Gravity currents propagating into shear

The present experiments explored the dynamical character of the gaseous jet injected flush into cross-flow for variable jet-to-cross-flow momentum flux ratios$J$(5, 12 and 41) and density ratios$S$(0.35 and 1.0). Contoured nozzle and straight pipe injectors were studied here, with the jet Reynolds number fixed at 1900 as other flow parameters were varied. Simultaneous acetone planar laser-induced fluorescence (PLIF) imaging and stereo particle image velocimetry (PIV) were used to study the relationships between scalar and velocity/vorticity fields, with a special focus on comparing PLIF-based extraction of scalar dissipation rates and local strain rates with PIV-based local strain rates in the upstream and downstream shear layers of the jet. There was remarkable similarity between the scalar and vorticity fields for the jet in cross-flow, spanning conditions for absolutely unstable upstream jet shear layers at low$J$or$S$values to conditions for convectively unstable shear layers for larger$J$, equidensity conditions (Megerianet al.,J. Fluid Mech., vol. 593, 2007, pp. 93–129; Getsingeret al.,Exp. Fluids, vol. 53, 2012, pp. 783–801). Proper orthogonal decomposition applied to both scalar and velocity fields revealed strengthening instabilities in both the upstream shear layer and in the jet’s wake as$J$was reduced. The simultaneous measurements allowed PLIF-extracted scalar dissipation rates and strain rates to be determined via a flamelet-like model and compared with PIV-extracted strain rates, each in the diffusion layer-normal direction. There was generally very good qualitative and quantitative agreement for these metrics in both the jet upstream and downstream shear layers for most flow conditions, with excellent correspondence to locations of shear layer vorticity roll up, although downstream shear layer strain rates in some cases showed lesser correspondence between PLIF- and PIV-based data. Such differences are shown to potentially result from diffusion and resolution effects as well as the influence of three-dimensional and transient effects which can be more significant in the lee side of the jet. Nevertheless, the present results reveal interesting dynamics and demonstrate the importance of strain fields in enhanced diffusion and transport phenomena.

The tri-global stability and sensitivity of the low-speed jet in cross-flow are studied using the adjoint equations and finite-time horizon optimal disturbance analysis at Reynolds number $Re=2000$, based on the average velocity at the jet exit, the jet nozzle exit diameter and the kinematic viscosity of the jet, for two jet-to-cross-flow velocity ratios $R=2$ and $4$. A novel capability is developed on unstructured grids and parallel platforms for this purpose. Asymmetric modes are more important to the overall dynamics at $R=4$, suggesting increased sensitivity to experimental asymmetries at higher $R$. Low-frequency modes show a connection to wake vortices. Adjoint modes show that the upstream shear layer is most sensitive to perturbations along the upstream side of the jet nozzle. Lower frequency downstream modes are sensitive in the cross-flow boundary layer. For $R=2$, optimal analysis reveals that for short time horizons, asymmetric perturbations dominate and grow along the counter-rotating vortex pair observed in the cross-section. However, as the time horizon increases, large transient growth is observed along the upstream shear layer. When $R=4$, the optimal perturbations for short time scales grow along the downstream shear layer. For long time horizons, they become hybrid modes that grow along both the upstream and downstream shear layers.

We present results of three-dimensional direct numerical simulations (DNS) and large eddy simulations (LES) of turbulent gravity currents with a discontinuous Galerkin finite elements method. In particular, we consider the lock-exchange test case as a benchmark for gravity currents. Since, to the best of our knowledge, non-Boussinesq three-dimensional reference DNS are not available in the literature for this test case, we first perform a DNS experiment. The DNS provides an accurate description of the turbulent phenomena and highlights some differences with respect to the Boussinesq regime, like the non-symmetric pattern in the evolution of instabilities at the interfacial region and the fact that less turbulent structures are present due to greater stratification. A periodic pattern is also evident in the time evolution of turbulent mixing. The DNS is then employed to assess the performance of different LES models. In particular, we have considered the isotropic dynamic model and an anisotropic dynamic model. The LES results provide a first indication about the superiority of dynamic models with respect to no-model LES. However, the considered Reynolds numbers in the non-Boussinesq context are still too low to draw firm conclusions about the superiority of the present explicit LES approach with respect to an implicit LES approach.

