Parameterization Of Turbulent Mixing Research Articles

Studies on parameterizations of turbulent mixing in the deep ocean

Studies on parameterizations of turbulent mixing in the deep ocean

Impacts of inertial internal wave breaking mixing parameterization on a global ocean model

A parameterization of vertical mixing induced by fine-scale near-inertial internal waves (F-scheme) is implemented in the Parallel Ocean Program, version 2 (POP2). The F-scheme is based on the spectrum model via solving the non-traditional approximation internal wave equations and the observed internal wave spectra. The structure of the resulting dissipation and diffusivity fields and its impacts on the ocean model simulations are investigated. The diffusivity coefficient derived from F-scheme varies spatiotemporally, and is generally in consistent magnitude with observed results in the middle to high latitude ocean, and show the similar latitude dependent characteristics with the current observations, depending on the product of the horizontal and vertical components of the Coriolis parameter (f·f∼) as well as the local stratification condition. The interior mixing induced by F-scheme has some noticeable impacts on the temperature and salinity structure near the main thermocline, the meridional overturning circulation and northward heat transport as has been demonstrated in the other two OGCMs (LICOM and MOM4). The temperature and salinity structure simulated using F-scheme are statistically closer to observations, especially it improves the simulation of the Pacific Ocean, Indian Ocean and Antarctic Circumpolar Circulation. But the involved background mixing coefficients or F-scheme enlarges the temperature and salinity biases in the Atlantic Ocean, the cause is related to the pre-existing weak Antarctic Intermediate Water intrusion toward north and the inexact Atlantic Meridional Overturn Circulation simulation in the present model. F-scheme provides weak mixing in some regions, where an appropriate parameterization of turbulent mixing induced by wave-wave interaction also should be considered in the future.

Deep Ocean Learning of Small Scale Turbulence

AbstractTurbulent mixing at the sub‐meter scale is an essential component of the ocean's meridional overturning circulation and its associated global redistribution of heat, carbon, nutrients, pollutants, and other tracers. Whereas direct turbulence observations in the ocean interior are limited to a modest collection of field programs, basic information such as temperature, salinity, and depth is available globally. Here, we show that supervised machine learning algorithms can be trained on the existing turbulence data to develop skillful predictions of the key properties of turbulence from T, S, Z, and topographic data. This constitutes a promising first step toward a hybrid physics‐artificial intelligence approach to parameterization of turbulent mixing in ocean and climate models.

Enhanced Near-Inertial Waves and Turbulent Diapycnal Mixing Observed in a Cold- and Warm-Core Eddy in the Kuroshio Extension Region

Abstract Shipboard observations of upper-ocean current, temperature–salinity, and turbulent dissipation rate were used to study near-inertial waves (NIWs) and turbulent diapycnal mixing in a cold-core eddy (CE) and warm-core eddy (WE) in the Kuroshio Extension (KE) region. The two eddies shed from the KE were energetic, with the maximum velocity exceeding 1 m s−1 and relative vorticity magnitude as high as 0.6f. The mode regression method was proposed to extract NIWs from the shipboard ADCP velocities. The NIW amplitudes were 0.15 and 0.3 m s−1 in the CE and WE, respectively, and their constant phase lines were nearly slanted along the heaving isopycnals. In the WE, the NIWs were trapped in the negative vorticity core and amplified at the eddy base (at 350–650 m), which was consistent with the “inertial chimney” effect documented in existing literature. Outstanding NIWs in the background wavefield were also observed inside the positive vorticity core of the CE, despite their lower strength and shallower residence (above 350 m) compared to the counterparts in the WE. Particularly, the near-inertial kinetic energy efficiently propagated downward and amplified below the surface layer in both eddies, leading to an elevated turbulent dissipation rate of up to 10−7 W kg−1. In addition, bidirectional energy exchanges between the NIWs and mesoscale balanced flow occurred during NIWs’ downward propagation. The present study provides observational evidence for the enhanced downward NIW propagation by mesoscale eddies, which has significant implications for parameterizing the wind-driven diapycnal mixing in the eddying ocean. Significance Statement We provide observational evidence for the downward propagation of near-inertial waves enhanced by mesoscale eddies. This is significant because the down-taking of wind energy by the near-inertial waves is an important energy source for turbulent mixing in the interior ocean, which is essential to the shaping of ocean circulation and climate. The anticyclonic eddies are widely regarded as a conduit for the downward near-inertial energy propagation, while the cyclonic eddies activity influencing the near-inertial waves propagation lacks clear cognition. In this study, enhanced near-inertial waves and turbulent dissipation were observed inside both cyclonic and anticyclonic eddies in the Kuroshio Extension region, which has significant implications for improving the parameterization of turbulent mixing in ocean circulation and climate models.

