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Register a new userNew Relativistic Effects in the Dynamics of Nonlinear Hydrodynamical Waves
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In Newtonian and relativistic hydrodynamics the Riemann problem consists of calculating the evolution of a fluid which is initially characterized by two states having different values of uniform rest-mass density, pressure and velocity. When the fluid is allowed to relax, one of three possible wave-patterns is produced, corresponding to the propagation in opposite directions of two nonlinear hydrodynamical waves. New effects emerge in a special relativistic Riemann problem when velocities tangential to the initial discontinuity surface are present. We show that a smooth transition from one wave-pattern to another can be produced by varying the initial tangential velocities while otherwise maintaining the initial states unmodified. These special relativistic effects are produced by the coupling through the relativistic Lorentz factors and do not have a Newtonian counterpart.
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A Riemann problem with prescribed initial conditions will produce one of three possible wave patterns corresponding to the propagation of the different discontinuities that will be produced once the system is allowed to relax. In general, when solving the Riemann problem numerically, the determination of the specific wave pattern produced is obtained through some initial guess which can be successively discarded or improved. We here discuss a new procedure, suitable for implementation in an exact Riemann solver in one dimension, which removes the initial ambiguity in the wave pattern. In particular we focus our attention on the relativistic velocity jump between the two initial states and use this to determine, through some analytic conditions, the wave pattern produced by the decay of the initial discontinuity. The exact Riemann problem is then solved by means of calculating the root of a nonlinear equation. Interestingly, in the case of two rarefaction waves, this root can even be found analytically. Our procedure is straightforward to implement numerically and improves the efficiency of numerical codes based on exact Riemann solvers.
The nonlinear interaction of a time-harmonic acoustic wave with an anisotropic particle gives rise to the radiation force and torque effects. These phenomena are at the heart of the acoustofluidics technology, where microparticles such as cells and microorganisms are acoustically manipulated. We present a theoretical model considering a generic acoustic beam interacting with a subwavelength spheroidal particle in a nonviscous fluid. Concise analytical expressions of the radiation force and torque are obtained in the scattering dipole approximation. The radiation force is given in terms of a gradient and scattering force; while the radiation torque has two fundamental contributions, namely, the momentum arm and acoustic spin (spin-torque effect). As a practical example, we use the theory to describe the interaction of two crossed plane waves and a prolate spheroidal particle. The results reveal the particle is transversely trapped in a pressure node and is axially pushed by the radiation force. Also, the momentum arm aligns the particle in the axial direction. At certain specific positions, only the spin-torque occurs. Our findings are remarkably consistent with finite-element simulations. The success of our model enables its use as an investigation tool for the manipulation of anisotropic microparticles in acoustofluidics.
We extend our approach for the exact solution of the Riemann problem in relativistic hydrodynamics to the case in which the fluid velocity has components tangential to the initial discontinuity. As in one-dimensional flows, we here show that the wave-pattern produced in a multidimensional relativistic Riemann problem can be predicted entirely by examining the initial conditions. Our method is logically very simple and allows for a numerical implementation of an exact Riemann solver which is both straightforward and computationally efficient. The simplicity of the approach is also important for revealing special relativistic effects responsible for a smooth transition from one wave-pattern to another when the tangential velocities in the initial states are suitably varied. While the content of this paper is focussed on a flat spacetime, the local Lorentz invariance allows its use also in fully general relativistic calculations.
It is shown that, in the framework of Relativistic Theory of Gravitation with massive graviton, gravitational waves, due to the causality condition, do not bear negative energy flows.
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