Modifications to the K-Profile parameterization with nondiffusive fluxes for Langmuir turbulence

2021 ◽  
Author(s):  
Tomas Chor ◽  
James C. McWilliams ◽  
Marcelo Chamecki
Keyword(s):  
Vertical Mixing ◽  
Turbulent Fluxes ◽  
Common Method ◽  
Diagnostic Approach ◽  
Langmuir Turbulence ◽  
Modeling Approach ◽  
Wave Effects ◽  
Diffusive Term ◽  
Langmuir Circulations ◽  
Surface Buoyancy

AbstractThe K-profile parameterization (KPP) is a common method to model turbulent fluxes in regional and global oceanic models. Many versions of KPP exist in the oceanic sciences community and one of their main differences is how they take the effects of nonbreaking waves into account. Although there is qualitative consensus that nonbreaking waves enhance vertical mixing due to the ensuing Langmuir circulations, there is no consensus on the quantitative aspects and modeling approach. In this paper we use a recently-developed method to estimate both components of KPP (the diffusive term, usually called local, and the nondiffusive component, usually called nonlocal) based on numerically-simulated turbulent fluxes without any a priori assumptions about their scaling or their shape. Through this method we show that the cubic shape usually used in KPP is not optimal for wavy situation and propose new ones. Furthermore we show that the formulation for the nondiffusive fluxes, which currently only depend on the presence of surface buoyancy fluxes, should also take wave effects into account. Finally, we investigate how the application of these changes to KPP improves the representation of turbulent fluxes in a diagnostic approach when compared to previous models.

scholarly journals A Parameterization with a Constrained Potential Energy Conversion Rate of Vertical Mixing Due to Langmuir Turbulence

2019 ◽  
Vol 49 (11) ◽  
pp. 2935-2959 ◽  
Author(s):  
Brandon G. Reichl ◽  
Qing Li
Keyword(s):  
Turbulent Mixing ◽  
Vertical Mixing ◽  
Stable Stratification ◽  
Surface Boundary ◽  
Langmuir Turbulence ◽  
Surface Boundary Layer ◽  
Eddy Simulation ◽  
Available Energy ◽  
Climate Simulations ◽  
Surface Buoyancy

AbstractIn this study we develop a new parameterization for turbulent mixing in the ocean surface boundary layer (OSBL), including the effect of Langmuir turbulence. This new parameterization builds on a recent study (Reichl and Hallberg 2018, hereafter RH18), which predicts the available energy for turbulent mixing against stable stratification driven by shear and convective turbulence. To investigate the role of Langmuir turbulence in the framework of RH18, we utilize data from a suite of previously published large-eddy simulation (LES) experiments (Li and Fox-Kemper 2017, hereafter LF17) with and without Langmuir turbulence under different idealized forcing conditions. We find that the parameterization of RH18 is able to reproduce the mixing simulated by the LES in the non-Langmuir cases, but not the Langmuir cases. We therefore investigate the enhancement of the integrated vertical buoyancy flux within the entrainment layer in the presence of Langmuir turbulence using the LES data. An additional factor is introduced in the RH18 framework to capture the enhanced mixing due to Langmuir turbulence. This additional factor depends on the surface-layer averaged Langmuir number with a reduction in the presence of destabilizing surface buoyancy fluxes. It is demonstrated that including this factor within the RH18 OSBL turbulent mixing parameterization framework captures the simulated effect of Langmuir turbulence in the LES, which can be used for simulating the effect of Langmuir turbulence in climate simulations. This new parameterization is compared to the KPP-based Langmuir entrainment parameterization introduced by LF17, and differences are explored in detail.

scholarly journals Submesoscale Cold Filaments in the Gulf Stream

2014 ◽  
Vol 44 (10) ◽  
pp. 2617-2643 ◽  
Author(s):  
Jonathan Gula ◽  
M. Jeroen Molemaker ◽  
James C. McWilliams
Keyword(s):  
Life Cycle ◽  
Gulf Stream ◽  
Baroclinic Instability ◽  
Vertical Mixing ◽  
Thermal Wind ◽  
Filament Dynamics ◽  
Oceanic Surface ◽  
Secondary Circulations ◽  
Order Of Magnitude ◽  
Surface Buoyancy

