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Richardson Number (richardson + number)
Selected AbstractsRelationships among vertically structured in situ measures of turbulence, larval fish abundance and feeding success and copepods on Western Bank, Scotian ShelfFISHERIES OCEANOGRAPHY, Issue 3 2002ChristianS. Using vertically stratified data of the abundance of silver hake (Merluccius bilinearis) larvae and concentrations of copepods collected in the field, we examine relationships among the vertical distribution of larval fish, their potential prey, feeding success and water column turbulence. Water column turbulence and associated stratification parameters were estimated from: (i) in situ measures of turbulent kinetic energy dissipation (,) provided by an EPSONDE profiler; (ii) in situ wind speed; (iii) the Richardson number (Ri); and (iv) the buoyancy frequency (N2). Small (< 5 mm total length) silver hake were more abundant in the least turbulent waters (i.e. at a minimum in the rate of dissipation of turbulent kinetic energy, , < 10,7 W kg,1; Ri > 0.25; N2 > 0.001 (rad s,1)2). Partial correlations amongst ,, N2 and small hake larvae were significant only for N2. The abundance of larger (> 5 mm total length) hake larvae was positively correlated with depth and was not associated with either , or N2. Vertical distributions of three potential prey (classified by stage) were variable. Early stage copepodids were positively correlated with N2 and negatively correlated with ,. We found no evidence of diel distribution patterns for small (< 5 mm total length) hake larvae or for any of the developmental stages of the copepods examined. Neither estimate of water column turbulence inferred from wind speed nor from Ri was meaningfully related to in situ estimates of , or to larval fish abundance. Feeding success, measured either as prey items (gut),1, average prey length, or total prey volume (gut),1, was not related to predicted encounter rates between days. However, the average prey length (gut),1 was significantly (P < 0.01) related to water column turbulence. These conflicting results suggest that the relationship between larval feeding and the environment is more complicated than assumed. We conclude that without substantial high resolution in situ examination of the relationship between the vertical distributions of turbulence, larvae and their prey, the growing acceptance in the secondary literature that turbulence has a positive and biologically meaningful effect on trophic interactions between fish and their zooplankton prey (a generalization based largely on modelling and laboratory experiments) is premature. [source] Heat and fluid flow characteristics inside differentially heated square enclosures with single and multiple sliding wallsHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 7 2009E.M. Wahba Abstract Fluid flow and heat transfer characteristics of differentially heated lid driven cavities are numerically modeled and analyzed in the present study. One-, two-, and four-sided lid driven cavity configurations are considered with the vertical walls being maintained at different temperatures and the horizontal walls being thermally insulated. Eight different cavity configurations are considered depending on the direction of wall motion. The Prandtl number Pr is taken to be 0.7, the Grashof number is taken to be 104, while two values for the Richardson number Ri are considered, 0.1 and 10. It is found that both the Richardson number and the cavity configuration affect the heat and fluid flow characteristics in the cavity. It is concluded that for Ri=0.1, a four-sided driven cavity configuration with all walls rotating in the same direction would triple the value of the average Nusselt number at the cold wall when compared to a one-sided driven cavity configuration. However, for Ri=10, the cavity configuration has minimal effect and all eight cases result in an average Nusselt number value at the cold wall ranging between 1.3 and 1.9. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience (www.interscience. wiley.com). DOI 10.1002/htj.20264 [source] Modelling hydrodynamics in Yachiyo Lake using a non-hydrostatic general circulation model with spatially and temporally varying meteorological conditionsHYDROLOGICAL PROCESSES, Issue 14 2009Han Soo Lee Abstract In this study, a three-dimensional (3D) non-hydrostatic circulation model was applied to study the thermal structure, its evolution and water circulation of Yachiyo Lake in Hiroshima, Japan. The simulations were conducted for 1 month during July 2006. The meteorological forcing variables such as wind stress, surface atmospheric pressure and heat flux transfer through the lake surface were provided by an atmospheric mesoscale model run. The vertical mixing process of the lake was calculated using the Mellor-Yamada turbulence model. The 1-month numerical simulation revealed the wind-induced currents of the lake, two gyres