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Entrainment of density flows is a key parameter in constructing predictive models of global climate, ocean flows, and turbidity currents. Our numerical experiment, which included 10 subaqueous dilu...

The stability of stratified shear flows with multilayered density distributions and monotonic velocity profiles without inflection points is studied using a class of flows of an ideal incompressible three–layer medium as a model. The flow velocity Vx=U(z) is assumed to be increasing from zero at the bottom (z=0) to its maximum value U0 (when z→∞), with d2U/dz2

Large eddy simulations are used to examine the evolution of a shear layer in a thermocline with non-uniform density stratification. Unlike previous studies, the density in the present study is continuously stratified and has stratification in the upper half different from the lower half of the shear layer. The stratification in the upper half is fixed at Ju = 0.05, while the stratification in the lower half is increased to Jd = 0.05, 0.15, 0.25 and 0.35, leading to a progressively stronger asymmetry of the Rig profile in the four cases. Here, J is the bulk Richardson number and Rig is the gradient Richardson number. The type of shear instability and the properties of the ensuing turbulence are found to depend strongly on the degree of asymmetry in stratification. The shear instability changes from a Kelvin–Helmholtz (KH) mode at Jd = 0.05 to a Holmboe (H) mode at Jd = 0.35 and exhibits characteristics of both KH and H modes at intermediate values of Jd. Differences in the evolution among the cases are qua...

The effect of Richardson number ratio of the walls on the laminar mixed convection of a nanofluid flowing in an annulus which was heated uniformly is studied numerically. The finite volume technique is utilized to discretize and to solve a set of three-dimensional elliptic governing equations. The secondary flows and contour of the dimensionless axial velocity and dimensionless temperature are presented and discussed. For a given inner or outer wall Ri, the convective heat transfer coefficient of the walls changes differently with Richardson number ratio ( and γ) while inner, outer, and area average friction coefficients do not significantly change. The dimensionless axial velocity profiles shift toward the wall whose Richardson number has a fixed value at the upper vertical plane. The most effect on the axial velocity occurs at the upper vertical plane with respect to or γ. Also, for a given Rii or Rio, the inner and outer wall convective heat transfer coefficient does not increase permanently with incre...

The nondimensional parameters involved in a four-equation depth-averaged model of gravity flows have been studied using a vertical structure resolving numerical model at both field and laboratory scales. The main findings of this study are: (i) Water entrainment coefficient of gravity flows depends strongly on the bed slope, but compared with the bulk Richardson number, it has a weak dependence on entrainment/deposition at the bottom boundary; (ii) Depositional flow at laboratory scale may become erosive and thus change its characteristics significantly at the field scale if scaled by the densimetric Froude number; (iii)Values of the shape factors of depth-averaged models deviate from those approximated by the top-hat assumption, but they vary little with changes in channel bed slope, inflow, erosion/deposition at the bottom boundary, or scale. Two different sets of shape factors are recommended, one for conservative density flows and another for turbidity currents.

We examine the transmission of internal gravity waves through a non‐uniformly stratified fluid with vertically varying background shear. To quantify wave transmission we show that the appropriate measure is the ratio of the flux of transmitted to incident pseudoenergy, T. We derive an analytic prediction of T for the transmission of waves through a piecewise‐linear shear flow in two cases. In both, the fluid is unstratified over the depth of the shear and uniformly stratified elsewhere. In one study, the density profile is continuous. Such a basic state is unstable but with vanishingly small growth rate as the bulk Richardson number, Ri, becomes large. In the limit of an infinitely large Richardson number (no shear), we recover the tunnelling prediction of Sutherland and Yewchuk (2004). In weak shear, incident waves can transmit weakly, even if the phase speed matches the flow speed within the shear layer (a critical level). However, no transmission occurs when the phase speed of incident waves e...

This study presents a semi‐analytic non‐iterative solution for the Monin‐Obukhov similarity equations under unstable surface conditions. The solution is represented in terms of the non‐dimensional Monin‐Obukhov stability parameter z/L. This parameter is given as a function of the bulk Richardson number and other surface parameters including the heat and momentum roughness lengths which are generally assumed to be different in this formulation. The proposed formulations give results that are both quantitatively and qualitatively consistent with the fully iterated numerical solution for a wide range of surface parameters.

The meteorological situations in which heavy rainfall events occur over the western Mediterranean region are presented and discussed. The study of such situations has been made looking for mechanisms able to maintain convection during larger intervals than the life cycle of a single convective cell. These mechanisms have been analysed firstly from a thermodynamic standpoint, involving the determination of stability, precipitable water mass, convective available potential energy (CAPE), and bulk Richardson number (bRi). This permits definition of some features of these events and establishment of some thresholds for different variables. Secondly, resort has been made to objective analysis focused on the diagnosis of spatial and temporal distributions of quasi‐geostrophic forcing for vertical motion, convective instability, water vapour divergence/convergence at low levels and CAPE. Following this analysis compound maps were obtained, showing the zones of superimposition of the above four variables. These z...

This paper presents the results ofan experimental study on the near-field diffusion of bluff buoyant turbulent surface jets with small (source) Richardson number in a large body of water without any ambient currents. It has been found that the velocity scale decreases inversely with the axial distance x from the outfall whereas the vertical and surface length scales h and b grow linearly with x. The variation of the coefficients in the relations for these scales, with the source Richardson number has been evaluated using the experimental observations.

The linear stability of certain two-dimensional disturbances in turbulent density-stratified shear flow is examined. The vertical, turbulent transports of momentum and buoyancy are modelled as gradient transports, and the interaction between velocity and momentum fields through the gradient Richardson number is included. It is argued that solutions should be stable, since the ensemble-averaged equations may no longer exhibit the small-scale instabilities related to turbulence. The stability conditions obtained constitute a generalization of those obtained by Kranenburg (1980a, b) for one-dimensional disturbances, and set certain bounds to the dependence of eddy viscosity and diffusivity on the Richardson number.

An entrainment model is developed which includes the effect of the buoyancy flux by molecular diffusion across a density interface. This effect is incorporated into the conservation equation for turbulent kinetic energy through a “diffusion parameter” RiPe -1/2, where Ri is the bulk Richardson number and Pe the Peclet number. As RiPRiPe -1/2e increases and approaches a critical limiting value the net entrainment, defined as the rate of deepening of the mixed layer, becomes zero. Based on a numerical study and on results from two experiments of different scales, it is shown that the limiting value of this parameter for entrainment to occur is approximately 10 for a salt-stratified system, though this value may depend on the diffusivity of the stratified component.

A simple model is derived to explain the form ofthe relationship between the normalized entrainment rate of quiescent fluid into a turbulent mixed layer and the bulk Richardson number. The model is based on a parameterization ofthe turbulent kinetic energy budget and includes the effect of molecular diffusivity through the gravity work term. Results show good agreement with available data.

Understanding the influence of vertical stratification on large scale motions is of prime geophysical interest for both the stable and unstable cases. Here we present a generalization of the Lorenz (1962) model which includes externally imposed stratifications of either sign. Various flow regimes are determined, according to the values of the thermal Rossby number RoT the nondimensional rotation rate Ω and the ratio of temperature differences in the vertical, δ, and horizontal directions, δT. It is found that the stability curve in the RoT,R plane, while preserving its general shape which was found by Hide (1953,1969) for δT=0, moves towards the lower right with increasing δT>0, other conditions being equal, and to the upper left for the slightly unstable case. The curve separates the Hadley axisymmetrical regimes from the Rossby wave regimes. Introduction of a bulk Richardson number helps to separate regular and irregular wave regimes for the case of unstable stratification. Laboratory experimen...