A New Parameterization of Turbulent Mixing Enhanced Over Rough Seafloor Topography

AbstractExisting parameterizations of turbulent mixing enhanced over high‐wavenumber seafloor topography miss the fact that internal tidal waves emanating from the seafloor transform to internal lee waves as the tide‐topography interaction strengthens. This motivates us to replace the vertical decay scale of bottom‐enhanced turbulent mixing with the “vertical mean free path” of internal lee waves, namely, the average vertical distance over which internal lee waves propagate until they discharge their energy through interactions with the background internal waves. The resulting formula shows that the vertical extent of turbulent mixing becomes proportional to the abyssal barotropic tidal or steady flow amplitude squared and the inverse abyssal buoyancy frequency squared, but independent of the wavenumber of the seafloor, consistent with recent eikonal calculations and field observations. We propose a new parameterization of turbulent mixing enhanced over high‐wavenumber seafloor topography through incorporating the formulated vertical decay scale.

Sensitivity of large eddy simulations of tropical cyclone to sub-grid scale mixing parameterization

The surface wind structure and vertical turbulent transport processes in the eyewall of hurricane Isabel (2003) are investigated using six large-eddy simulations (LESs) with different horizontal grid spacing and three-dimensional (3D) sub-grid scale (SGS) turbulent mixing models and a convection permitting simulation that uses a coarser grid spacing and one-dimensional vertical turbulent mixing scheme. The mean radius-height distribution of storm tangential wind and radial flow, vertical velocity structure, and turbulent kinetic energy and momentum fluxes in the boundary layer generated by LESs are consistent with those derived from historical dropsonde composites, Doppler radar, and aircraft measurements. Unlike the convection permitting simulation that produces storm wind fields lacking small-scale disturbances, all LESs are able to produce sub-kilometer and kilometer scale eddy circulations in the eyewall. The inter-LES differences generally reduce with the decrease of model grid spacing. At 100-m horizontal grid spacing, the vertical momentum fluxes induced by the model-resolved eddies and the associated eddy exchange coefficients in the eyewall simulated by the LESs with different 3D SGS mixing schemes are fairly consistent. Although with uncertainties, the decomposition in terms of eddy scales suggests that sub-kilometer eddies are mainly responsible for the vertical turbulent transport within the boundary layer (~1 km depth following the conventional definition) whereas eddies greater than 1 km become the dominant contributors to the vertical momentum transport above the boundary layer in the eyewall. The strong dependence of vertical turbulent transport on eddy scales suggests that the vertical turbulent mixing parameterization in mesoscale simulations of tropical cyclones is ultimately a scale-sensitive problem.

Estimation of Vertical Heat Diffusivity at the Base of the Mixed Layer in the Bay of Bengal

AbstractOne approach to estimating vertical heat diffusivity (KT) is to compute it from the residual of the mixed layer (ML) heat budget. Based on this approach, we use moored buoy data at 15°N, 12°N, and 8°N along 90°E over the period of 2007–2018 to estimate the seasonal average of KT at the base of the mixed layer in the Bay of Bengal (BoB). We find that KT is lower during spring and higher during winter compared to summer and fall at the mooring locations. Moreover, KT is generally higher in the southern BoB compared to the northern BoB. The present study also shows that the seasonal and spatial variability of KT is modulated both by stratification at the base of ML and by seasonal and spatial heterogeneity in atmospheric forcing, most notably wind stress and buoyancy flux. The availability of information on the spatial and seasonal variability of KT in the BoB will facilitate evaluation and validation of turbulent mixing parameterization schemes incorporated into ocean models.

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

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.

Toward Understanding the Dynamics of Spinup in Emanuel’s Tropical Cyclone Model

AbstractWe seek to understand the mechanism of vortex spinup in Emanuel’s 2012 axisymmetric theory for tropical cyclone intensification in physical coordinates, starting from first principles. It is noted that, while spinup of the maximum tangential wind must occur at low levels, within or at the top of the friction layer, this spinup is unconstrained by a radial momentum equation in this layer. Instead, the spinup is controlled by a parameterization of turbulent mixing in the upper-tropospheric outflow layer, which, as is shown, determines indirectly the rate of inward movement of the absolute angular momentum surfaces. Nevertheless, the physics of how upper-tropospheric mixing leads to spinup in or at the top of the friction layer are unclear and, as discussed, may be irrelevant to spinup in the model.