in the mid-layer, and depth-averaged monthly mean currents. Further numerical experiments studying the mechanism of the two gyres in the lake showed the important role of topography in gyre formation. The thermal structure of the lake and its evolution both in space and in time as predicted by the model showed very good agreement with the observed values and characteristics of Yachiyo Lake. The internal gravity waves, which are crucial for mixing in the stratified lake, are depicted by the vertical fluctuation of isotherms. Using the non-dimensional gradient Richardson number, Yachiyo Lake was determined to be stable under strong stratification during the study period, and therefore very sensitive to wind stress. Copyright © 2009 John Wiley & Sons, Ltd. [source] Comparison of the atmosphere above the South Pole, Dome C and Dome A: first attemptMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2008S. Hagelin ABSTRACT The atmospheric properties above three sites (Dome C, Dome A and the South Pole) on the Internal Antarctic Plateau are investigated for astronomical applications using the monthly median of the analyses from ECMWF (the European Centre for Medium-Range Weather Forecasts). Radiosoundings extended on a yearly time-scale at the South Pole and Dome C are used to quantify the reliability of the ECMWF analyses in the free atmosphere as well as in the boundary and surface layers, and to characterize the median wind speed in the first 100 m above the two sites. Thermodynamic instability properties in the free atmosphere above the three sites are quantified with monthly median values of the Richardson number. We find that the probability to trigger thermodynamic instabilities above 100 m is smaller on the Internal Antarctic Plateau than on mid-latitude sites. In spite of the generally more stable atmospheric conditions of the Antarctic sites compared to mid-latitude sites, Dome C shows worse thermodynamic instability conditions than those predicted above the South Pole and Dome A above 100 m. A rank of the Antarctic sites done with respect to the strength of the wind speed in the free atmosphere (ECMWF analyses) as well as the wind shear in the surface layer (radiosoundings) is presented. [source] Do transient gravity waves in a shear flow break?THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 634 2008M. Pulido Abstract The propagation of transient gravity waves in a shear flow towards their critical levels is examined using a ray tracing approximation and a higher-degree (quasi-optic) approximation. Because of its transient forcing, the amplitude of transient waves decays to zero in the neighbourhood of the critical region so that it is not clear whether transient gravity waves will reach the convective instability threshold or not. The analysis shows that the horizontal perturbation decays asymptotically as the inverse of the square root of time, while the vertical wavenumber depends linearly on time, thus transient gravity waves attain convective instability for long times. The theoretical results are compared with numerical simulations. The ray path approximation is not able to reproduce the maximum amplitude, but the quasi-optic approximation gives a reasonable agreement at short and long times. There are three breaking regimes for transient gravity waves. For wave packets with a narrow frequency spectrum (quasi-steady waves) and large enough initial wave amplitude, the wave breaking is similar to the abrupt monochromatic wave overturning. On the other hand, highly transient wave packets will dissipate near the critical region for very long times with small wave amplitudes and high vertical wavenumber. The third regime is a transition between the two extremes; in this case both wave amplitude and vertical wavenumber are important to produce the convective threshold. The dependencies of the convective instability height (a quantity that may be useful for gravity wave parametrizations) on the Richardson number and the frequency spectral width are obtained. Copyright © 2008 Royal Meteorological Society [source] Turbulence energetics in stably stratified geophysical flows: Strong and weak mixing regimesTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 633 2008S. S. Zilitinkevich Abstract Traditionally, turbulence energetics is characterised by turbulent kinetic energy (TKE) and modelled using solely the TKE budget equation. In stable stratification, TKE is generated by the velocity shear and expended through viscous dissipation and work against buoyancy forces. The effect of stratification is characterised by the ratio of the buoyancy gradient to squared shear, called the Richardson number, Ri. It is widely believed that at Ri exceeding a critical value, Ric, local shear cannot maintain turbulence, and the flow becomes laminar. We revise this concept by extending the energy analysis to turbulent potential and total energies (TPE, and TTE = TKE + TPE), consider their budget