ALBERT

Description: 〈div data-abstract-type="normal"〉〈p〉Scaling arguments are presented to quantify the widely used diapycnal (irreversible) mixing coefficient 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 in stratified flows as a function of the turbulent Froude number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. Here, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the buoyancy frequency, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the turbulent kinetic energy, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the rate of dissipation of turbulent kinetic energy and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the rate of dissipation of turbulent potential energy. We show that for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline7.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline8.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline9.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline10.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline11.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline12.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. These scaling results are tested using high-resolution direct numerical simulation (DNS) data from three different studies and are found to hold reasonably well across a wide range of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline13.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 that encompasses weakly stratified to strongly stratified flow conditions. Given that the 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline14.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 cannot be readily computed from direct field measurements, we propose a practical approach that can be used to infer the 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline15.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 from readily measurable quantities in the field. Scaling analyses show that 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline16.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline17.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline18.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline19.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline20.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline21.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, where 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline22.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the Thorpe length scale and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline23.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the Ozmidov length scale. These formulations are also tested with DNS data to highlight their validity. These novel findings could prove to be a significant breakthrough not only in providing a unifying (and practically useful) parameterization for the mixing efficiency in stably stratified turbulence but also for inferring the dynamic state of turbulence in geophysical flows.〈/p〉〈/div〉

Description: Direct numerical simulations are used to study mixing and dispersion in decaying stably stratified turbulence from a Lagrangian perspective. The change in density of fluid particles owing to small-scale mixing is extracted from the simulations to provide insight into the mixing process. These changes are driven by temporally and spatially intermittent events that are strongly suppressed as the stratification increases and overturning motions disappear. This occurs for times Nt 〉 2π i.e. after one buoyancy period, where N is the buoyancy frequency. The role of small-scale mixing processes in the density (or buoyancy) flux is analysed. After an initial transient, we find that diapycnal displacements due to mixing dominate the dispersion of fluid particles, even in weak stratification. The relationship between the diapycnal diffusivity and vertical dispersion coefficients is found to be strongly dependent on stratification. Models for the mixing following fluid particles are investigated. The time scale for the density changes due to small-scale mixing is shown to be approximately independent of N and instead remains linked to the energy decay time scale which is relatively insensitive to stratification. There are large changes in the structure of these flows as they evolve under the influence of buoyancy forces. We investigate these changes and their relationship to mixing. We find that strong mixing events are closely linked to the presence of overturning regions in the flow, and that they occur close to (but not within) these regions. The results reported here have implications for the development of improved models of diffusion in stably stratified turbulence. © 2006 Cambridge University Press.

Description: High-resolution two- and three-dimensional numerical simulations are performed of first-mode internal gravity waves interacting with a shelf break in a linearly stratified fluid. The interaction of nonlinear incident waves with the shelf break results in the formation of upslope-surging vortex cores of dense fluid (referred to here as internal boluses) that propagate onto the shelf. This paper primarily focuses on understanding the dynamics of the interaction process with particular emphasis on the formation, structure and propagation of internal boluses onshelf. A possible mechanism is identified for the excitation of vortex cores that are lifted over the shelf break, from where (from the simplest viewpoint) they essentially propagate as gravity currents into a linearly stratified ambient fluid. © 2007 Cambridge University Press.

