/ρw ≡ ∈ ≪ 1, the wind and the ripples are weakly coupled, and the eigenvalue problem can be solved perturbatively. At the leading order, the eigenvalue is equal to the phase speed c0 of surface waves. At order ∈, the eigenvalue has a finite imaginary part, which implies growth. Miles (J. Fluid Mech., vol. 3, 1957, pp. 185-204) showed that the growth rate is proportional to the square modulus of the leading-order eigenfunction evaluated at the so-called critical level z = zc, where the wind speed is equal to c0 and the waves extract energy from the wind. Here, we construct uniform asymptotic approximations of the leading-order eigenfunction for long waves, which we use to calculate the growth rate as a function of k. In the strong wind limit, we find that the fastest growing wave is such that the aerodynamic pressure is in phase with the wave slope. The results are confirmed numerically. [ABSTRACT FROM AUTHOR]

As expected, we observe Kolmogorov scaling Graph $E(k)\sim k^{-5/3}$ for Graph $k and a pseudo-turbulence scaling Graph $E(k) \sim k^{-3}$ for Graph $k>k {d}$. Hence for both of these cases we obtain Graph $E(k) \sim k^{-3}$ for Graph $k > k {d}$ and Graph $E(k)\sim k^{-5/3}$ for Graph $k. In figure 13 we plot the p.d.f. of Graph ${\rm \pi} {K}(\boldsymbol {x})$ with Graph $K=k {d}$ for Graph $b=0$, Graph $b=0.13$ and Graph $b=\infty$. For all the runs, Graph $L=2{\rm \pi}$ and Graph $d=0.46$, and the dimensionless numbers Graph $Ga= 302$, Graph $Bo =1.8$, Graph $At = 0.04$ and Graph $\varPhi = 1.64\,\%$ are kept fixed. \end{equation} In figure 3( I a i , I b i ) we plot the velocity streamlines of the average velocity field Graph ${\boldsymbol {u}}^{CM}({\boldsymbol {\xi }})$ for Graph $b=\infty$ (Graph ${\texttt {R0}}$) and Graph $b=0.13$ (Graph ${\texttt {R3}}$). [Extracted from the article]

The effect of turbulence on the mass transfer between a fluid and embedded small heavy inertial particles that experience surface reactions is studied. For simplicity, the surface reaction, which takes place when a gas phase reactant is converted to a gas phase product at the external surface of the particles, is unimolar and isothermal. Two effects are identified. The first effect is due to the relative velocity between the fluid and the particles, and a model for the relative velocity is presented. The second effect is due to the clustering of particles, where the mass transfer rate is inhibited due to the rapid depletion of the consumed species inside the dense particle clusters. This last effect is relevant for large Damköhler numbers, where the Damköhler number is defined as the ratio of the turbulent and chemical time scales, and it may totally control the mass transfer rate for Damköhler numbers larger than unity. A model that describes how this effect should be incorporated into existing simulation tools that utilize the Reynolds averaged Navier-Stokes approach is presented. [ABSTRACT FROM AUTHOR]

The chiral symmetry breaking properties of the Tayler instability are discussed. Effective amplitude equations are determined in one case. This model has three free parameters that are determined numerically. Comparison with chiral symmetry breaking in biochemistry is made. [ABSTRACT FROM PUBLISHER]

We present a unified three-dimensional model of the convection zone and upper atmosphere of the Sun in spherical geometry. In this model, magnetic fields, generated by a helically forced dynamo in the convection zone, emerge without the assistance of magnetic buoyancy. We use an isothermal equation of state with gravity and density stratification. Recurrent plasmoid ejections, which rise through the outer atmosphere, is observed. In addition, the current helicity of the small–scale field is transported outwards and form large structures like magnetic clouds. [ABSTRACT FROM PUBLISHER]

We summarise recent results form direct numerical simulations of both non-rotating helically forced and rotating convection driven MHD equations in spherical wedge-shape domains. In the former, using perfect-conductor boundary conditions along the latitudinal boundaries we observe oscillations, polarity reversals and equatorward migration of the large-scale magnetic fields. In the latter we obtain angular velocity with cylindrical contours and large-scale magnetic field which shows oscillations, polarity reversals but poleward migration. The occurrence of these behviours in direct numerical simulations is clearly of interest. However the present models as they stand are not directly applicable to the solar dynamo problem. Nevertheless, they provide general insights into the operation of turbulent dynamos. [ABSTRACT FROM PUBLISHER]