Why Does Fog Deepen? An Analytical Perspective

The overall depth of a fog layer is one of the important factors in determining the hazard that a fog event presents. With discrete observations and often coarse numerical grids, however, fog depth cannot always be accurately determined. To address this, we derive a simple analytical relation that describes the change in depth of a fog interface with time, which depends on the tendencies and vertical gradients of moisture. We also present a lengthscale estimate for the maximum depth over which mixing can occur in order for the fog layer to be sustained, assuming a uniform mixing of the vertical profiles of temperature and moisture. Even over several hours, and when coarse observational resolution is used, the analytical description is shown to accurately diagnose the depth of a fog layer when compared against observational data and the results of large-eddy simulations. Such an analytical description not only enables the estimation of sub-grid or inter-observation fog depth, but also provides a simple framework for interpreting the evolution of a fog layer in time.

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The Role of Wave-Induced Coriolis–Stokes Forcing on the Wind-Driven Mixed Layer

Journal of Physical Oceanography ◽

10.1175/jpo2701.1 ◽

2005 ◽

Vol 35 (4) ◽

pp. 444-457 ◽

Cited By ~ 126

Author(s):

Jeff A. Polton ◽

David M. Lewis ◽

Stephen E. Belcher

Keyword(s):

Analytical Solution ◽

Observational Data ◽

Mixed Layer ◽

Analytical Solutions ◽

Eddy Viscosity ◽

Large Eddy Simulations ◽

Current Profile ◽

Large Eddy ◽

The Mean ◽

Mean Current

Abstract The interaction between the Coriolis force and the Stokes drift associated with ocean surface waves leads to a vertical transport of momentum, which can be expressed as a force on the mean momentum equation in the direction along wave crests. How this Coriolis–Stokes forcing affects the mean current profile in a wind-driven mixed layer is investigated using simple models, results from large-eddy simulations, and observational data. The effects of the Coriolis–Stokes forcing on the mean current profile are examined by reappraising analytical solutions to the Ekman model that include the Coriolis–Stokes forcing. Turbulent momentum transfer is modeled using an eddy-viscosity model, first with a constant viscosity and second with a linearly varying eddy viscosity. Although the Coriolis–Stokes forcing penetrates only a small fraction of the depth of the wind-driven layer for parameter values typical of the ocean, the analytical solutions show how the current profile is substantially changed through the whole depth of the wind-driven layer. It is shown how, for this oceanic regime, the Coriolis–Stokes forcing supports a fraction of the applied wind stress, changing the boundary condition on the wind-driven component of the flow and hence changing the current profile through all depths. The analytical solution with the linearly varying eddy viscosity is shown to reproduce reasonably well the effects of the Coriolis–Stokes forcing on the current profile computed from large-eddy simulations, which resolve the three-dimensional overturning motions associated with the turbulent Langmuir circulations in the wind-driven layer. Last, the analytical solution with the Coriolis–Stokes forcing is shown to agree reasonably well with current profiles from previously published observational data and certainly agrees better than the standard Ekman model. This finding provides evidence that the Coriolis–Stokes forcing is an important mechanism in controlling the dynamics of the upper ocean.

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Departure from Flux-Gradient Relation in the Planetary Boundary Layer

Atmosphere ◽

10.3390/atmos12060672 ◽

2021 ◽

Vol 12 (6) ◽

pp. 672

Author(s):

Pedro Santos ◽

Alfredo Peña ◽

Jakob Mann

Keyword(s):

Wind Speed ◽

Mesoscale Model ◽

Large Eddy Simulations ◽

Horizontal Velocity ◽

Vertical Profiles ◽

Height Range ◽

Flux Gradient ◽

Large Eddy ◽

Momentum Fluxes ◽

The Mean

It is well known that when eddies are small, the eddy fluxes can be directly related to the mean vertical gradients, the so-called flux-gradient relation, but such a relation becomes weaker the larger the coherent structures. Here, we show that this relation does not hold at heights relevant for wind energy applications. The flux–gradient relation assumes that the angle (β) between the vector of vertical flux of horizontal momentum and the vector of the mean vertical gradient of horizontal velocity is zero, i.e., these vectors are aligned. Our observations do not support this assumption, either onshore or offshore. Here, we present analyses of a misalignment between these vectors from a Doppler wind lidar observations and large-eddy simulations. We also use a real-time mesoscale model output for inter-comparison with the lidar-observed vertical profiles of wind speed, wind direction, momentum fluxes, and the angle between the horizontal velocity vector and the momentum flux vector up to 500 m, both offshore and onshore. The observations show this within the height range 100–500 m, β=−18∘ offshore and β=−12∘ onshore, on average. However, the large-eddy simulations show β≈0∘ both offshore and onshore. We show that observed and mesoscale-simulated vertical profiles of mean wind speed and momentum fluxes agree well; however, the mesoscale results significantly deviate from the wind-turning observations.

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A Direct Measure of Entrainment

Journal of the Atmospheric Sciences ◽

10.1175/2010jas3371.1 ◽

2010 ◽

Vol 67 (6) ◽

pp. 1908-1927 ◽

Cited By ~ 98

Author(s):

David M. Romps

Keyword(s):

Spatial Distribution ◽

Direct Measurement ◽

Deep Convection ◽

Large Eddy Simulations ◽

The Other ◽

Vertical Profiles ◽

Direct Measure ◽

Total Water ◽

Convective Flux ◽

Large Eddy

Abstract A method is introduced for directly measuring convective entrainment and detrainment in a cloud-resolving simulation. This technique is used to quantify the errors in the entrainment and detrainment estimates obtained using the standard bulk-plume method. The bulk-plume method diagnoses these rates from the convective flux of some conserved tracer, such as total water in nonprecipitating convection. By not accounting for the variability of this tracer in clouds and in the environment, it is argued that the bulk-plume equations systematically underestimate entrainment. Using tracers with different vertical profiles, it is also shown that the bulk-plume estimates are tracer dependent and, in some cases, unphysical. The new direct-measurement technique diagnoses entrainment and detrainment at the gridcell level without any recourse to conserved tracers. Using this method in large-eddy simulations of shallow and deep convection, it is found that the bulk-plume method underestimates entrainment by roughly a factor of 2. The directly measured entrainment rates are then compared to cloud height and cloud buoyancy. Contrary to existing theories, fractional entrainment is not found to scale like the inverse of height, the cloud buoyancy, or the gradient of cloud buoyancy. On the other hand, fractional detrainment is found to scale linearly with cloud buoyancy. Finally, direct measurement is used to diagnose the spatial distribution of entrainment and detrainment during the evolution of an individual deep cumulonimbus.

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