Search results for "Richardson number"
showing 6 items of 6 documents
Influence of the Richardson number on EM force driven flow structures in square-shaped crucible
2014
Abstract This study is devoted to the experimental investigation of the turbulent melt motion in a square crucible where the flow is created by Lorentz forces generated by an external AC magnetic field. As a strong vertical thermal gradient is present in melt during a directional solidification process, a stratification effect takes place and motion in the vertical direction is damped by buoyancy forces. Such a situation arises if density of fluid layers decreases with height. Experimental velocity and temperature measurements are conducted. Transient effects, like collapse of stratification, are observed experimentally. The significance of stratification in the directional solidification m…
On the influence of gravitational and centrifugal buoyancy on laminar flow and heat transfer in curved pipes and coils
2015
Abstract The effects of gravitational and centrifugal buoyancy on laminar flow and heat transfer in curved and helical pipes were investigated by numerical simulation. Six dimensionless numbers characterizing the problem were identified, and an analysis was conducted on the possible combinations of signs of the gravitational and centrifugal buoyancy effects. Two distinct Richardson numbers were introduced in order to quantify the importance of the two types of buoyancy, and it was shown that, in the case of heating from the wall, a maximum realizable value of the centrifugal Richardson number exists which is a linear function of the curvature δ (ratio of pipe radius a to curvature radius c)…
Route to chaos in the weakly stratified Kolmogorov flow
2019
We consider a two-dimensional fluid exposed to Kolmogorov’s forcing cos(ny) and heated from above. The stabilizing effects of temperature are taken into account using the Boussinesq approximation. The fluid with no temperature stratification has been widely studied and, although relying on strong simplifications, it is considered an important tool for the theoretical and experimental study of transition to turbulence. In this paper, we are interested in the set of transitions leading the temperature stratified fluid from the laminar solution [U∝cos(ny),0, T ∝ y] to more complex states until the onset of chaotic states. We will consider Reynolds numbers 0 < Re ≤ 30, while the Richardson numb…
Modeling Atmospheric Turbulence via Rapid Distortion Theory: Spectral Tensor of Velocity and Buoyancy
2017
Abstract A spectral tensor model is presented for turbulent fluctuations of wind velocity components and temperature, assuming uniform vertical gradients in mean temperature and mean wind speed. The model is built upon rapid distortion theory (RDT) following studies by Mann and by Hanazaki and Hunt, using the eddy lifetime parameterization of Mann to make the model stationary. The buoyant spectral tensor model is driven via five parameters: the viscous dissipation rate ε, length scale of energy-containing eddies L, a turbulence anisotropy parameter , gradient Richardson number (Ri) representing the local atmospheric stability, and the rate of destruction of temperature variance . Model outp…
Validation of buoyancy driven spectral tensor model using HATS data
2016
We present a homogeneous spectral tensor model for wind velocity and temperature fluctuations, driven by mean vertical shear and mean temperature gradient. Results from the model, including one-dimensional velocity and temperature spectra and the associated co-spectra, are shown in this paper. The model also reproduces two-point statistics, such as coherence and phases, via cross-spectra between two points separated in space. Model results are compared with observations from the Horizontal Array Turbulence Study (HATS) field program (Horst et al. 2004). The spectral velocity tensor in the model is described via five parameters: the dissipation rate (), length scale of energy-containing eddi…
Transitions in a stratified Kolmogorov flow
2016
We study the Kolmogorov flow with weak stratification. We consider a stabilizing uniform temperature gradient and examine the transitions leading the flow to chaotic states. By solving the equations numerically we construct the bifurcation diagram describing how the Kolmogorov flow, through a sequence of transitions, passes from its laminar solution toward weakly chaotic states. We consider the case when the Richardson number (measure of the intensity of the temperature gradient) is $$Ri=10^{-5}$$ , and restrict our analysis to the range $$0<Re<30$$ . The effect of the stabilizing temperature is to shift bifurcation points and to reduce the region of existence of stable drifting states. The…