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

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...

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Bibliographic Details
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
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Summary: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.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym13122307