Direct numerical simulations (DNS) of a jet in cross-flow (JICF) with a triangular tab at two positions are performed at jet-to-cross-flow velocity ratios of $R = 2$ and $4$ with a jet Reynolds number of 2000 based on the jet's bulk velocity and exit diameter. The DNS and dynamic mode decomposition show the sensitivity of the tab's effect on the jet upstream shear layer (USL) structure and cross-section to $R$ , echoing the experimental discoveries of Harris et al. (J. Fluid Mech., vol. 918, 2021). Furthermore, DNS reveals that the presence of a tab placed on the upstream side of the nozzle significantly modifies the USL through production of streamwise vortices that curl around the spanwise vortex tubes originating from the primary instability of the USL. This provides an explanation for the improvement in mixing that has been associated with an upstream tab. The streamwise vortex structure shows remarkable similarities to the ‘strain-oriented vortex tubes’ observed for disturbed plane shear layers by Lasheras & Choi (J. Fluid Mech., vol. 189, 1988, pp. 53–86). For both $R$ cases, the USL instability is delayed, the jet penetration is reduced, and the jet cross-section is flattened, although the tab has a less pronounced effect on the USL structure at higher velocity ratios, where the formation of the streamwise vortices is delayed. In contrast, a tab placed 45 $^\circ$ from the upstream position produces significantly different effects compared with the upstream tab. At $R = 4$ , the jet cross-section is significantly skewed away from the tab and a tertiary vortex is formed, as observed in past studies of round JICFs at relatively high $R$ and low Reynolds numbers. The ability of the tab to produce a controllable steady-state tertiary vortex has implications for a variety of applications. The 45 $^\circ$ tab produces asymmetric effects in the wake of the jet at $R = 2$ , but the effect on the jet cross-section is much smaller, highlighting the sensitivity of jets at high $R$ to asymmetric perturbations.

Direct numerical simulation (DNS) is used to simulate lock-exchange flow to understand density currents over rough surfaces. This work is one of the first DNS to simulate density currents over rough walls. The simulations are performed at a Grashof number of 1.6×107. The non-dimensional height of the roughness elements with respect to the half-height of the channel is 0.12. Roughness reduces the speed of the front. Furthermore, the instabilities are significantly enhanced resulting in secondary instabilities that arise much earlier in time. Roughness introduces an additional vorticity generation mechanism which is comparable to the vorticity generated from Kelvin–Helmholtz and lobe–cleft type of instabilities. Flow exhibits significant differences near the leading edge or the nose of the front of the density currents due to roughness.

Direct numerical simulations (DNSs) of two-dimensional stratified gravity-current are simulated using OpenFOAM. Three different aspect ratio, h0/l0 (where h0 is the height of the dense fluid and l0 is the length of the dense fluid) are simulated with stratification ranging from 0 (homogenous ambient) to 0.2 with a constant Reynolds number (Re) of 4000. The stratificationof the ambient air is determined by the density difference between the bottom and the top walls of the channel (ρb- ρ0, where ρb is the density at the bottom of the domain and ρ0 is the density at the top). The magnitude of the stratification (S=ԑb/ԑ) can be determined by calculating the reduced density differences of the bottom fluid with the ambient fluid (ԑb = (ρb- ρ0)/ ρ0) and the dense fluid with the ambient fluid (ԑ = (ρc-ρ0)/ ρ0, where ρc represents the density of the dense fluid). The configuration of the simulation is validated with a test case from Birman, Meiburg & Ungraish and the contour and front velocity (propagation speed) were in good agreement. The gravity current flow in the stratified ambient is analyzed qualitatively and compared with the gravity current in the homogenous ambient. Gravity current in homogenous ambient (S=0) and weak stratification (S=0.2) are supercritical flow where the flow is turbulent and Kelvin-Helmholtz (K-H) billow formed behind the gravity current head. The front location of the gravity is reduced as the stratification increase and denotes that the front velocity of the gravity current is reduced by the stratification.