Improving Hurricane Analyses and Predictions with TCI, IFEX Field Campaign Observations, and CIMSS AMVs Using the Advanced Hybrid Data Assimilation System for HWRF. Part I: What is Missing to Capture the Rapid Intensification of Hurricane Patricia (2015) when HWRF is already Initialized with a More Realistic Analysis?

AbstractAssimilating inner-core observations collected from recent field campaign programs such as Tropical Cyclone Intensity (TCI) and Intensity Forecasting Experiment (IFEX) together with the enhanced atmospheric motion vectors (AMVs) produce realistic three-dimensional (3D) analyses using the newly developed GSI-based, continuously cycled, dual-resolution hybrid ensemble–variational data assimilation (DA) system for the Hurricane Weather Research and Forecasting (HWRF) Model for Hurricane Patricia (2015). However, more persistent surface wind maximum spindown is found in the intensity forecast initialized from the realistic analyses produced by the DA system but not from the unrealistic initial conditions produced through vortex modification. Diagnostics in this study reveal that the spindown issue is likely attributed to the deficient HWRF Model physics that are unable to maintain the realistic 3D structures from the DA analysis. The horizontal diffusion is too strong to maintain the realistically observed vertical oscillation of radial wind near the eyewall region. The vertical diffusion profile cannot produce a sufficiently strong secondary circulation connecting the realistically elevated upper-level outflow produced in the DA analysis. Further investigations with different model physics parameterizations demonstrate that spindown can be alleviated by modifying model physics parameterizations. In particular, a modified turbulent mixing parameterization scheme together with a reduced horizontal diffusion is found to significantly alleviate the spindown issue and to improve the intensity forecast. Additional experiments show that the peak-simulated intensity and rapid intensification rate can be further improved by increasing the model resolution. But the model resolution is not as important as model physics in the spindown alleviation.

A Physically Based Horizontal Subgrid-Scale Turbulent Mixing Parameterization for the Convective Boundary Layer

Abstract Compared to the representation of vertical turbulent mixing through various planetary boundary layer (PBL) schemes, the treatment of horizontal turbulent mixing in the boundary layer has received much less attention. In mesoscale and convective-scale models, subgrid-scale horizontal turbulent mixing has traditionally been associated with mesoscale circulations or eddies. Its parameterization most often adopts the gradient-diffusion model, where the horizontal mixing coefficients are usually set constant, or through the 2D Smagorinsky formulation, or in some cases based on the 1.5-order turbulence kinetic energy (TKE) closure. For horizontal turbulent mixing associated with boundary layer eddies, the traditional schemes are shown to perform poorly. This work investigates the characteristic turbulence velocity and length scales based on analysis of a well-resolved, wide-domain large-eddy simulation of a convective boundary layer (CBL). To improve the representation of horizontal turbulent mixing by CBL eddies, a class of schemes is proposed with different levels of sophistication. The first two schemes can be used together with first-order PBL schemes, while the third uses TKE to define its characteristic velocity scale and can be used together with TKE-based higher-order PBL schemes. The proposed parameterizations are tested a posteriori in idealized simulations of turbulent dispersion of a passive scalar. Comparisons show improved horizontal dispersion by the proposed schemes and further demonstrate the weakness of the existing schemes.

Sensitivity of 24-h Forecast Dryline Position and Structure to Boundary Layer Parameterizations in Convection-Allowing WRF Model Simulations

