By Morton E. Gurtin (Eds.)
This booklet offers an advent to the classical theories of continuum mechanics; particularly, to the theories of excellent, compressible, and viscous fluids, and to the linear and nonlinear theories of elasticity. those theories are very important, not just simply because they're appropriate to a majority of the issues in continuum mechanics bobbing up in perform, yet simply because they shape a pretty good base upon which you possibly can effortlessly build extra advanced theories of fabric habit. additional, even supposing realization is restricted to the classical theories, the remedy is sleek with an incredible emphasis on foundations and constitution
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Additional info for An Introduction to Continuum Mechanics
The best known example of buoyancy-induced instability occurs in the problem of a fluid layer heated from below which was studied by Benard (1900,1901). Cellular convective motion of the Benard type can be induced by surfacetension forces as well as by buoyancy forces. When a layer of liquid is heated 22 VIII. The Oberbeck-Boussinesq Equations from below (or above), small variations in the surface temperature can induce surface tractions, which cause the liquid below to flow, and under certain circumstances the induced motion will persist leading to heat transport by convection as well as conduction.
It is easy to give a priori conditions which are sufficient to guarantee this coincidence. If the basic state is motionless, then U =0. 3) by linearization and the use of the exponential time factor e- at . 3) required on the optimum energy stability boundary. 3). Now we are ready to state necessary and sufficient conditions for the global stability of the motionless solution. Let the spatial variations of the gravity-vector field and temperature and concentration gradient fields of the motionless state be proportional so that 'I = 'IT = -1/c.
In liquids the interfacial tension (force/length) (J generally decreases with increasing temperature. Then (J = (J 0 - seT - T R), where TR is a reference temperature and s > 0, gives the linear approximation to the equation of state for the surface tension; and (J' = - se' where e' is a disturbance of T - TR . Literature on surface tension instability is reviewed in the paper of Berg, Acrivos and Boudart (1966). § 61. Necessary and Sufficient Conditions for Stability When linear and energy stability limits coincide, all stable disturbances, whatever their size, will decay exponentially from the initial instant.