Ion heat and parallel momentum transport by stochastic magnetic fields and turbulence

The theory of turbulent transport of parallel momentum and ion heat by the interaction of stochastic magnetic fields and turbulence is presented. Attention is focused on determining the kinetic stress and the compressive energy flux. A critical parameter is identified as the ratio of the turbulent scattering rate to the rate of parallel acoustic dispersion. For the parameter large, the kinetic stress takes the form of a viscous stress. For the parameter small, the quasilinear residual stress is recovered. In practice, the viscous stress is the relevant form, and the quasilinear limit is not observable. This is the principal prediction of this paper. A simple physical picture is developed and shown to recover the results of the detailed analysis.

Viscoplastic plates

An asymptotic model is constructed to describe the bending of thin sheets, or plates, of viscoplastic fluid described by the Herschel–Bulkley constitutive law, which incorporates the von Mises yield condition and a nonlinear viscous stress. The model reduces to a number of previous ones from plasticity theory and viscous fluid mechanics in various limits. It is characterized by a yield criterion proposed by Ilyushin which compactly combines the effect of the bending moment and in-plane stress tensors through three particular invariants. The model is used to explore the bending of loaded flat plates, the deflection of impulsively driven circular plates, and the tension-controlled deflection of loaded beams.

Three-Dimensional Central Moment Lattice Boltzmann Method on a Cuboid Lattice for Anisotropic and Inhomogeneous Flows

Lattice Boltzmann (LB) methods are usually developed on cubic lattices that discretize the configuration space using uniform grids. For efficient computations of anisotropic and inhomogeneous flows, it would be beneficial to develop LB algorithms involving the collision-and-stream steps based on orthorhombic cuboid lattices. We present a new 3D central moment LB scheme based on a cuboid D3Q27 lattice. This scheme involves two free parameters representing the ratios of the characteristic particle speeds along the two directions with respect to those in the remaining direction, and these parameters are referred to as the grid aspect ratios. Unlike the existing LB schemes for cuboid lattices, which are based on orthogonalized raw moments, we construct the collision step based on the relaxation of central moments and avoid the orthogonalization of moment basis, which leads to a more robust formulation. Moreover, prior cuboid LB algorithms prescribe the mappings between the distribution functions and raw moments before and after collision by using a moment basis designed to separate the trace of the second order moments (related to bulk viscosity) from its other components (related to shear viscosity), which lead to cumbersome relations for the transformations. By contrast, in our approach, the bulk and shear viscosity effects associated with the viscous stress tensor are naturally segregated only within the collision step and not for such mappings, while the grid aspect ratios are introduced via simpler pre- and post-collision diagonal scaling matrices in the above mappings. These lead to a compact approach, which can be interpreted based on special matrices. It also results in a modular 3D LB scheme on the cuboid lattice, which allows the existing cubic lattice implementations to be readily extended to those based on the more general cuboid lattices. To maintain the isotropy of the viscous stress tensor of the 3D Navier–Stokes equations using the cuboid lattice, corrections for eliminating the truncation errors resulting from the grid anisotropy as well as those from the aliasing effects are derived using a Chapman–Enskog analysis. Such local corrections, which involve the diagonal components of the velocity gradient tensor and are parameterized by two grid aspect ratios, augment the second order moment equilibria in the collision step. We present a numerical study validating the accuracy of our approach for various benchmark problems at different grid aspect ratios. In addition, we show that our 3D cuboid central moment LB method is numerically more robust than its corresponding raw moment formulation. Finally, we demonstrate the effectiveness of the 3D cuboid central moment LB scheme for the simulations of anisotropic and inhomogeneous flows and show significant savings in memory storage and computational cost when used in lieu of that based on the cubic lattice.

