4 results
Development of gravity currents on slopes under different interfacial instability conditions
- Antoine Martin, M. Eletta Negretti, E. J. Hopfinger
-
- Journal:
- Journal of Fluid Mechanics / Volume 880 / 10 December 2019
- Published online by Cambridge University Press:
- 07 October 2019, pp. 180-208
-
- Article
- Export citation
-
We present experimental results on the development of gravity currents moving onto sloping boundaries with slope angles $\unicode[STIX]{x1D703}=7^{\circ }$, $10^{\circ }$ and $15^{\circ }$. Different regimes of flow development are observed depending on the slope angle and on the initial velocity and density profiles, characterized by the Richardson number $J_{i}=\unicode[STIX]{x1D6FF}_{i}{g_{0}}^{\prime }/\unicode[STIX]{x0394}u_{i}^{2}$, where $\unicode[STIX]{x1D6FF}_{i}$, $\unicode[STIX]{x0394}u_{i}$ and $g_{0}^{\prime }$ are, respectively, the velocity interface thickness, the maximum velocity difference and reduced gravity at the beginning of the slope. For $J_{i}>0.7$ and the larger slope angle, the flow strongly accelerates, reaches a maximum at the beginning of the Kelvin–Helmholtz instability, then decelerates and re-accelerates again. For $0.3<J_{i}<0.6$, instability occurs earlier and velocity oscillations are less. When $J_{i}\leqslant 0.3$ the increase in velocity is smooth. The magnitude of velocity oscillation depends on the combined effect of $J_{i}$ and slope angle, expressed by an overall acceleration parameter $\overline{T_{a}}=(\unicode[STIX]{x1D6FF}_{i}/U_{i})((U_{c}-U_{i})/x_{c})$, which, to first order, is given by $J_{i}\sin \unicode[STIX]{x1D703}$, where $U_{c}$ and $x_{c}$ are, respectively, the velocity and position at instability onset. The velocity increases smoothly up to an equilibrium state when $\overline{T_{a}}\leqslant 0.06$ and exhibits an irregular behaviour at larger values of $\overline{T_{a}}$. The critical Richardson number $J_{c}$ decreases with increasing $J_{i}$ (increasing $\unicode[STIX]{x1D6FF}_{i}/h_{i}$) which is due to wall effects and $\unicode[STIX]{x1D6FF}/\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D70C}}\neq 1$. After the beginning of Kelvin–Helmholtz instability, entrainment rates are close to those of a mixing layer, decreasing to values of a gravity current after the mixing layer reaches the boundary. It is shown here that the interfacial instability during current development affects the bottom shear stress which can reach values of $c_{D}\approx 0.03$ regardless of initial conditions. By solving numerically the depth integrated governing equations, the gravity flow velocity, depth and buoyant acceleration in the flow direction can be well predicted for all the performed experiments over the full measurement domain. The numerical results for the experiments with $J_{i}>0.3$ predict that the current requires a distance of at least $x_{n}\approx 40h_{i}$ to reach a normal state of constant velocity, which is much larger than the distance $x_{n}\approx 10h_{i}$ required in the case of a current with $J_{i}\leqslant 0.3$ that is commonly assumed for downslope currents.
Development of gravity currents on rapidly changing slopes
- M. E. Negretti, J.-B. Flòr, E. J. Hopfinger
-
- Journal:
- Journal of Fluid Mechanics / Volume 833 / 25 December 2017
- Published online by Cambridge University Press:
- 02 November 2017, pp. 70-97
-
- Article
- Export citation
-
Gravity currents often occur on complex topographies and are therefore subject to spatial development. We present experimental results on continuously supplied gravity currents moving from a horizontal to a sloping boundary, which is either concave or straight. The change in boundary slope and the consequent acceleration give rise to a transition from a stable subcritical current with a large Richardson number to a Kelvin–Helmholtz (KH) unstable current. It is shown here that depending on the overall acceleration parameter $\overline{T_{a}}$, expressing the rate of velocity increase, the currents can adjust gradually to the slope conditions (small $\overline{T_{a}}$) or go through acceleration–deceleration cycles (large $\overline{T_{a}}$). In the latter case, the KH billows at the interface have a strong effect on the flow dynamics, and are observed to cause boundary layer separation. Comparison of currents on concave and straight slopes reveals that the downhill deceleration on concave slopes has no qualitative influence, i.e. the dynamics is entirely dominated by the initial acceleration and ensuing KH billows. Following the similarity theory of Turner 1973 (Buoyancy Effects in Fluids. Cambridge University Press), we derive a general equation for the depth-integrated velocity that exhibits all driving and retarding forces. Comparison of this equation with the experimental velocity data shows that when $\overline{T_{a}}$ is large, bottom friction and entrainment are large in the region of appearance of KH billows. The large bottom friction is confirmed by the measured high Reynolds stresses in these regions. The head velocity does not exhibit the same behaviour as the layer velocity. It gradually approaches an equilibrium state even when the acceleration parameter of the layer is large.
