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We study turbulent flows in a smooth straight pipe of circular cross--section up to $Re_{\tau} \approx 6000$ using direct--numerical-simulation (DNS) of the Navier--Stokes equations. The DNS results highlight systematic deviations from…
In this paper, we establish the mathematical validity of the Prandtl boundary layer theory for a class of nonlinear plane parallel flows of viscous incompressible magnetohydrodynamic (MHD) flow with no-slip boundary condition of velocity…
We consider two laminar incompressible flows coupled by the continuous law at a fixed interface. We approach the system by one that satisfies a friction Navier law, and we show that when the friction coefficient goes to infinity, the…
A new two-layer model has been proposed to study microscale heat transfer associated with a developing flow boundary layer. As an example, a cold, microscale film of liquid impinging on an isothermal hot, horizontal surface has been…
The boundary layer structure of the velocity and temperature fields in turbulent Rayleigh-Benard flows in closed cylindrical cells of unit aspect ratio is revisited from a transitional and turbulent viscous boundary layer perspective. When…
A global approach leading to a self-consistent solution to the Navier-Stokes-Prandtl equations for zero-pressure-gradient boundary layers is presented. It is shown that as $Re_{\delta}\rightarrow \infty$, the dynamically defined boundary…
The problems of numerical modeling of viscous incompressible fluid flows are widely considered in computational fluid dynamics. Stationary solutions of boundary value problems for the Navier-Stokes equations exist at large Reynolds numbers,…
In this report, We investigated the nonlinear phenomena in the study of flow dynamics of velocity component. In our studies, we observed nonlinear term in the vertical component of velocity by vittori et al \cite{vit} The time series…
One of the most enigmatic science question concerning inertial particle transport by a turbulent boundary layer flow is the value of the turbulent Schmidt number as the ratio of particle diffusivity and turbulent eddy viscosity. Using…
In this paper, we study the 2D free boundary incompressible Euler equations with surface tension, where the fluid domain is periodic in $x_1$, and has finite depth. We construct initial data with a flat free boundary and arbitrarily small…
This paper concerns compressible subsonic jet flows for a given surrounding pressure from a two-dimensional finitely long convergent nozzle with straight solid wall, which are governed by a free boundary problem for a quasilinear elliptic…
This work analyzes the turbulent velocity distribution in proximity of the wall using the finite-scale Lyapunov theory just presented in previous works. This theory is here applied to the steady boundary layer under the hypothesis of…
The estimation of the permeability of porous media to fluids is of fundamental importance in fields as diverse as oil and gas industry, agriculture, hydrology and medicine. Despite more than 150 years since the publication of Darcy's linear…
Large-eddy simulations of a flat-plate boundary layer, without a leading edge, subject to multiple levels of incoming free stream turbulence are considered in the present work. Within an input-output model where non-linear terms of the…
A small, spherical bubble of high internal pressure is inserted into water at constant ambient pressure as a model of a laser-induced bubble. Its subsequent dynamics near a flat solid boundary is studied in dependence on the distance of the…
In a variety of physical situations, a bulk viscous flow is induced by a distribution of surface velocities, for example in diffusiophoresis (as a result of chemical gradients) and above carpets of cilia (as a result of biological…
The problem of forced convection along an isothermal moving plate is a classical problem of fluid mechanics that has been solved for the first time in 1961 by Sakiadis (1961). It appears that the first work concerning mixed convection along…
The projection method is the standard approach for numerically integrating the incompressible Navier-Stokes equation initial-boundary-value problem. Typical boundary conditions specify either the velocity or the gradient velocity on the…
Analytic predictions of mean velocity profile (MVP) and streamwise ($x$) development of related integral quantities are presented for flows in channel and turbulent boundary layer (TBL), based on a symmetry analysis of eddy length and total…
A well-developed method to induce mixing on microscopic scales is to exploit flows generated by steady streaming. Steady streaming is a classical fluid dynamics phenomenon whereby a time-periodic forcing in the bulk or along a boundary is…