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Generalized wall-functions in application to high-Reynolds-number turbulence models are derived. The wall-functions are based on transfer of a boundary condition from a wall to some intermediate boundary near the wall (usually the first…

We develop a theory of turbulence of weak random gravity waves on surface of deep water in which the main nonlinear process at high-frequency part of the spectrum is a nonlocal interaction with a strong low-frequency component. The latter…

A fractional generalization of variations is used to define a stability of non-integer order. Fractional variational derivatives are suggested to describe the properties of dynamical systems at fractional perturbations. We formulate…

When studying fluid mechanics in terms of instability, bifurcation and invariant solutions one quickly finds out how little can be done by pen and paper. For flows on sufficiently simple domains and under sufficiently simple boundary…

Rotating turbulence is ubiquitous in nature. Previous works suggest that such turbulence could be described as an ensemble of interacting inertial waves across a wide range of length scales. For turbulence in macroscopic quantum…

Real world water waves often propagate on current. And, the measurement of waves and current is an important task for coastal and marine engineers. Modern marine measurement technologies (i.e. unmanned autonomous vehicles, drones) often…

We propose a generalized perspective on the behavior of high-order derivative moments in turbulent shear flows by taking account of the roles of small-scale intermittency and mean shear, in addition to the Reynolds number. Two asymptotic…

Wave turbulence is by nature a multiple time scale problem for which there is a natural asymptotic closure. The main result of this analytical theory is the kinetic equation that describes the long-time statistical behaviour of such…

The study points out that the traditional solutions to wave equation of dissipative wave and motion equation of block for a multi-degree-of-freedom mass spring damper system are the possible solutions, which are not necessarily objective…

In the framework of the variational principle the canonical variables describing ideal magnetohydrodynamic (MHD) flows of general type (i.e., with spatially varying entropy and nonzero values of all topological invariants) are introduced.…

Turbulence is characterized by the non-linear cascades of energy and other inviscid invariants across a huge range of scales, from where they are injected to where they are dissipated. Recently, new experimental, numerical and theoretical…

Model of laminated wave turbulence allows to study statistical and discrete layers of turbulence in the frame of the same model. Statistical layer is described by Zakharov-Kolmogorov energy spectra in the case of irrational enough…

High-frequency wave propagation in near-inertial wave shear has been considered fundamental in setting the spectral character of the oceanic internal wave continuum and for transporting energy to wave-breaking. We compare idealized ray…

The use of gyrokinetics, wherein phase-space coordinate transformations result in a phase-space dimensionality reduction as well as the removal of fast time scales, has enabled the simulation of microturbulence in fusion devices. The…

As stated in the title, the present research proposes a mathematical definition of laminar and turbulent flows, i.e., a definition that may be used to conceive and prove mathematical theorems about such flows. The definition is based on an…

The aim of this paper is to derive the averaged governing equations for non-degenerated oscillatory flows, in which the magnitudes of mean velocity and oscillating velocity are similar. We derive the averaged equations for a scalar passive…

General turbulent mean statistics are shown to be characterized by a variational principle. The variational functionals, or ``effective actions'', have experimental consequences for turbulence fluctuations and are subject to realizability…

The scaling invariance for chaotic orbits near a transition from unlimited to limited diffusion in a dissipative standard mapping is explained via the analytical solution of the diffusion equation. It gives the probability of observing a…

We obtain a general solution for the water waves resulting from a general, time-dependent surface pressure distribution, in the presence of a shear current of uniform vorticity beneath the surface, in three dimensions. Linearized governing…

The phenomenology of the scaling behavior of higher order structure functions of velocity differences across a scale $R$ in turbulence should be built around the irreducible representations of the rotation symmetry group. Every irreducible…