Abstract A set of realistic, very high-resolution simulations is made for the Gulf Stream region using the oceanic model Regional Oceanic Modeling System (ROMS) to study the life cycle of the intense submesoscale cold filaments that form on the subtropical gyre, interior wall of the Gulf Stream. The surface buoyancy gradients and ageostrophic secondary circulations intensify in response to the mesoscale strain field as predicted by the theory of filamentogenesis. It can be understood in terms of a dual frontogenetic process, along the lines understood for a single front. There is, however, a stronger secondary circulation due to the amplification at the center of a cold filament. Filament dynamics in the presence of a mixed layer are not adequately described by the classical thermal wind balance. The effect of vertical mixing of momentum due to turbulence in the surface layer is of the same order of magnitude as the pressure gradient and Coriolis force and contributes equally to a so-called turbulent thermal wind balance. Filamentogenesis is disrupted by vigorous submesoscale instabilities. The cause of the instability is the lateral shear as energy production by the horizontal Reynolds stress is the primary fluctuation source during the process; this contrasts with the usual baroclinic instability of submesoscale surface fronts. The filaments are lines of strong oceanic surface convergence as illustrated by the release of Lagrangian parcels in the Gulf Stream. Diabatic mixing is strong as parcels move across the filaments and downwell into the pycnocline. The life cycle of a filament is typically a few days in duration, from intensification to quasi stationarity to instability to dissipation.

scholarly journals Reply to “Comments on ‘A Wave-Resolving Simulation of Langmuir Circulations with a Nonhydrostatic Free-Surface Model: Comparison with Craik–Leibovich Theory and an Alternative Eulerian View of the Driving Mechanism’”

2019 ◽  
Vol 49 (3) ◽  
pp. 889-892 ◽  
Author(s):  
Yasushi Fujiwara ◽  
Yutaka Yoshikawa ◽  
Yoshimasa Matsumura
Keyword(s):  
Model Comparison ◽  
Three Dimensional ◽  
Momentum Equation ◽  
Surface Model ◽  
Driving Mechanism ◽  
Radiation Stress ◽  
Wave Effect ◽  
Wave Effects ◽  
Langmuir Circulations ◽  
Free Surface Model

AbstractFujiwara et al. explicitly simulated Langmuir circulations using a wave-resolving simulation (WRS) technique and found that the residual wave effect on vorticity was well represented by the vortex force of the Craik–Leibovich (CL) equation, at least in the simulated situation. In response to the simulation results, Mellor has proposed a view that ubiquitous applicability of the CL formulation is still questionable and that the three-dimensional radiation stress (3DRS) formulation that he has derived encompasses both of the vortex force effect and an effect that is lower order in terms of wave steepness. Here, these opinions are discussed in terms of the approximations used in the wave-averaged formulations. The asymptotic expansion of the Eulerian-averaged momentum equation allows the separate discussion of two different wave effects: pressure correction and torque. It is argued that the approximation adopted in Mellor’s 3DRS formulation is presumably not accurate enough to properly parameterize the wave torque effect, and possible approaches to examine its performance are proposed. We agree with the view that the applicability of the CL formulation needs further investigation. WRS will be a helpful tool for this purpose.

scholarly journals The Effects of Surface Wind Stress and Buoyancy Flux on the Evolution of a Front in a Turbulent Thermal Wind Balance

Fluids ◽  
2020 ◽  
Vol 5 (2) ◽  
pp. 87
Author(s):  
Matthew N. Crowe ◽  
John R. Taylor
Keyword(s):  
Wind Stress ◽  
Numerical Solutions ◽  
Surface Wind ◽  
Vertical Mixing ◽  
Spreading Rate ◽  
Buoyancy Flux ◽  
Thermal Wind ◽  
Surface Wind Stress ◽  
Shear Dispersion ◽  
Surface Buoyancy

Here we consider the effects of surface buoyancy flux and wind stress on a front in turbulent thermal wind (TTW) balance using the framework of Crowe and Taylor (2018). The changes in the velocity and density profiles induced by the wind stress and buoyancy flux interact with the TTW and can qualitatively change the evolution of the front. In the absence of surface-forcing, Crowe and Taylor (2018) found that shear dispersion associated with the TTW circulation causes the frontal width to increase. In many cases, the flow induced by the surface-forcing enhances the spreading rate. However, if the wind stress drives a cross-front flow which opposes the frontal buoyancy gradient or the buoyancy flux drives an unstable stratification, it is possible to obtain an up-gradient cross-front buoyancy flux, which can act to sharpen the front. In certain conditions, an equilibrium state develops where the tendency for the TTW circulation to spread the front is balanced by the frontogenetic tendency of the surface forces. We use numerical solutions to a nonlinear diffusion equation in order to test these predictions. Finally, we describe the connection between surface-forcing and vertical mixing and discuss typical parameters for mid-ocean fronts.

scholarly journals Toward a K-Profile Parameterization of Langmuir Turbulence in Shallow Coastal Shelves

2015 ◽  
Vol 45 (12) ◽  
pp. 2869-2895 ◽  
Author(s):  
Nityanand Sinha ◽  
Andres E. Tejada-Martínez ◽  
Cigdem Akan ◽  
Chester E. Grosch
Keyword(s):  
Shear Stress ◽  
Shallow Water ◽  
Water Column ◽  
Reynolds Shear Stress ◽  
Vertical Mixing ◽  
Stokes Drift ◽  
Langmuir Turbulence ◽  
Mean Velocity ◽  
Shear Current ◽  
Log Law