Abstract Recent NOAA Hazardous Weather Testbed Spring Forecasting Experiments have emphasized the sensitivity of forecast sensible weather fields to how boundary layer processes are represented in the Weather Research and Forecasting (WRF) Model. Thus, since 2010, the Center for Analysis and Prediction of Storms has configured at least three members of their WRF-based Storm-Scale Ensemble Forecast (SSEF) system specifically for examination of sensitivities to parameterizations of turbulent mixing, including the Mellor–Yamada–Janjić (MYJ); quasi-normal scale elimination (QNSE); Asymmetrical Convective Model, version 2 (ACM2); Yonsei University (YSU); and Mellor–Yamada–Nakanishi–Niino (MYNN) schemes (hereafter PBL members). In postexperiment analyses, significant differences in forecast boundary layer structure and evolution have been observed, and for preconvective environments MYNN was found to have a superior depiction of temperature and moisture profiles. This study evaluates the 24-h forecast dryline positions in the SSEF system PBL members during the period April–June 2010–12 and documents sensitivities of the vertical distribution of thermodynamic and kinematic variables in near-dryline environments. Main results include the following. Despite having superior temperature and moisture profiles, as indicated by a previous study, MYNN was one of the worst-performing PBL members, exhibiting large eastward errors in forecast dryline position. During April–June 2010–11, a dry bias in the North American Mesoscale Forecast System (NAM) initial conditions largely contributed to eastward dryline errors in all PBL members. An upgrade to the NAM and assimilation system in October 2011 apparently fixed the dry bias, reducing eastward errors. Large sensitivities of CAPE and low-level shear to the PBL schemes were found, which were largest between 1.0° and 3.0° to the east of drylines. Finally, modifications to YSU to decrease vertical mixing and mitigate its warm and dry bias greatly reduced eastward dryline errors.

A Shear-Based Parameterization of Turbulent Mixing in the Stable Atmospheric Boundary Layer

AbstractIn this study, shear-based parameterizations of turbulent mixing in the stable atmospheric boundary layer (SABL) are proposed. A relevant length-scale estimate for the mixing length of the turbulent momentum field is constructed from the turbulent kinetic energy and the mean shear rate S as . Using observational data from two field campaigns—the Surface Heat Budget of the Arctic Ocean (SHEBA) experiment and the 1999 Cooperative Atmosphere–Surface Exchange Study (CASES-99)— is shown to have a strong correlation with . The relationship between and corresponds to the ratio of the magnitude of the tangential components of the turbulent momentum flux tensor to , known as stress intensity ratio, . The field data clearly show that is linked to stability. The stress intensity ratio also depends on the flow energetics that can be assessed using a shear-production Reynolds number, , where P is shear production of turbulent kinetic energy and is the kinematic viscosity. This analysis shows that high mixing rates can indeed persist at strong stability. On this basis, shear-based parameterizations are proposed for the eddy diffusivity for momentum, , and eddy diffusivity for heat, , showing remarkable agreement with the exact quantities. Furthermore, a broader assessment of the proposed parameterizations is given through an a priori evaluation of large-eddy simulation (LES) data from the first GEWEX Atmospheric Boundary Layer Study (GABLS). The shear-based parameterizations outperform many existing models in predicting turbulent mixing in the SABL. The results of this study provide a framework for improved representation of the SABL in operational models.

Sensitivities of eyewall replacement cycle to model physics, vortex structure, and background winds in numerical simulations of tropical cyclones

AbstractA series of sensitivity experiments by the Weather Research and Forecasting (WRF) model is used to investigate the impact of model physics, vortex axisymmetric radial structure, and background wind on secondary eyewall formation (SEF) and eyewall replacement cycle (ERC) in three‐dimensional full physics numerical simulations. It is found that the vertical turbulent mixing parameterization can substantially affect the concentric ring structure of tangential wind associated with SEF through a complicated interaction among eyewall and outer rainband heating, radial inflow in the boundary layer, surface layer processes, and shallow convection in the moat. Large snow terminal velocity can substantially change the vertical distribution of eyewall diabatic heating to result in a strong radial inflow in the boundary layer, and thus, favors the development of shallow convection in the moat allowing the outer rainband convection to move closer to the inner eyewall, which may leave little room both temporally and spatially for a full development of a secondary maximum of tangential wind. Small radius of maximum wind (RMW) of a vortex and small potential vorticity (PV) skirt outside the RMW tend to generate double‐eyewall replacement and may lead to an ERC without a clean secondary concentric maximum of tangential wind. A sufficiently large background wind can smooth out an ERC that would otherwise occur without background wind for a vortex with a small or moderate PV skirt. However, background wind does not appear to have an impact on an ERC if the vortex has a sufficiently large PV skirt.

