# Biot-Savart Law

The Experts below are selected from a list of 318 Experts worldwide ranked by ideXlab platform

### Makoto Tsubota – 1st expert on this subject based on the ideXlab platform

• ##### steady state counterflow quantum turbulence simulation of vortex filaments using the full biot savart Law
Physical Review B, 2010
Co-Authors: Hiroyuki Adachi, Shoji Fujiyama, Makoto Tsubota

Abstract:

We perform a numerical simulation of quantum turbulence produced by thermal counterflow in superfluid $^{4}\text{H}\text{e}$ by using the vortex filament model with the full Biot-Savart Law. The pioneering work of Schwarz has two shortcomings: it neglects the nonlocal terms of the Biot-Savart integral [known as the localized induction approximation (LIA)] and it employs an unphysical mixing procedure to sustain the statistically steady state of turbulence. We have succeeded in generating the statistically steady state under periodic boundary conditions without using the LIA or the mixing procedure. This state exhibits the characteristic relation $L={\ensuremath{\gamma}}^{2}{v}_{ns}^{2}$ between the line-length density $L$ and the counterflow relative velocity ${v}_{ns}$ and there is quantitative agreement between the coefficient $\ensuremath{\gamma}$ and some measured values. The parameter $\ensuremath{\gamma}$ and some anisotropy parameters are calculated as functions of temperature and the counterflow relative velocity. The numerical results obtained using the full Biot-Savart Law are compared with those obtained using the LIA. The LIA calculation constructs a layered structure of vortices and does not proceed to a turbulent state but rather to another anisotropic vortex state; thus, the LIA is not suitable for simulations of turbulence.

• ##### energy spectrum of superfluid turbulence with no normal fluid component
Physical Review Letters, 2002
Co-Authors: Tsunehiko Araki, Makoto Tsubota, Sergey K Nemirovskii

Abstract:

: The energy of superfluid turbulence without the normal fluid is studied numerically under the vortex filament model. Time evolution of the Taylor-Green vortex is calculated under the full nonlocal Biot-Savart Law. It is shown that for k<2pi/l the energy spectrum is very similar to the Kolmogorov's -5/3 Law which is the most important statistical property of the conventional turbulence, where k is the wave number of the Fourier component of the velocity field and l is the average intervortex spacing. The vortex length distribution converges to a scaling property reflecting the self-similarity of the tangle.

### A V Gorshkov – 2nd expert on this subject based on the ideXlab platform

• ##### Associated Weber–Orr Transform, Biot–Savart Law and Explicit Form of the Solution of 2D Stokes System in Exterior of the Disc
Journal of Mathematical Fluid Mechanics, 2019
Co-Authors: A V Gorshkov

Abstract:

In this article we derive the explicit formula for the solution of 2-D Stokes system in exterior of the disc with no-slip condition on inner boundary and given velocity $$\mathbf {v}_\infty$$ at infinity. It turned out it is the first application of the associated Weber–Orr transform to mathematical physics in comparison to classical Weber–Orr transform which is used in many researches. From no-slip condition for velocity field we will obtain Robin-type boundary condition for vorticity. Then the initial-boundary value problem for vorticity will be solved with help of the associated Weber–Orr transform. Also the explicit formula of Biot–Savart Law in polar coordinates will be given.

• ##### associated weber orr transform biot savart Law and explicit form of the solution of 2d stokes system in exterior of the disc
Journal of Mathematical Fluid Mechanics, 2019
Co-Authors: A V Gorshkov

Abstract:

In this article we derive the explicit formula for the solution of 2-D Stokes system in exterior of the disc with no-slip condition on inner boundary and given velocity $$\mathbf {v}_\infty$$ at infinity. It turned out it is the first application of the associated Weber–Orr transform to mathematical physics in comparison to classical Weber–Orr transform which is used in many researches. From no-slip condition for velocity field we will obtain Robin-type boundary condition for vorticity. Then the initial-boundary value problem for vorticity will be solved with help of the associated Weber–Orr transform. Also the explicit formula of Biot–Savart Law in polar coordinates will be given.

• ##### associated weber orr transform biot savart Law and explicit solution of 2d stokes system in exterior of the disc
arXiv: Analysis of PDEs, 2019
Co-Authors: A V Gorshkov

Abstract:

In this article we derive the explicit solution of 2-D Stokes system in exterior of the disc with no-slip condition on inner boundary and given velocity $\mathbf{v}_\infty$ at infinity. It turned out it is the first application of the associated Weber-Orr transform to mathematical physics in comparison to classical Weber-Orr transform which is used in many researches. From no-slip condition for velocity field we will obtain Robin-type boundary condition for vorticity. Then the initial-boundary value problem for vorticity will be solved with help of the associated Weber-Orr transform. Also the explicit formula of Biot-Savart Law in polar coordinates will be given.

### Sergey K Nemirovskii – 3rd expert on this subject based on the ideXlab platform

• ##### energy spectrum of superfluid turbulence with no normal fluid component
Physical Review Letters, 2002
Co-Authors: Tsunehiko Araki, Makoto Tsubota, Sergey K Nemirovskii

Abstract:

: The energy of superfluid turbulence without the normal fluid is studied numerically under the vortex filament model. Time evolution of the Taylor-Green vortex is calculated under the full nonlocal Biot-Savart Law. It is shown that for k<2pi/l the energy spectrum is very similar to the Kolmogorov's -5/3 Law which is the most important statistical property of the conventional turbulence, where k is the wave number of the Fourier component of the velocity field and l is the average intervortex spacing. The vortex length distribution converges to a scaling property reflecting the self-similarity of the tangle.