ALBERT

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: Here we show that the distribution of energy of internal gravity waves over a patch of seabed corrugations strongly depends on the distance of the patch to adjacent seafloor features located downstream of the patch. Specifically, we consider the steady state energy distribution due to an incident internal wave arriving at a patch of seabed ripples neighbouring (i)Â another patch of ripples (i.e. a second patch) and (ii)Â a vertical wall. Seabed undulations with dominant wavenumber twice as large as overpassing internal waves reflect back part of the energy of the incident internal waves (Bragg reflection) and allow the rest of the energy to transmit downstream. In the presence of a neighbouring topography on the downstream side, the transmitted energy from the patch may reflect back; partially if the downstream topography is another set of seabed ripples or fully if it is a vertical wall. The reflected wave from the downstream topography is again reflected back by the patch of ripples through the same mechanism. This consecutive reflection goes on indefinitely, leading to a complex interaction pattern including constructive and destructive interference of multiply reflected waves as well as an interplay between higher mode internal waves resonated over the topography. We show here that when steady state is reached both the qualitative and quantitative behaviour of the energy distribution over the patch is a strong function of the distance between the patch and the downstream topography: it can increase or decrease exponentially fast along the patch or stay (nearly) unchanged. As a result, for instance, the local energy density in the water column can become an order of magnitude larger in certain areas merely based on where the downstream topography is. This may result in the formation of steep waves in specific areas of the ocean, leading to breaking and enhanced mixing. At a particular distance, the wall or the second patch may also result in a complete disappearance of the trace of the seabed undulations on the upstream and the downstream wave field. © 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.

Description: Author Posting. © American Geophysical Union, 2018. This article is posted here by permission of [publisher] for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research: Oceans 123 (2018): 6531-6548, doi:10.1029/2017JC013639.

Description: We consider two factors that affect the mixed layer depth (MLD) and potentially contribute to phytoplankton sustenance over winter—variability of air‐sea fluxes and three‐dimensional processes arising from horizontal density gradients (fronts). The role of these two factors is addressed using several three‐dimensional idealized numerical simulations in a process study ocean model forced with air‐sea fluxes at different temporal averaging frequencies. Results show that in winter, when the average mixed layer is much deeper than the euphotic layer and the period of daylight is short, phytoplankton production is relatively insensitive to high‐frequency variability in air‐sea fluxes. Short‐lived stratification events during light‐limited conditions have very little impact on phytoplankton production. On the other hand, the slumping of fronts shallows the mixed layer in a patchy manner and the associated restratification persists considerably longer than that caused by changes in air‐sea fluxes. Simulations with fronts show that in winter, the average MLD is about 600 m shallower than simulations without fronts. Prior to spring warming, the depth‐integrated phytoplankton concentration in the model with fronts is about twice as large as the case without fronts. Hence, even in winter, restratification by fronts is important for setting the MLD; it increases the residence time of phytoplankton in the euphotic layer and contributes to phytoplankton growth, thereby sustaining phytoplankton populations in winter. Higher model resolution intensifies submesoscale dynamics, leading to stronger restratification, shallower mixed layers, greater variability in the MLD, and more production of phytoplankton.

Description: National Science Foundation Grant Numbers: OCE-1434512, OCE-1434788

Description: 2019-03-14