Convection at an isothermal wall in an enclosure and establishment of stratification
- T. Caudwell, J.-B. Flór, M. E. Negretti
-
- Journal:
- Journal of Fluid Mechanics / Volume 799 / 25 July 2016
- Published online by Cambridge University Press:
- 23 June 2016, pp. 448-475
-
- Article
- Export citation
-
In this experimental–theoretical investigation, we consider a turbulent plume generated by an isothermal wall in a closed cavity and the formation of heat stratification in the interior. The buoyancy of the plume near the wall and the temperature stratification are measured across a vertical plane with the temperature laser induced fluorescence method, which is shown to be accurate and efficient (precision of $0.2\,^{\circ }$C) for experimental studies on convection. The simultaneous measurement of the velocity field with particle image velocimetry allows for the calculation of the flow characteristics such as the Richardson number and Reynolds stress. This enables us to give a refined description of the wall plume, as well as the circulation and evolution of the stratification in the interior. The wall plume is found to have an inner layer close to the heated boundary with a laminar transport of hardly mixed fluid which causes a relatively warm top layer and an outer layer with a transition from laminar to turbulent at a considerable height. The measured entrainment coefficient is found to be dramatically influenced by the increase in stratification of the ambient fluid. To model the flow, the entrainment model of Morton, Taylor & Turner (Proc. R. Soc. Lond. A, vol. 234 (1196), 1956, pp. 1–23) has first been adapted to the case of an isothermal wall. Differences due to their boundary condition of a constant buoyancy flux, modelled with salt by Cooper & Hunt (J. Fluid Mech., vol. 646, 2010, pp. 39–58), turn out to be small. Next, to include the laminar–turbulent transition of the boundary layer, a hybrid model is constructed which is based on the similarity solutions reported by Worster & Leitch (J. Fluid Mech., vol. 156, 1985, pp. 301–319) for the laminar part and the entrainment model for the turbulent part. Finally, the observed variation of the global entrainment coefficient, which is due to the increased presence of an upper stratified layer with a relatively low entrainment coefficient, is incorporated into both models. All models show reasonable agreement with experimental measurements for the volume, momentum and buoyancy fluxes as well as for the evolution of the stratification in the interior. In particular, the introduction of the variable entrainment coefficient improves all models significantly.
On shallow-water wakes: an analytical study
- M. E. NEGRETTI, G. VIGNOLI, M. TUBINO, M. BROCCHINI
-
- Journal:
- Journal of Fluid Mechanics / Volume 567 / 25 November 2006
- Published online by Cambridge University Press:
- 19 October 2006, pp. 457-475
-
- Article
- Export citation
-
Analytical solutions for the characteristic scales of a turbulent wake in shallow flows are presented for two asymptotic cases: in one case, boundary-layer effects dominate whereas in the other, wake effects prevail. The latter case degenerates into the solution valid for an unbounded two-dimensional wake. These solutions show that the momentum deficit decreases exponentially in the longitudinal direction while the transverse velocity profile reveals a wake region characterized by a reduced velocity deficit compared to that of an unbounded wake. When wake-turbulence dominates there is a non-uniform turbulent viscosity in the longitudinal direction. These analytical solutions are compared with experimental data showing good agreement.