On the Semi-Analytical Solutions in Hydrodynamics of Ideal Fluid Flows Governed by Large-Scale Coherent Structures of Spiral-Type

• Published in: Symmetry (Basel) 2021-12, Vol.13 (12), p.2307
• Main Authors: Ershkov, Sergey V., Rachinskaya, Alla, Prosviryakov, Evgenii Yu, Shamin, Roman V.
• Format: Article
• Language: English
• Subjects: Algorithms; Approximation; Boundary conditions; Coasts; Euler-Lagrange equation; Exact solutions; Fallout; Flow velocity; Fluid dynamics; Fluid flow; Fluid mechanics; Ideal fluids; Incompressible flow; Incompressible fluids; Invariants; large-scale coherent structures; Ordinary differential equations; spiral-type solutions; symmetry reduction; Tracing
• ISSN: 2073-8994; 2073-8994
• DOI: 10.3390/sym13122307

We have presented here a clearly formulated algorithm or semi-analytical solving procedure for obtaining or tracing approximate hydrodynamical fields of flows (and thus, videlicet, their trajectories) for ideal incompressible fluids governed by external large-scale coherent structures of spiral-type, which can be recognized as special invariant at symmetry reduction. Examples of such structures are widely presented in nature in “wind-water-coastline” interactions during a long-time period. Our suggested mathematical approach has obvious practical meaning as tracing process of formation of the paths or trajectories for material flows of fallout descending near ocean coastlines which are forming its geometry or bottom surface of the ocean. In our presentation, we explore (as first approximation) the case of non-stationary flows of Euler equations for incompressible fluids, which should conserve the Bernoulli-function as being invariant for the aforementioned system. The current research assumes approximated solution (with numerical findings), which stems from presenting the Euler equations in a special form with a partial type of approximated components of vortex field in a fluid. Conditions and restrictions for the existence of the 2D and 3D non-stationary solutions of the aforementioned type have been formulated as well.