Math. Model. Nat. Phenom.
Volume 13, Number 2, 2018
Shock Waves, Discontinuities and Singularities in Natural Phenomena
|Number of page(s)||29|
|Published online||17 May 2018|
Singular perturbed components of flows – linear precursors of shock waves
A. Yu. Ishlinskiy Institute for Problems in Mechanics RAS, Prospect Vernadskogo,
* Corresponding author: firstname.lastname@example.org
Accepted: 26 October 2017
A comparative analysis of the infinitesimal symmetries of various well-known systems of governing equations used for mathematical descriptions of flows and waves in fluids has shown that only the basic system of equations, including the empirical equation of state and the partial differential equations of mass, momentum, energy and matter transport, is characterized by a ten-parameter Galilean transformation group. An analysis of the complete solutions of the linearized system of fundamental equations for weakly dissipating media reveals a wide class of previously unknown singularly perturbed solutions supplementing well investigated regular solutions describing propagating waves. Fine flow components, whose geometry is typical for internal boundary layers that supplement the wave fields exist both at the boundaries and inside the volume of the liquid, are classified as linear precursors of shock waves. The calculated pattern of periodic internal waves beams covered with high-gradient envelopes agrees with data from independently performed experiments on measurements and visualization of the fine structure of linear and nonlinear waves in continuously stratified media.
Mathematics Subject Classification: 76M60 / 76M45
Key words: Set of fundamental equation / continuous groups analysis / complete solutions / internal waves / experiment
© EDP Sciences, 2018
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