AbstractInteraction between the wind-driven shear current and the Stokes drift velocity induced by surface gravity waves gives rise to Langmuir turbulence in the upper ocean. Langmuir turbulence consists of Langmuir circulation (LC) characterized by a wide range of scales. In unstratified shallow water, the largest scales of Langmuir turbulence engulf the entire water column and thus are referred to as full-depth LC. Large-eddy simulations (LESs) of Langmuir turbulence with full-depth LC in a wind-driven shear current have revealed that vertical mixing due to LC erodes the bottom log-law velocity profile, inducing a profile resembling a wake law. Furthermore, in the interior of the water column, two sources of Reynolds shear stress, turbulent (nonlocal) transport and local Stokes drift shear production, can combine to lead to negative mean velocity shear. Meanwhile, near the surface, Stokes drift shear serves to intensify small-scale eddies leading to enhanced vertical mixing and disruption of the surface log law. A K-profile parameterization (KPP) of the Reynolds shear stress comprising local and nonlocal components is introduced, capturing these basic mechanisms by which Langmuir turbulence in unstratified shallow water impacts the vertical mixing of momentum. Single-water-column, Reynolds-averaged Navier–Stokes simulations with the new parameterization are presented, showing good agreement with LES in terms of mean velocity. Results show that coefficients in the KPP may be parameterized based on attributes of the full-depth LC.

Vertical Mixing by Langmuir Circulations

2000 ◽  
Vol 6 (3-4) ◽  
pp. 225-237 ◽  
Author(s):  
James C. McWilliams ◽  
Peter P. Sullivan
Keyword(s):  
Vertical Mixing ◽  
Langmuir Circulations

scholarly journals Evaluating Monin-Obukhov Scaling in the Unstable Oceanic Surface Layer

2020 ◽  
Author(s):  
Zhihua Zheng ◽  
Ramsey R. Harcourt ◽  
Eric A. D’Asaro
Keyword(s):  
Surface Layer ◽  
Surface Waves ◽  
Scaling Laws ◽  
Similarity Theory ◽  
Vertical Mixing ◽  
Temperature Gradients ◽  
Langmuir Turbulence ◽  
Near Surface ◽  
Oceanic Surface ◽  
Using Data

AbstractMonin-Obukhov Similarity Theory (MOST) provides important scaling laws for flow properties in the surface layer of the atmosphere and has contributed to most of our understanding of the near-surface turbulence. The prediction of near-surface vertical mixing in most operational ocean models is largely built upon this theory. However, the validity of MOST in the upper ocean is questionable due to the demonstrated importance of surface waves in the region. Here we examine the validity of MOST in the statically unstable oceanic surface layer, using data collected from two open ocean sites with different wave conditions. The observed vertical temperature gradients are found to be about half of those predicted by MOST. We hypothesize this is attributable to either the breaking of surface waves, or Langmuir turbulence generated by the wave-current interaction. Existing turbulence closure models for surface wave breaking and for Langmuir turbulence are simplified to test these two hypotheses. Although both models predict reduced temperature gradients, the simplified Langmuir turbulence model matches observations more closely, when appropriately tuned.

Diffusive–Nondiffusive Flux Decompositions in Atmospheric Boundary Layers

2020 ◽  
Vol 77 (10) ◽  
pp. 3479-3494
Author(s):  
Tomas Chor ◽  
James C. McWilliams ◽  
Marcelo Chamecki
Keyword(s):  
Boundary Layers ◽  
A Priori ◽  
Eddy Diffusivity ◽  
Turbulent Fluxes ◽  
Atmospheric Boundary Layers ◽  
Convective Boundary ◽  
Atmospheric Sciences ◽  
Diffusive Term ◽  
Novel Method ◽  
Neutral Conditions

AbstractEddy diffusivity models are a common method to parameterize turbulent fluxes in the atmospheric sciences community. However, their inability to handle convective boundary layers leads to the addition of a nondiffusive flux component (usually called nonlocal) alongside the original diffusive term (usually called local). Both components are often modeled for convective conditions based on the shape of the eddy diffusivity profile for neutral conditions. This assumption of shape is traditionally employed due to the difficulty of estimating both components based on numerically simulated turbulent fluxes without any a priori assumptions. In this manuscript we propose a novel method to avoid this issue and estimate both components from numerical simulations without having to assume any a priori shape or scaling for either. Our approach is based on optimizing results from a modeling perspective and taking as much advantage as possible from the diffusive term, thus maximizing the eddy diffusivity. We use our method to diagnostically investigate four different large-eddy simulations spanning different stability regimes, which reveal that nondiffusive fluxes are important even when trying to minimize them. Furthermore, the calculated profiles for both diffusive and nondiffusive fluxes suggest that their shapes change with stability, which is an effect that is not included in most models currently in use. Finally, we use our results to discuss modeling approaches and identify opportunities for improving current models.

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