arXiv subjects

Tsutomu Kambe

Publications and source records attributed to Tsutomu Kambe.

5 recordsLinked to original sources

arXiv2017

New scenario of turbulence theory and wall-bounded turbulence: Theoretical significance

General scenario of turbulence theory is proposed and applied to streaky wall-bounded turbulence. This scenario introduces a new field of transverse waves. Significance of the theory rests on a mathematical theorem associated with the conservation law of current flux, expressed in a form of 4d physical space-time representation, which predicts a system of Maxwell-type equation and supports transverse waves traveling with a phase speed c_t. In regard to the streaky wall flows, there exist both dynamical mechanism and energy channel which excite transverse waves and exchange energy between flow field and wave field. Energy is supplied from the flow field to the wave field if wavelengths are sufficiently large. The waves are accompanied with a new mechanism of energy dissipation, an internal friction analogous to the Ohm's effect. Some part of the energy is dissipated into heat. Thus, there exists a sustaining mechanism, which implies that the streaky structure of wall-bounded turbulence is a dissipative structure. The predictions are consistent with experimental observations of wall turbulence: (i) Existence of traveling waves: The waves are characterized by two scales of wavelength and a damping-length d. (ii) Existence of two large scales (LSM and VLSM) observed in turbulent shear flows: Those are interpreted by the waves amplified with the transient growth mechanism and maintained by interaction with the new transverse wave field. The waves are robust since they have their own energy and momentum. (iii) Enhanced energy dissipation in wavy turbulence. Its bulk rate of energy dissipation takes a form resembling the models of eddy-viscosity, and its coefficient ν_D is estimated to be of the order of c_t d and much larger than the molecular viscosity. No self-contradiction is incurred by the new field introduced.

physics.flu-dyn↗

arXiv2008

Variational formulation of ideal fluid flows according to gauge principle

On the basis of the gauge principle of field theory, a new variational formulation is presented for flows of an ideal fluid. The fluid is defined thermodynamically by mass density and entropy density, and its flow fields are characterized by symmetries of translation and rotation. The rotational transformations are regarded as gauge transformations as well as the translational ones. In addition to the Lagrangians representing the translation symmetry, a structure of rotation symmetry is equipped with a Lagrangian $Λ_A$ including the vorticity and a vector potential bilinearly. Euler's equation of motion is derived from variations according to the action principle. In addition, the equations of continuity and entropy are derived from the variations. Equations of conserved currents are deduced as the Noether theorem in the space of Lagrangian coordinate $\ba$. Without $Λ_A$, the action principle results in the Clebsch solution with vanishing helicity. The Lagrangian $Λ_A$ yields non-vanishing vorticity and provides a source term of non-vanishing helicity. The vorticity equation is derived as an equation of the gauge field, and the $Λ_A$ characterizes topology of the field. The present formulation is comprehensive and provides a consistent basis for a unique transformation between the Lagrangian $\ba$ space and the Eulerian $\bx$ space. In contrast, with translation symmetry alone, there is an arbitrariness in the ransformation between these spaces.

nlin.CD↗

arXiv2007

Variational formulation of the motion of an ideal fluid on the basis of gauge principle

On the basis of gauge principle in the field theory, a new variational formulation is presented for flows of an ideal fluid. The fluid is defined thermodynamically by mass density and entropy density, and its flow fields are characterized by symmetries of translation and rotation. A structure of rotation symmetry is equipped with a Lagrangian $Λ_A$ including vorticity, in addition to Lagrangians of translation symmetry. From the action principle, Euler's equation of motion is derived. In addition, the equations of continuity and entropy are derived from the variations. Equations of conserved currents are deduced as the Noether theorem in the space of Lagrangian coordinate $\ba$. It is shown that, with the translation symmetry alone, there is freedom in the transformation between the Lagrangian $\ba$-space and Eulerian $\bx$-space. The Lagrangian $Λ_A$ provides non-trivial topology of vorticity field and yields a source term of the helicity. The vorticity equation is derived as an equation of the gauge field. Present formulation provides a basis on which the transformation between the $\ba$ space and the $\bx$ space is determined uniquely.

nlin.CD↗

arXiv1998

Probability Density Function of Longitudinal Velocity Increment in Homogeneous Turbulence

Two conditional averages for the longitudinal velocity increment u_r of the simulated turbulence are calculated: h(u_r) is the average of the increment of the longitudinal Laplacian velocity field with u_r fixed, while g(u_r) is the corresponding one of the square of the difference of the gradient of the velocity field. Based on the physical argument, we suggest the formulae for h and g, which are quite satisfactorily fitted to the 512^3 DNS data. The predicted PDF is characterized as (1) the Gaussian distribution for the small amplitudes, (2) the exponential distribution for the large ones, and (3) a prefactor before the exponential function for the intermediate ones.

chao-dyn↗

arXiv1997

Conditional Averages and Probability Density Functions in the Passive Scalar Field

Two conditional averages for the increment Delta(x,x+r) = T(x)-T(x+r) of the scalar field are estimated for DNS data: H(Delta)= and G(Delta)=<|nabla Delta(x,x+r)|^2| Delta(x,x+r)>. The probability density function P(Delta) for Delta(x,x+r) is also calculated. If Delta, P(Delta), H(Delta), and G(Delta) are expressed as theta, P(theta), h(theta), and g(theta) in a dimensionless form, the data analysis has revealed interesting simple relationships between them. These relations may be helpful to construct a turbulence model.

chao-dyn↗