Intruding gravity currents and their recirculation in a rotating frame: Numerical results

Abstract

Direct numerical simulations (DNS) of planar gravity current in the Boussinesq limit have been conducted with the objective of identifying, visualizing, and describing turbulent structures and their influence on the flow dynamics. The simulations are performed for Reynolds numbers of Re = 8950 and Re = 15,000 with 31‐ and 131‐million grid point resolutions, respectively. This range of Reynolds numbers ensures fully developed turbulent gravity currents, which have never been simulated before using DNS. The flow develops zones with different turbulence characteristics, which eventually interact with each other. The near‐wall bottom flow resembles boundary layer flow with several hairpin‐like vortices oriented in the direction of the flow and preferential patterns of low‐ and high‐speed streaks. The separation between low‐speed streaks at the front scales with the lobe size, which is about 200 wall units for Re = 15,000. Upstream of the front, the separation between low‐speed streaks scales with the well‐accepted value of 100 wall units for turbulent boundary layers. These patterns have associated regions of low and high bottom shear stresses with implications for sediment erosion and bed load transport. Most of the erosive power of the flow is found in the gravity current front. The interface between heavy and light fluids rolls up by baroclinic generation of Kelvin‐Helmholtz vortices, which undergo sudden breakup and decay to small‐scale turbulence. The effect of turbulence and three‐dimensionality on the flow dynamics is addressed by comparing two‐ and three‐dimensional simulations. Three‐dimensional simulations present active mechanisms that undermine the strong flow coherence, comparing well with experimental observations.

High-fidelity simulations of gravity currents using a high-order finite-difference spectral vanishing viscosity approach

We develop a vorticity‐based approach for modelling quasi‐steady, supercritical gravity currents propagating into a finite‐height channel with arbitrary density and velocity stratification. The model enforces the conservation of mass, horizontal and vertical momentum. In contrast to previous approaches, it does not rely on empirical, energy‐based closure assumptions. Instead, the effective energy loss of the flow can be calculated a posteriori. The present model results in the formulation of a second‐order, nonlinear ordinary differential equation (ODE) that can be solved in a straightforward fashion to determine the gravity‐current velocity, along with the downstream ambient velocity and density profiles. Comparisons between model predictions and direct numerical simulations (DNS) show excellent agreement. Furthermore, they indicate that, for high Reynolds numbers, the gravity‐current height adjusts itself so as to maximize the loss of energy.

A laboratory study of the effect of wave action on turbulent gravity currents generated by an instantaneous release of dense fluid is described. Dense fluid is released in the centre of the flume, generating a gravity current propagating horizontally with two fronts. This gravity current type, in the absence of waves, spreads symmetrically and propagating with the length scales according to the standard box models. In the presence of gravity waves the length of the gravity current is, to leading order unchanged, but the centre is advected in the direction of the wave motion. The shear of the mean flow generated by the oscillatory wave motion modifies the shape of the gravity current, inducing an asymmetry in the current height. Copyright ASCE 2006.

<p>We investigate the removal of a dense bottom layer by a gravity current, via Navier-Stokes Boussinesq simulations. The problem is governed by a dimensionless thickness parameter for the bottom layer, and by the ratio of two density differences. A quasisteady gravity current propagates along the interface and displaces some of the dense bottom fluid, which accumulates ahead of the gravity current and forms an undular bore or a series of internal gravity waves. Depending on the ratio of the gravity current front velocity to the linear shallow-water wave velocity, we observe small-amplitude waves or a train of steep, nonlinear internal waves. We develop a self-contained model based on the conservation principles for mass and vorticity that does not require empirical closure assumptions. This model is able to predict the gravity current height and the internal wave or bore velocity, generally to within about 10% accuracy. An energy budget analysis provides information on the rates at which potential energy is converted into kinetic energy and then dissipated, and on the processes by which energy is transferred from the gravity current fluid to the dense and ambient fluids. We observe that the energy content of thicker and denser bottom layers grows more rapidly.</p>

Gravity currents from instantaneous sources down a slope were modeled with classic thermal theory, which has formed the basis for many subsequent studies. Considering entrainment of ambient fluid and conservation of total buoyancy, thermal theory predicted the height, length, and velocity of the gravity current head. In this study, the problem with direct numerical simulations was re-investigated, and the results compared with thermal theory. The predictions based on thermal theory are shown to be appropriate only for the acceleration phase, not for the entire gravity current motion. In particular, for the current head forms on a 10° slope produced from an instantaneous buoyancy source, the contained buoyancy in the head is approximately 58% of the total buoyancy at most and is not conserved during the motion as assumed in thermal theory. In the deceleration phase, the height and aspect ratio of the head and the buoyancy contained within it may all decrease with downslope distance. Thermal theory relies o...

Simulación directa de turbulencia en corrientes de gravedad con efecto Coriolis