Matter is commonly found in the form of materials. Analytical mechanics turned its back upon this fact, creating the centrally useful but abstract concepts of the mass point and the rigid body, in which matter manifests itself only through its inertia, independent of its constitution; “modern” physics likewise turns its back, since it concerns solely the small particles of matter, declining to face the problem of how a specimen made up of such particles will behave in the typical circumstances in which we meet it. Materials, however, continue to furnish the masses of matter we see and use from day to day: air, water, earth, flesh, wood, stone, steel, concrete, glass, rubber, ... All are deformable. A theory aiming to describe their mechanical behavior must take heed of their deformability and represent the definite principles it obeys.

The non-linear field theories of mechanics

A Rankine vortex model is used as the basis for an equation for critical submergence of intakes. The equation relates critical submergence to Froude number, circulation number, Reynolds number, and Weber number. The Froude and circulation numbers are the major controlling parameters. The model accounts for the effect of eddy viscosity on vortex-core characteristics. The equation for critical submergence is in agreement with experimental results. Criteria for neglect of surface tension and kinematic viscosity are established.

Free‐Surface Air Core Vortex

Equations for the development of streamwise (or secondary) vorticity, for stationary and rotating systems, are derived directly from the vector equation for vorticity, using intrinsic co-ordinates. This approach places emphasis on the coupled equations for the vorticity components parallel and normal to the streamline. The equations derived are more general than those hitherto available, being valid for compressible, stratified and viscous flow. Some interpretation is given of the physical mechanism causing secondary flow.

Generalized expressions for secondary vorticity using intrinsic co-ordinates

Controllable states of elastic dielectrics

A modified Lundgren model is applied for the description of stationary bathtub vortices in a viscous liquid with a free surface. Laminar liquid flow through the circular bottom orifice is considered in the horizontally unbounded domain. The liquid is assumed to be undisturbed at infinity and its depth is taken to be constant. Three different drainage regimes are studied: (i) subcritical, where whirlpool dents are less than the fluid depth; (ii) critical, where the whirlpool tips touch the outlet orifice; and (iii) supercritical, where surface vortices entrain air into the intake pipe. Particular attention is paid to critical vortices; the condition for their existence is determined and analysed. The influence of surface tension on subcritical whirlpools is investigated. Comparison of results with known experimental data is discussed.

/pdf/stationary-bathtub-vortices-and-a-critical-regime-of-liquid-1h02rucd8s.pdf

Stationary bathtub vortices and a critical regime of liquid discharge

Theory of the Bathtub Vortex

The Generation of Secondary Vorticity in an Incompressible Fluid

On the Bending of Streamlines Toward Vortex Lines

This paper postulates that the stress tensor of a Cauchy-elastic material depends upon the first temperature-gradient vector in addition to the deformation gradient and local temperature. Consequences of this postulate are examined for the particular cases of a body constrained to no deformation and to simple isochoric shear.

A. W. Marris

Papers

Theory of the Bathtub Vortex

The Generation of Secondary Vorticity in an Incompressible Fluid

On the Bending of Streamlines Toward Vortex Lines

Dependence of Stress Upon Temperature Gradient for an Ideally Elastic Solid Isotropic and Homogeneous in the Reference State

The Reduction of the Simple Hygrosteric Fluid to the Stokesian Fluid