The Experts below are selected from a list of 234 Experts worldwide ranked by ideXlab platform

Koji Ohkitani - One of the best experts on this subject based on the ideXlab platform.

  • dynamical equations for the vector Potential and the Velocity Potential in incompressible irrotational euler flows a refined bernoulli theorem
    Physical Review E, 2015
    Co-Authors: Koji Ohkitani
    Abstract:

    We consider incompressible Euler flows in terms of the stream function in two dimensions and the vector Potential in three dimensions. We pay special attention to the case with singular distributions of the vorticity, e.g., point vortices in two dimensions. An explicit equation governing the Velocity Potentials is derived in two steps. (i) Starting from the equation for the stream function [Ohkitani, Nonlinearity 21, T255 (2009)], which is valid for smooth flows as well, we derive an equation for the complex Velocity Potential. (ii) Taking a real part of this equation, we find a dynamical equation for the Velocity Potential, which may be regarded as a refinement of Bernoulli theorem. In three-dimensional incompressible flows, we first derive dynamical equations for the vector Potentials which are valid for smooth fields and then recast them in hypercomplex form. The equation for the Velocity Potential is identified as its real part and is valid, for example, flows with vortex layers. As an application, the Kelvin-Helmholtz problem has been worked out on the basis the current formalism. A connection to the Navier-Stokes regularity problem is addressed as a physical application of the equations for the vector Potentials for smooth fields.

  • Dynamical equations for the vector Potential and the Velocity Potential in incompressible irrotational Euler flows: a refined Bernoulli theorem.
    Physical review. E Statistical nonlinear and soft matter physics, 2015
    Co-Authors: Koji Ohkitani
    Abstract:

    We consider incompressible Euler flows in terms of the stream function in two dimensions and the vector Potential in three dimensions. We pay special attention to the case with singular distributions of the vorticity, e.g., point vortices in two dimensions. An explicit equation governing the Velocity Potentials is derived in two steps. (i) Starting from the equation for the stream function [Ohkitani, Nonlinearity 21, T255 (2009)NONLE50951-771510.1088/0951-7715/21/12/T02], which is valid for smooth flows as well, we derive an equation for the complex Velocity Potential. (ii) Taking a real part of this equation, we find a dynamical equation for the Velocity Potential, which may be regarded as a refinement of Bernoulli theorem. In three-dimensional incompressible flows, we first derive dynamical equations for the vector Potentials which are valid for smooth fields and then recast them in hypercomplex form. The equation for the Velocity Potential is identified as its real part and is valid, for example, flows with vortex layers. As an application, the Kelvin-Helmholtz problem has been worked out on the basis the current formalism. A connection to the Navier-Stokes regularity problem is addressed as a physical application of the equations for the vector Potentials for smooth fields.

Ziad H. Musslimani - One of the best experts on this subject based on the ideXlab platform.

  • On a new non-local formulation of water waves
    Journal of Fluid Mechanics, 2006
    Co-Authors: Mark J. Ablowitz, Athanassios S. Fokas, Ziad H. Musslimani
    Abstract:

    The classical equations of water waves are reformulated as a system of two equations, one of which is an explicit non-local equation, for the wave height and for the Velocity Potential evaluated on the free surface. Evaluation of the Velocity Potential as a function of the depth is not required in order to calculate the wave height and the Velocity Potential on the free surface. The non-local system yields integral relations related to mass and centre of mass, and is shown to reduce to known asymptotic limits in shallow and deep water. Included in these asymptotic reductions are the

Andreas Buchleitner - One of the best experts on this subject based on the ideXlab platform.

  • Liquid surface waves in parabolic tanks
    Physics of Fluids, 2008
    Co-Authors: Y. Núñez-fernández, C. Trallero-giner, Andreas Buchleitner
    Abstract:

    Surface waves in cylindrical tanks with parabolic cross section formed by two confocal parabolas are studied. Exact general solutions for the inviscid gravity-capillary waves as function of the parabolic curvatures are presented, and the symmetry of the eigensolutions for the Velocity Potential modes is also investigated. For a complete characterization of the Velocity Potential and of the amplitude of the liquid surface, their analytic expressions in terms of hypergeometric functions are given. It is shown that for the particular case of two confocal parabolas with the same curvature, the Velocity Potential is described by the cylindrical functions. The evolution of the nodal structure for gravity-capillary waves for variable excitation, and in terms of the parabolic tank curvature, is analyzed.

Hai-long Pei - One of the best experts on this subject based on the ideXlab platform.

  • Identification of Water Depth and Velocity Potential for Water Waves
    Systems & Control Letters, 2019
    Co-Authors: Hai-long Pei
    Abstract:

    Abstract The purpose of this paper is to investigate the identification of the water depth and the water Velocity Potential in a coastal region by using the linearized water wave equation (LWWE). Existence and uniqueness of the solutions to the partial differential equation LWWE are shown by using the semigroup theory. Moreover the analytical solution is found by the separation of variables method. We assume that the surface wave elevation is measurable. We like to recover the water depth and the water Velocity Potential from the measurement. This identification problem is shown to be well-posed by proving the parameters’ identifiability by the surface elevation. Based on the classical gradient descent method we elaborate an identification algorithm to recover simultaneously both the water depth and the Velocity Potential. Numerical simulations are carried out to illustrate effectiveness of the algorithm.

Mark J. Ablowitz - One of the best experts on this subject based on the ideXlab platform.

  • On a new non-local formulation of water waves
    Journal of Fluid Mechanics, 2006
    Co-Authors: Mark J. Ablowitz, Athanassios S. Fokas, Ziad H. Musslimani
    Abstract:

    The classical equations of water waves are reformulated as a system of two equations, one of which is an explicit non-local equation, for the wave height and for the Velocity Potential evaluated on the free surface. Evaluation of the Velocity Potential as a function of the depth is not required in order to calculate the wave height and the Velocity Potential on the free surface. The non-local system yields integral relations related to mass and centre of mass, and is shown to reduce to known asymptotic limits in shallow and deep water. Included in these asymptotic reductions are the