This paper considers the problem of viscous dissipation in the flow of Newtonian fluid through a tube of annular cross section, with Dirichlet boundary conditions. The solution of the problem is obtained by a series expansion about the complete eigenfunctions system of a Sturm-Liouville problem. Eigenfunctions and eigenvalues of this Sturm-Liouville problem are obtained by Galerkin’s method.

Adopting the setting for the study of existence and scale locality of the energy cascade in 3D viscous flows in physical space recently introduced by the authors to 3D inviscid flows, it is shown that the anomalous dissipation is – in the case of decaying turbulence – indeed capable of triggering the cascade which then continues ad infinitum, confirming Onsager’s predictions.

Direct determination of the irreversible turbulent flux of salinity in the ocean has not been possible because of the complexity of measuring salinity on the smallest scales over which it mixes. Presented is an analysis of turbulent salinity microstructure from measurements using a combined fast-conductivity/temperature probe on a slowly falling vertical microstructure profiler. Four hundred pa...

We study local instabilities of a differentially rotating viscous flow of electrically conducting incompressible fluid subject to an external azimuthal magnetic field. In the presence of the magnetic field, the hydrodynamically stable flow can demonstrate non-axisymmetric azimuthal magnetorotational instability (AMRI) both in the diffusionless case and in the double-diffusive case with viscous ...

The purpose of toroidal flow, i.e., strike-slip motion and plate spin, in the plate-tectonic style of mantle convection is enigmatic. It is a purely horizontal, dissipative flow field that makes no apparent contribution to the release of heat. However, when plate-like toroidal motion is allowed to arise as a phenomenon of non-Newtonian mantle dynamics, it in fact acts to reduce the net amount o...

The evolution of a viscous thin film on a curved geometry is numerically approximated based on the natural time discretization of the underlying gradient flow. This discretization leads to a variational problem to be solved at each time step, which reflects the balance between the decay of the free (gravitational and surface) energy and the viscous dissipation. Both dissipation and energy are d...

The dissipation of an elastic wave in dry and wet glass bead packings is measured using multiple sound scattering. The interplay of a linear viscoelastic loss and a nonlinear frictional one is observed in dry media. The Mindlin model provides a qualitative description of the experiment, but fails to quantitatively account for the data due to grain roughness. In weakly wet media, we find that th...

We consider the shear rheology of concentrated suspensions of non-Brownian frictional particles. The key result of our study is the emergence of a pronounced shear-thickening regime, where frictionless particles would normally undergo shear thinning. We can clarify that shear thickening in our simulations is due to enhanced energy dissipation via frictional interparticle forces. Moreover, we ev...

Boundary Layer Flow past a stretching surface with constant wall temperature, of a nanofluid is studied for heat transfer characteristics. The system of partial differential equations describing such a flow is subjected to similarity transformations gives rise to a boundary value problem involving a system of ordinary differential equations. This system is solved by a shooting method. Effect of...

Feeding and escape swimming in adult females of the calanoid copepod Temora longicornis Müller were investigated and compared. Swimming velocities were calculated using a 3-D filming setup. Foraging velocities ranged between 2 and 6 mm s(-1), while maximum velocities of up to 80 mm s(-1) were reached during escape responses. Foraging took place at Reynolds numbers between 2 and 6, indicating th...