Similarity Criteria

Abstract

Since the large spatial and time scales of geodynamic processes renders their direct observation and investigation impossible in most cases, the methods of quantitative modeling become very important. Frequently, modeling is the only way to get some ideas about geological phenomena. Most popular is mathematical modeling. Another method, physical (scale, laboratory or experimental) modeling is relatively seldom used, in spite of its obvious merits. There are several reasons for this. The most important seems to be the difficulty of making laboratory models that satisfy the necessary requirements, similarity criteria in the first place. Experimental models that are only qualitatively similar to the original no longer seem satisfactory to researchers and are below the level of mathematical modeling. At the same time the need for correctly set laboratory experiments is increasing. This is largely associated with the mathematical difficulties which numerical modeling encounters when constructing progressively more complex, and adequate models. Compact analytic or numerical solutions can frequently be obtained only by excessively simplifying the formulation of the problem. These simplifications largely determine the final result. Sometimes it is not even clear how to formulate the problem mathematically. Physical modeling can in principle obviate these difficulties. A major problem is the fulfillment of similarity criteria.