Interactions of a gasdynamic type. Two significant multidimensional examples of a constructive and classifying approach
Seminar Room 2, Newton Institute Gatehouse
AbstractWe associate each of the two mentioned examples of interaction with a pair of interactive gasdynamic elements: shock-turbulence or, respectively, wave-wave. The nature of each exemplified interaction essentially depends on the presence of a shock discontinuity: which contributes as an interactive element or, respectively, as a precursory structuring element.
The first example constructs and describes, in presence of a minimal nonlinearity [in the form of a nonlinear subconscious (following P.D. Lax and A.Majda)], a significant deterministic substructure reflecting the shock-turbulence interaction. This example has essentially two objectives: (a) structuring [via identifying a gasdynamic inner coherence] an explicit, closed, and optimal form for the interaction solution, and (b) offering [via identifying some Lorentz type arguments of pseudo-relativistic criticity] an exhaustively classifying characterization of this mentioned solution.
The second example uses, in an anisentropic context [which reflects the structuring presence of a precursory shock wave], two genuinely nonlinear, geometrical approaches [of a Burnat type, respectively of a Martin type] to construct two analogous classes of solutions - of a wave-wave regular interaction type. These two approaches are coincident in a very restrictive frame [isentropic context; two independent variables]. We finally parallel the two anisentropic approaches by using various comparisons between the mentioned analogous classes: to identify some significant consonances and, concurrently, some highly nontrivial contrasts: a classifying aspect.