Experiments on Ekman layer instability
Ekman layer velocity instabilities measured by hot wire anemometers
HOT-WIRE ANEMOMETER↗
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Experiments on Ekman layer instability.
Instabilities of Ekman layer measured using hot- wire anemometers
EKMAN LAYER↗
A numerical study of the turbulent Ekman layer
The three-dimensional time-dependent turbulent flow in a neutrally stratified Ekman layer over a smooth flat surface was numerically simulated by directly solving the Navier-Stokes equations. Issues addressed using the direct numerical simulation (DNS) fields include the presence or absence of large-scale coherent structures ('longitudinal' or 'roll' vortices) in neutrally stratified Ekman-layer turbulence, the effects of the horizontal component of the angular velocity vector (i.e., latitude), and implications for models of the PBL. Experimental and DNS profiles are compared.
Coleman, G. N.↗
Direct simulation of the stably stratified turbulent Ekman layer
The Navier-Stokes equations and the Boussinesq approximation were used to compute a 3D time-dependent turbulent flow in the stably stratified Ekman layer over a smooth surface. The simulation data are found to be in very good agreement with atmospheric measurements when nondimensionalized according to Nieuwstadt's local scaling scheme. Results suggest that, when Reynolds number effects are taken into account, the 'constant Froud number' stable layer model (Brost and Wyngaard, 1978) and the 'shearing length' stable layer model (Hunt, 1985) for the dissipitation rate of turbulent kinetic energy are both valid. It is concluded that there is good agreement between the direct numerical simulation results and large-eddy simulation results obtained by Mason and Derbyshire (1990).
Coleman, G. N.↗
A numerical study of the instability of the laminar Ekman boundary layer.
Instability of laminar Ekman boundary layer, obtaining critical values of Reynolds numbers, perturbation growth rates and equilibrium finite amplitude solutions
PERTURBATION THEORY↗
Oscillatory and transitory Ekman boundary layers
Numerical solutions for differences in ocean planetary boundary layer flow from that of steady-state spiral resulting from temporal wind variations
NUMERICAL ANALYSIS↗
An analysis of the stability of the compressible Ekman boundary layer
The linear stability problem for the compressible Ekman boundary layer common to rotating fluids is formulated and the stability properties determined numerically. Three classes of unstable waves are identified (called class A, B, and C), their properties are described. The class C waves have only recently been reported in the literature and are present only in compressible Ekman boundary layers. Most of the calculations presented here are for uranium hexafluoride gas; however, critical Reynolds numbers are also computed for air and ammonia gas. Compressibility is generally found to decrease the critical Reynolds number for each class of wave. A comparison of results for the three different gases shows the stability to be largely unaffected by changes in the gas properties. Maximum growth rate calculations for each wave show the class A and B waves to be the dominant instabilities.
Spall, J. R.↗
The AGCE related studies of baroclinic flows in spherical geometry
Steady state, axisymmetric motions of a Boussineaq fluid continued in rotating spherical anmulus are considered. The motions are driven by latitudinally varying temperature gradient at the shells. Linearized formulations for a narrow gap are derived and the flow field is divided into the Ekman layers and the geostrophic interior. The Ekman layer flows are consistent with the known results for cylindrical geometries. Within the framework of rather restrictive assumptions, the interior flows are solved by a series of associated Legendre polynomials. The solutions show qualitative features valid at midlatitudes.
Hyun, J. M.↗
A PBL-radiation model for application to regional numerical weather prediction
Often in the short-range limited-area numerical weather prediction (NWP) of extratropical weather systems the effects of planetary boundary layer (PBL) processes are considered secondarily important. However, it may not be the case for the regional NWP of mesoscale convective systems over the arid and semi-arid highlands of the southwestern and south-central United States in late spring and summer. Over these dry regions, the PBL can grow quite high up into the lower middle troposphere (600 mb) due to very effective solar heating and hence a vigorous air-land thermal interaction can occur. The interaction representing a major heat source for regional dynamical systems can not be ignored. A one-dimensional PBL-radiation model was developed. The model PBL consists of a constant-flux surface layer superposed with a well-mixed (Ekman) layer. The vertical eddy mixing coefficients for heat and momentum in the surface layer are determined according to the surface similarity theory, while their vertical profiles in the Ekman layer are specified with a cubic polynomial. Prognostic equations are used for predicting the height of the nonneutral PBL. The atmospheric radiation is parameterized to define the surface heat source/sink for the growth and decay of the PBL. A series of real-data numerical experiments has been carried out to obtain a physical understanding how the model performs under various atmospheric and surface conditions. This one-dimensional model will eventually be incorporated into a mesoscale prediction system. The ultimate goal of this research is to improve the NWP of mesoscale convective storms over land.
Chang, Chia-Bo↗
Investigations of stability and transition in rotating boundary layers.