Overturning circulation driven by breaking internal waves in the deep ocean

AbstractA global estimate of the water‐mass transformation by internal wave‐driven mixing in the deep ocean is presented. The estimate is based on the energy conversion from tidal and geostrophic motions into internal waves combined with a turbulent mixing parameterization. We show that internal wave‐driven mixing in the deep ocean can sustain 20–30 Sv of water‐mass transformation. One third or more of this transformation is attributed to lee waves generated by geostrophic motions flowing over rough topography, primarily in the Southern Ocean. While these results are uncertain due to many assumptions, poorly constrained parameters and data noise that enter in the calculation, the result that lee wave‐driven mixing plays an important role in the abyssal ocean circulation is likely robust. The implication is that lee wave‐driven mixing should be represented in ocean and climate models, but currently it is not.

Identifying and quantifying nonconservative energy production/destruction terms in hydrostatic Boussinesq primitive equation models

This paper seeks to illustrate the point that physical inconsistencies between thermodynamics and dynamics usually introduce nonconservative production/destruction terms in the local total energy balance equation in numerical ocean general circulation models (OGCMs). Such terms potentially give rise to undesirable forces and/or diabatic terms in the momentum and thermodynamic equations, respectively, which could explain some of the observed errors in simulated ocean currents and water masses. In this paper, a theoretical framework is developed to provide a practical method to determine such nonconservative terms, which is illustrated in the context of a relatively simple form of the hydrostatic Boussinesq primitive equation used in early versions of OGCMs, for which at least four main potential sources of energy nonconservation are identified; they arise from: (1) the “hanging” kinetic energy dissipation term; (2) assuming potential or conservative temperature to be a conservative quantity; (3) the interaction of the Boussinesq approximation with the parameterizations of turbulent mixing of temperature and salinity; (4) some adiabatic compressibility effects due to the Boussinesq approximation. In practice, OGCMs also possess spurious numerical energy sources and sinks, but they are not explicitly addressed here. Apart from (1), the identified nonconservative energy sources/sinks are not sign definite, allowing for possible widespread cancellation when integrated globally. Locally, however, these terms may be of the same order of magnitude as actual energy conversion terms thought to occur in the oceans. Although the actual impact of these nonconservative energy terms on the overall accuracy and physical realism of the oceans is difficult to ascertain, an important issue is whether they could impact on transient simulations, and on the transition toward different circulation regimes associated with a significant reorganization of the different energy reservoirs. Some possible solutions for improvement are examined. It is thus found that the term (2) can be substantially reduced by at least one order of magnitude by using conservative temperature instead of potential temperature. Using the anelastic approximation, however, which was initially thought as a possible way to greatly improve the accuracy of the energy budget, would only marginally reduce the term (4) with no impact on the terms (1), (2) and (3).

Regional modelling of tracer transport by tropical convection – Part 1: Sensitivity to convection parameterization

Abstract. The general objective of this series of papers is to evaluate long duration limited area simulations with idealised tracers as a tool to assess tracer transport in chemistry-transport models (CTMs). In this first paper, we analyse the results of six simulations using different convection closures and parameterizations. The simulations are using the Grell and Dévényi (2002) mass-flux framework for the convection parameterization with different closures (Grell = GR, Arakawa-Shubert = AS, Kain-Fritch = KF, Low omega = LO, Moisture convergence = MC) and an ensemble parameterization (EN) based on the other five closures. The simulations are run for one month during the SCOUT-O3 field campaign lead from Darwin (Australia). They have a 60 km horizontal resolution and a fine vertical resolution in the upper troposphere/lower stratosphere. Meteorological results are compared with satellite products, radiosoundings and SCOUT-O3 aircraft campaign data. They show that the model is generally in good agreement with the measurements with less variability in the model. Except for the precipitation field, the differences between the six simulations are small on average with respect to the differences with the meteorological observations. The comparison with TRMM rainrates shows that the six parameterizations or closures have similar behaviour concerning convection triggering times and locations. However, the 6 simulations provide two different behaviours for rainfall values, with the EN, AS and KF parameterizations (Group 1) modelling better rain fields than LO, MC and GR (Group 2). The vertical distribution of tropospheric tracers is very different for the two groups showing significantly more transport into the TTL for Group 1 related to the larger average values of the upward velocities. Nevertheless the low values for the Group 1 fluxes at and above the cold point level indicate that the model does not simulate significant overshooting. For stratospheric tracers, the differences between the two groups are small indicating that the downward transport from the stratosphere is more related to the turbulent mixing parameterization than to the convection parameterization.