S-wave propagation across material discontinuities in poroelasticity

The shear motion in Newtonian fluids, i.e., the fluid vorticity, represents an intrinsic loss mechanism governed by a diffusion equation. Its description involves the trace-free part of the fluid viscous stress tensor. This part is missing in the Biot theory of poroelasticity. As a result, the fluid vorticity is not captured, and only one S-wave is predicted. The missing fluid vorticity has implications for the propagation of S-waves across discontinuities. This becomes most apparent in the problem of S-wave propagation across the welded contact of an elastic solid with a porous medium. At such a contact, the no-slip condition between the elastic solid and the constituent parts of the porous medium, the solid-frame, and the pore-fluid, must hold. This requirement translates into a vanishing relative motion of the fluid with respect to the solid-frame, i.e., filtration field, at the contact. Nevertheless, our analysis shows that for the Biot theory, in the low-frequency regime, a non-zero, although insignificantly small filtration field exists at the contact. But, more importantly, the filtration field is noticeable when the transition to the high-frequency regime occurs. This constitutes a disagreement with the requirement of a no-slip boundary condition and renders the prediction unphysical. This shortcoming is circumvented by including the fluid viscous stress tensor into the poroelastic constitutive relations, as stipulated by the de la Cruz-Spanos poroelasticity theory. Then, a second S-wave is predicted which manifests as the fluid vorticity at macroscale. This process is distinct from the fast S-wave, the other predicted S-wave akin to the Biot S-wave. We find that the generation of this process at the contact induces a filtration field equal and opposite to that associated with the fast S-wave. Therefore, the no-slip condition is satisfied, and the S-wave reflection/transmission across a discontinuity becomes physically meaningful.

Buckling, crumpling, and tumbling of semiflexible sheets in simple shear flow

Athermal semiflexible sheets dispersed in a fluid are simulated under simple shear flow, and the dynamical behavior of the sheets is found to depend strongly on initial orientation and the ratio of bending stress to viscous stress.

Semiflow Selection to Models of General Compressible Viscous Fluids

We prove the existence of a semiflow selection with range the space of càglàd, i.e. left-continuous and having right-hand limits functions defined on $$[0,\infty )$$ [ 0 , ∞ ) and taking values in a Hilbert space. Afterwards, we apply this abstract result to the system arising from a compressible viscous fluid with a barotropic pressure of the type $$a\varrho ^{\gamma }, \gamma \ge 1$$ a ϱ γ , γ ≥ 1 , with a viscous stress tensor being a nonlinear function of the symmetric velocity gradient.

On the Vorticity Balance over Steep Slopes: Kuroshio Intrusions Northeast of Taiwan

The circulation of the Kuroshio northeast of Taiwan is characterized by a large anticyclonic loop of surface intrusion and strong upwelling at the shelfbreak. To study the mechanisms of Kuroshio intrusions, the vorticity balance is examined using a high-resolution nested numerical model. In the 2D depth-averaged vorticity equation, the advection of geostrophic potential vorticity (APV) term and the joint effect of baroclinicity and relief (JEBAR) term are dominant. On the other hand, in the 2D depth-integrated vorticity equation, the main balance is between nonlinear advection and bottom pressure torque. It is shown that JEBAR and APV tend to compensate, and their difference is comparable to bottom pressure torque. Perhaps most significantly, a general framework is provided for examination of vorticity balance over steep slopes through a full 3D depth-dependent vorticity equation. The 3D analysis reveals a well-defined bottom boundary layer over the shelfbreak, about 40 m deep and capped by the vertical velocity maximum. In the upper frictionless layer from the surface to about 100 m, the primary balance is between nonlinear advection and horizontal divergence. In the lower frictional layer, viscous stress is balanced by nonlinear advection and horizontal divergence. The bottom pressure torque, which corresponds to the depth-integrated viscous effect, is a proxy for viscous stress divergence at the bottom. The importance of nonlinear advection is further demonstrated in a sensitivity experiment by removing advective terms from momentum equations. Without nonlinear advection, the bottom pressure torque becomes trivial, the boundary layer vanishes, and the on-shelf intrusion is considerably weakened.