Rotating Ekman boundary layer stability and transition for two-dimensional roll vortices superimposed upon basic boundary layer flow
BOUNDARY LAYER TRANSITION↗
Ocean-Science Mission Needs: Real-Time AUV Data for Command, Control, and Model Inputs
Predictive models for tides, hydrodynamics, and bio-optical properties affecting the visibility and buoyancy of coastal waters are needed to evaluate the safety of personnel and equipment engaged in maritime operations under potentially hazardous conditions. Predicted currents can be markedly different for two-layer systems affected by terrestrial runoff than for well-mixed conditions because the layering decouples the surface and bottom Ekman layers and rectifies the current response to oscillatory upwelling-and downwelling-favorable winds. Standard ocean models (e.g. Princeton Ocean Model) require initial-and boundary data on the physical and optical properties of the multilayered water column to provide accurate simulations of heat budgets and circulation. Two observational systems are designed to measure vertically structured conditions on the West Florida Shelf (WFS): a tethered buoy network and an autonomous underwater vehicle (AUV) observational system. The AUV system is described with a focus on the observational systems that challenge or limit the communications command and control network for various types of measurement programs. These include vertical oscillatory missions on shelf transects to observe the optical and hydrographic properties of the water column, and bottom-following missions for measuring the bottom albedo. Models of light propagation, absorption, and conversion to heat as well as determination of the buoyancy terms for physical models require these measurements. High data rates associated with video bottom imagery are the most challenging for the real-time, command and control communications system, but they are met through a combination of loss-less and lossy data-compression methods, depending upon the data-rate of the radio links.
Carder, Kendall L.↗
The effects of curvature and viscosity on baroclinic instability: A two-layer model
A linear stability analysis of a baroclinic zonal current contained between two parallel rigid boundaries is presented. Curvature is included by performing the analysis on a beta b-plane and viscosity by allowing for the effects of Ekman layers on the rigid boundaries. A two-layer model is used. This calculation was carried out to assist in the design of a spherical model of the general circulation of the earth's atmosphere for Spacelab. In the low-gravity environment on an orbiting vehicle, a dominant radial dielectric body force, analogous to planetary gravity, can be achieved over a volume of liquid held between two concentric spheres. The results show the Eady short wavelength cutoff, and long wavelength cutoffs due to Ekman damping and curvature.
Fowlis, W. W.↗
Theoretical and numerical study of a three-dimensional turbulent boundary layer
A boundary layer created on an infinite flat plate by a time-dependent freestream velocity vector whose magnitude is independent of time but whose direction changes at a constant angular velocity is theoretically studied using Reynolds-number scaling laws and numerical simulations performed over a range of Reynolds numbers. Results obtained with a higher-order version of existing theories of the Ekman layer are shown to agree well with the numerical results at three Reynolds numbers. The present results can be extrapolated to the case of high Reynolds numbers. The Reynolds-averaged equations reduce to a one-dimensional steady problem, making possible the easy and accurate testing of turbulence models.
Spalart, Philippe R.↗
Sea Surface Temperature and Wind-Generated Current Variations in the Arabian Sea During 1992 and 1993
Monthly mean wind-generated Ekman and Sverdup transports and the vertical transport into and out of the Ekman layer were computed from satellite scatterometer estimates of 10-m height wind speed components recorded from April 1992 to December 1993...This brief report describes a search for correspondence between variations of monthly mean SST and wind-driven currents in the Arabian Sea during April 1992 and December 1993.
north indian ocean clouds wind mixing heat advecti↗
Numerical solutions and laser-Doppler measurements of spin-up
The spin-up flow in a cylinder of homogeneous fluid has been examined both experimentally and numerically. A series of laser-Doppler measurements was made of the zonal flow over a range of Ekman numbers and Rossby numbers at various locations in the interior of the flow. These measurements exceed previous ones in accuracy. The weak inertial modes excited by the impulsive start are detectable. The numerical simulations used the primitive equations in axisymmetric form and employed finite-difference techniques on both constant and variable grids. The number of grid points necessary to resolve the Ekman layers was determined. A thorough comparison of the simulations and the experimental measurements is made which includes the details of the amplitude and frequency of the inertial modes. Agreement to within the experimental tolerance is achieved. Analytical results for conditions identical to those in the experiments are not available but some similar linear and nonlinear theories are also compared with the experiments.
Warn-Varnas, A.↗
Numerical modeling of baroclinic instability
The Eady model of baroclinic instability applied to a rotating channel with Ekman layers at the top and bottom is extended to a beta-plane channel. Changes in the shape and position of the boundary separating the regions of axially symmetric and wavelike motion are predicted.
Geisler, J. F.↗
Numerical solutions for spin-up from rest in a cylinder
A set of three-dimensional flow-field data for the region around a cylinder impulsively spun-up from rest was derived with a numerical model based on the Navier-Stokes equations. Laser-Doppler anemometer data in the azimuthal direction was employed to test the model predictions, and data was developed for a flowfield with Ekman numbers from 9.18/1,000,000 to 9.18/10,000. The contributions of inviscid and viscous terms were determined as functions of radius and time. It was found that immediately after start-up viscous diffusion is the dominant factor, which is replaced by nonlinear radial advection. The Coriolis force dominates in the later stages of spin-up. The inward radial flow is a maximum near the front, where the vertical velocity is small, but features strong radial gradients, as it does at the edge of the Ekman layer.
Hyun, J. M.↗
Cumulus role in tropical circulations
The present investigation is concerned with the effects of cumulus clouds upon their surroundings, and the interaction of the cumulus scale of motion with the larger scales of motion in the tropics. Charney and Eliassen (1964) have conducted a study of the growth of the hurricane depression and proposed the CISK (Conditional Instability of the Second Kind) mechanism. The CISK concept was used in several of the pioneering models of hurricanes and tropical disturbances. Since the 1960's, the CISK concept has been generalized and extended. However, the feedback between convection and the large-scale flow is still positive. In the present investigation the philosophy is extended to a negative feedback which contributes to the stability (mainly in direction) of the trade winds. Attention is given to the classical Ekman layer and early CISK, cumulus momentum transports, the role of cumuli in the trade-wind moisture and heat budgets, the trade wind model, and the equatorial trough and hot tower hypothesis.
Simpson, J.↗