Impact of consistent boundary layer mixing approaches between NAM and CMAQ

Discrepancies in grid structure, dynamics and physics packages in the offline coupled NWS/NCEP NAM meteorological model with the U.S. Environmental Protection Agency Community Multiscale Air Quality (CMAQ) model can give rise to inconsistencies. This study investigates the use of three vertical mixing schemes to drive chemistry tracers in the National Air Quality Forecast Capability (NAQFC). The three schemes evaluated in this study represent various degrees of coupling to improve the commonality in turbulence parameterization between the meteorological and chemistry models. The methods tested include: (1) using NAM predicted TKE-based planetary boundary height, h, as the prime parameter to derive CMAQ vertical diffusivity; (2) using the NAM mixed layer depth to determine h and then proceeding as in (1); and (3) using NAM predicted vertical diffusivity directly to parameterize turbulence mixing within CMAQ. A two week period with elevated surface O3 concentrations during the summer 2006 has been selected to test these schemes in a sensitivity study. The study results are verified and evaluated using the EPA AIRNow monitoring network and other ozonesonde data. The third method is preferred a priori as it represents the tightest coupling option studied in this work for turbulent mixing processes between the meteorological and air quality models. It was found to accurately reproduce the upper bounds of turbulent mixing and provide the best agreement between predicted h and ozonesonde observed relative humidity profile inferred h for sites investigated in this study. However, this did not translate into the best agreement in surface O3 concentrations. Overall verification results during the test period of two weeks in August 2006, did not show superiority of this method over the other 2 methods in all regions of the continental U.S. Further efforts in model improvement for the parameterizations of turbulent mixing and other surface O3 forecast related processes are warranted.

Two-dimensional cascades and mixing: a physical space approach

We develop an analysis of the two-dimensional cascade of a tracer (passive or active Lagrangian-conserved scalar), locally in space and time, and establish connections with the modelling of turbulent mixing. We define a local scale-to-scale flux of tracer variance based on the dynamics of tracer increments. This flux reduces at small scales to the production or destruction rate of tracer gradients by stirring as a function of their local orientation with respect to the compressional axis of the strain-rate tensor. The local detailed budget of tracer variance on which this approach is based is compared to the global statistical budget expressed by Yaglom's equation. The spatial pattern of the local transfers produced by a numerical simulation as well as their statistical distribution are discussed.We then address the problem of the parameterization of turbulent mixing. We consider an anisotropic tensor diffusivity proportional to the velocity gradients. In this model the tracer dissipation involves the axes of the strain-rate tensor and we shall refer to it as strain diffusivity. We show analytically that it locally matches the scale-to-scale flux through the cutoff scale. This matching is studied numerically in decaying two-dimensional turbulence. A comparison is made with eddy diffusivity and hyperdiffusivity. The presence of a numerical instability and ways to suppress it are discussed from numerical and fundamental points of view.We consider the special case of vorticity, an active scalar in two dimensions. When applied to vorticity, models affect the energy budget. The two-dimensional inverse energy cascade requires that parameterizations conserve energy and we show that strain diffusivity conserves energy. We finally study the sensitivity of the large scales of the flow to the operator used on vorticity in forced stationary simulations. Strain diffusivity is found to produce more realistic spectral features than hyperviscosity.

Observations And Modelling Of The On-Ice And Off-Ice Air Flow Over The Northern Baltic Sea

Two cases of on-ice and off-ice air flow characterizing the opposite weather situations over the ice-edge zone in the northern Baltic Sea are analysed on the basis of aircraft observations, and modelled using atwo-dimensional mesoscale model. The stable boundary layer (SBL) during theon-ice flow exhibited little thermal modification, but a low-level jet (LLJ) was generated at the 250-m high top of the SBL. In the model, the LLJ was associated with inertial oscillations in space, while the baroclinicity explained the shape of the wind profile well above the SBL. Although the observed LLJ was most pronounced over the ice, the modelling suggests that it was not generated by the ice edge but by the coastline some 400 km upwind of the ice edge, where a much more drastic change in the thermal stratification and surface roughness took place. The generation, maintenance, and strength of the LLJ were very sensitive to the parameterization of turbulent mixing in the SBL. In the case of the off-ice flow, the modification of the air mass and the development of a convective boundary layer (CBL) both over the ice and open sea were reasonably well modelled. Sensitivity runs suggested that it was essential to take into account the effects of subgrid-scale leads, a forest in the archipelago (which was crossed by the air flow), and water vapour condensationinto ice crystals. The heat flux from leads was particularly important for the heatbudget of the CBL, and the observed growth of the CBL was partly due to theeffective mixing over the rough and relatively warm forest.