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In this study we suggest new approach to turbulence modeling. To develop this approach, we construct the set of the vortex-like dynamical systems evolving in the space $E_3$. These systems are constructed using the AKNS hierarchy so that…
A plethora of studies in the past decade describe tsunami hazards and study their evolution from the source to the target coastline, but mainly focus on coastal inundation and maximum runup. Nonetheless, anecdotal reports from eyewitnesses,…
Disordered hyperuniform structures are locally random while uniform like crystals at large length scales. Recently, an exotic hyperuniform fluid state was found in several non-equilibrium systems, while the underlying physics remains…
We cast the non--isentropic relativistic Euler system into a symmetric hyperbolic form. Such systems are very suited to treat initial value problems of hyperbolic type. We obtain this form by using the pressure $p$ and not the density…
When fully conservative methods are used to simulate transcritical flow, spurious pressure oscillations and numerical instability are generated. The strength and speed of propagation of shock waves cannot be represented correctly using a…
We study stochastic acceleration models for the Fermi bubbles. Turbulence is excited just behind the shock front via Kelvin--Helmholtz, Rayleigh--Taylor, or Richtmyer--Meshkov instabilities, and plasma particles are continuously accelerated…
Dense particle suspensions are widely encountered in many applications and in environmental flows. While many previous studies investigate their rheological properties in laminar flows, little is known on the behaviour of these suspensions…
We have developed a phenomenological turbulent model with one-dimensional (1D) simulation based on Reynolds decomposition. Using this method, we have systematically studied models with different effects of compression, mixing length…
In recent works, we proposed a hypothesis, according to which turbulence in gases is created by the mean field effect of an intermolecular potential. We discovered that, in a numerically simulated inertial flow, turbulent solutions indeed…
We examine a two-dimensional deep-water surface gravity wave packet generated by a pressure disturbance in the Lagrangian reference frame. The pressure disturbance has the form of a narrow-banded weakly nonlinear deep-water wave packet.…
This report addresses the solution of Riemann problems for hyperbolic equations when the nonlinear characteristic fields loose their genuine nonlinearity. In this context, exact solvers for nonconvex 1D Riemann problems are developed. First…
The continuity equation requires that energy released in nuclear fusion flows away from the point of interaction and is not immediately thermalised into the CMB. It is seen that consequently the bulk of thermo-nuclear energy released in BBN…
We construct a solution to a $2\times 2$ strictly hyperbolic system of conservation laws, showing that the Godunov scheme \cite{Godunov59} can produce an arbitrarily large amount of oscillations. This happens when the speed of a shock is…
Experiments (Mullin and Kreswell, 2005) show that transition to turbulence can start at Reynolds numbers lower than it is predicted by the linear stability analysis - the subcritical transition to turbulence. To explain these observations…
Simulations of core-collapse supernovae (CCSNe) result in successful explosions once the neutrino luminosity exceeds a critical curve, and recent simulations indicate that turbulence further enables explosion by reducing this critical…
With the evolution of modern warfare and the increased use of improvised explosive devices (IEDs), there has been an increase in blast-induced traumatic brain injuries (bTBI) among military personnel and civilians. The increased prevalence…
In view of highly decentralized and diversified power generation concepts, in particular with renewable energies such as wind and solar power, the analysis and control of the stability and the synchronization of power networks is an…
One of the most profound questions of mathematical physics is that of establishing from first principles the hydrodynamic equations in large, isolated, strongly interacting many-body systems. This involves understanding relaxation at long…
The standard analytical approach for studying gravity free-surface waves generated by a moving body often relies upon a linearization of the physical geometry, where the body is considered asymptotically small in one or several of its…
We have developed a parallel cosmological hydrodynamic simulation code designed for the study of formation and evolution of cosmological structures. The gravitational force is calculated using the TreePM method and the hydrodynamics is…