| Popis: |
A numerical method is used to simulate the gravitational spreading of a nappe consisting of Newtonian material with high viscosity coefficient. The theory is based on maximizing the rate of decline of potential energy which also means maximizing the rate of dissipation due to strain and basal friction as well as maximizing the rate of production of entropy. A polynomial stream function is used to describe the velocity field and the displacement field. The nappe is permitted to slip against friction at the base, a wide variation of friction coefficients being used in the numerical tests. A result with great implication is that each nappe has a theoretical critical friction limit, μ crit , which chiefly depends upon the aspect ratio: the larger the aspect ratio, the smaller the friction limit. If the true friction coefficient is greater than μ crit , then the potential energy is incapable of making the nappe slip at the base. In this case the spreading is solely due to motion within the bulk of the nappe, generating a protruding lobe or recumbent fold in the front. Unless the friction coefficient for natural nappes is considerably less than measured experimentally, it is not easy to understand that gravitational spreading is able to make nappes slip at the base if the aspect ratio is say 10 and more. However, by using stream functions with enough freedom (i.e. of high enough degree) and realistic nappe profiles, it is found that the foremost sections of nappes may slip along the base, pushed by the protruded lobe of the spreading hind portion which is coherent to the base. |