Description: In this paper, we revisit the eddy viscosity formulation to highlight a number of important issues that have direct implications for the prediction of near-wall turbulence. For steady wall-bounded turbulent flows, we make the equilibrium assumption between rates of production (P) and dissipation (ε) of turbulent kinetic energy (κ) in the near-wall region to propose that the eddy viscosity should be given by vt ε/S2, where S is the mean shear rate. We then argue that the appropriate velocity scale is given by (STL)-1/2 k1/2 where TL = k ε is the turbulence (decay) time scale. The difference between this velocity scale and the commonly assumed velocity scale of k1/2 is subtle but the consequences are significant for near-wall effects. We then extend our discussion to show that the fundamental length and time scales that capture the near-wall behaviour in wall-bounded shear flows are the shear mixing length scale LS = ε/S3)1/2 and the mean shear time scale 1/S, respectively. With these appropriate length and time scales (or equivalently velocity and time scales), the eddy viscosity can be rewritten in the familiar form of the k- ε model as vt = (1/ST L)2k2/ε. We use the direct numerical simulation (DNS) data of turbulent channel flow of Hoyas & Jiménez (Phys. Fluids, vol. 18, 2006, 011702) and the turbulent boundary layer flow of Jiménez et al. (J. Fluid Mech. vol. 657, 2010, pp. 335-360) to perform 'a priori' tests to check the validity of the revised eddy viscosity formulation. The comparisons with the exact computations from the DNS data are remarkable and highlight how well the equilibrium assumption holds in the near-wall region. These findings could prove to be useful in near-wall modelling of turbulent flows. © 2013 Cambridge University Press.

Description: The time-averaged flow dynamics of a suspended cylindrical canopy patch with a bulk diameter of D is investigated using large-eddy simulations (LES). The patch consists of Nc constituent solid circular cylinders of height h and diameter d, mimicking patchy vegetation suspended in deep water (H/h ≫ 1, where H is the total flow depth). After validation against published data, LES of a uniform incident flow impinging on the canopy patch was conducted to study the effects of canopy density (0.16 ≤ φ = Nc(d/D)2 ≤ 1, by varying Nc) and bulk aspect ratio (0.25 ≤ AR = h/D ≤ 1, by varying h) on the near-wake structure and adjustment of flow pathways. The relationships between patch geometry, local flow bleeding (three-dimensional redistribution of flow entering the patch) and global flow diversion (streamwise redistribution of upstream undisturbed flow) are identified. An increase in either φ or AR decreases/increases/increases bleeding velocities through the patch surface area along the streamwise/lateral/vertical directions, respectively. However, a volumetric flux budget shows that a larger AR causes a smaller proportion of the flow rate entering the patch to bleed out vertically. The global flow diversion is found to be determined by both the patch geometrical dimensions and the local bleeding which modifies the sizes of the patch-scale near wake. While loss of flow penetrating the patch increases monotonically with increasing φ, its partition into flow diversion around and beneath the patch shows a non-monotonic dependence. The spatial extents of the wake, the flow-diversion dynamics and the bulk drag coefficients of the patch jointly reveal the fundamental differences of flow responses between suspended porous patches and their solid counterparts. © 2018 Cambridge University Press.

Description: Scaling arguments are presented to quantify the widely used diapycnal (irreversible) mixing coefficient Γ = ∈PE/∈ in stratified flows as a function of the turbulent Froude number Fr = ∈/Nk. Here, N is the buoyancy frequency, k is the turbulent kinetic energy, ∈ is the rate of dissipation of turbulent kinetic energy and ∈PE is the rate of dissipation of turbulent potential energy. We show that for Fr≫1, Γ ∝ Fr-2, for Fr∼ O(1), Γ ∝ Fr-1 and for Fr ≪ 1, Γ ∝ Fr0. These scaling results are tested using highresolution direct numerical simulation (DNS) data from three different studies and are found to hold reasonably well across a wide range of Fr that encompasses weakly stratified to strongly stratified flow conditions. Given that the Fr cannot be readily computed from direct field measurements, we propose a practical approach that can be used to infer the Fr from readily measurable quantities in the field. Scaling analyses show that Fr ∝ (LT/LO)-2 for LT/LO 〉 O(1), Fr ∝ (LT/LO)-1 for LT/LO ∼ O(1), and Fr∝(LT/LO)-2/3 for LT/LO 〈O(1), where LT is the Thorpe length scale and LO is the Ozmidov length scale. These formulations are also tested with DNS data to highlight their validity. These novel findings could prove to be a significant breakthrough not only in providing a unifying (and practically useful) parameterization for the mixing efficiency in stably stratified turbulence but also for inferring the dynamic state of turbulence in geophysical flows. © 2019 Cambridge University Press.

Description: The propagation of full-depth lock-exchange bottom gravity currents past a submerged array of circular cylinders is investigated using laboratory experiments and large eddy simulations. Firstly, to investigate the front velocity of gravity currents across the whole range of array density (i.e. the volume fraction of solids), the array is densified from a flat bed towards a solid slab under a particular submergence ratio , where is the flow depth and is the array height. The time-averaged front velocity in the slumping phase of the gravity current is found to first decrease and then increase with increasing . Next, a new geometrical framework consisting of a streamwise array density and a spanwise array density is proposed to account for organized but non-equidistant arrays , where and are the streamwise and spanwise cylinder spacings, respectively, and is the cylinder diameter. It is argued that this two-dimensional parameter space can provide a more quantitative and unambiguous description of the current-array interaction compared with the array density given by . Both in-line and staggered arrays are investigated. Four dynamically different flow regimes are identified: (i) through-flow propagating in the array interior subject to individual cylinder wakes ( : small for in-line array and arbitrary for staggered array; : small); (ii) over-flow propagating on the top of the array subject to vertical convective instability ( : large; : large); (iii) plunging-flow climbing sparse close-to-impermeable rows of cylinders with minor streamwise intrusion ( : small; : large); and (iv) skimming-flow channelized by an in-line array into several subcurrents with strong wake sheltering ( : large; : small). The most remarkable difference between in-line and staggered arrays is the non-existence of skimming-flow in the latter due to the flow interruption by the offset rows. Our analysis reveals that as increases, the change of flow regime from through-flow towards over- or skimming-flow is responsible for increasing the gravity current front velocity. © 2017 Cambridge University Press.

Description: Most commonly used models for turbulent mixing in the ocean rely on a background stratification against which turbulence must work to stir the fluid. While this background stratification is typically well defined in idealized numerical models, it is more difficult to capture in observations. Here, a potential discrepancy in ocean mixing estimates due to the chosen calculation of the background stratification is explored using direct numerical simulation data of breaking internal waves on slopes. Two different methods for computing the buoyancy frequency , one based on a three-dimensionally sorted density field (often used in numerical models) and the other based on locally sorted vertical density profiles (often used in the field), are used to quantify the effect of on turbulence quantities. It is shown that how is calculated changes not only the flux Richardson number , which is often used to parameterize turbulent mixing, but also the turbulence activity number or the Gibson number , leading to potential errors in estimates of the mixing efficiency using -based parameterizations. © 2017 Cambridge University Press.

Description: In this study, we revisit the consequence of assuming equilibrium between the rates of production (P) and dissipation (∈) of the turbulent kinetic energy (k) in the highly anisotropic and inhomogeneous near-wall region. Analytical and dimensional arguments are made to determine the relevant scales inherent in the turbulent viscosity (ν〈inf〉t〈/inf〉) formulation of the standard k-∈ model, which is one of the most widely used turbulence closure schemes. This turbulent viscosity formulation is developed by assuming equilibrium and use of the turbulent kinetic energy (k) to infer the relevant velocity scale. We show that such turbulent viscosity formulations are not suitable for modelling near-wall turbulence. Furthermore, we use the turbulent viscosity (ν〈inf〉t〈/inf〉 formulation suggested by Durbin (Theor. Comput. Fluid Dyn., vol. 3, 1991, pp. 1-13) to highlight the appropriate scales that correctly capture the characteristic scales and behaviour of P/∈ in the near-wall region. We also show that the anisotropic Reynolds stress (u′¯v′¯) is correlated with the wall-normal, isotropic Reynolds stress (v′2¯) as -u′¯v′¯ = c′〈inf〉u〈/inf〉 (ST〈inf〉L〈/inf〉)(v′¯2), where S is the mean shear rate, T〈inf〉L〈/inf〉 =k/∈ is the turbulence (decay) time scale and c′〈inf〉u〈/inf〉 is a universal constant. 'A priori' tests are performed to assess the validity of the propositions using the direct numerical simulation (DNS) data of unstratified channel flow of Hoyas & Jiménez (Phys. Fluids, vol. 18, 2006, 011702). The comparisons with the data are excellent and confirm our findings. © 2014 Cambridge University Press.