equations, and conclude that TTE is a conservative parameter maintained by shear in any stratification. Hence there is no ,energetics Ric', in contrast to the hydrodynamic-instability threshold, Ric,instability, whose typical values vary from 0.25 to 1. We demonstrate that this interval, 0.25 < Ri < 1, separates two different turbulent regimes: strong mixing and weak mixing rather than the turbulent and the laminar regimes, as the classical concept states. This explains persistent occurrence of turbulence in the free atmosphere and deep ocean at Ri , 1, clarifies the principal difference between turbulent boundary layers and free flows, and provides the basis for improving operational turbulence closure models. Copyright © 2008 Royal Meteorological Society [source] Variance scaling in shallow-cumulus-topped mixed layersTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 628 2007R. A. J. Neggers Abstract Scaling of thermodynamic variance in shallow-cumulus-topped mixed layers is studied using large-eddy simulation (LES). First, the performance of the top-down scaling (the turbulent flux at mixed-layer top divided by w*) is evaluated for transient shallow-cumulus convection over land. The results indicate that this scaling fails to capture all the variance in the top half of the mixed layer when shallow cumulus clouds are present. A variance-budget analysis is then performed, to derive a new scaling for the variance at mixed-layer top, which differs from the standard top-down scaling by a factor of one Richardson number. The essential new features of the proposed scaling are that the local vertical gradient is retained and that a balance is assumed between gradient production of variance and removal by transport and dissipation, using an adjustment time-scale given by w*/h. Evaluation against LES for a range of different cases, including a dry convective boundary layer as well as steady-state marine and transient continental shallow cumulus, reveals a data-collapse of the newly-scaled variance, for all hours and all cases in the top half of the mixed layer. The corresponding vertical structure is shown to resemble a power-law function. The results suggest that the structure of variance in the dry convective boundary layer is similar to that in the sub-cloud mixed layer. In transient situations, the scaling reproduces the time-development of variance at sub-cloud mixed-layer top. The new cloud-base variance scale is then further interpreted in the context of statistical cloud schemes, which depend on the variance as the second moment of the associated probability density function. The results suggest that the area fraction of the moist convective thermals uniquely depends on the ratio of cloud-base transition-layer depth to sub-cloud mixed-layer depth. This puts ,valve'- or ventilation-type closures for the cloud-base mass flux in the context of the variance budget for the sub-cloud layer. Copyright © 2007 Royal Meteorological Society [source] A linear model of gravity wave drag for hydrostatic sheared flow over elliptical mountainsTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 620 2006M. A. C. Teixeira Abstract An analytical model of orographic gravity wave drag due to sheared flow past elliptical mountains is developed. The model extends the domain of applicability of the well-known Phillips model to wind profiles that vary relatively slowly in the vertical, so that they may be treated using a WKB approximation. The model illustrates how linear processes associated with wind profile shear and curvature affect the drag force exerted by the airflow on mountains, and how it is crucial to extend the WKB approximation to second order in the small perturbation parameter for these effects to be taken into account. For the simplest wind profiles, the normalized drag depends only on the Richardson number, Ri, of the flow at the surface and on the aspect ratio, ,, of the mountain. For a linear wind profile, the drag decreases as Ri decreases, and this variation is faster when the wind is across the mountain than when it is along the mountain. For a wind that rotates with height maintaining its magnitude, the drag generally increases as Ri decreases, by an amount depending on , and on the incidence angle. The results from WKB theory are compared with exact linear results and also with results from a non-hydrostatic nonlinear numerical model, showing in general encouraging agreement, down to values of Ri of order one. Copyright © 2006 Royal Meteorological Society [source] Resonant gravity-wave drag enhancement in linear stratified flow over mountainsTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 609 2005M. A. C. Teixeira Abstract High-drag states produced in stratified flow over a 2D ridge and an axisymmetric mountain are investigated using a linear, hydrostatic, analytical model. A wind profile is assumed where the background velocity is constant up to a height z1 and then decreases linearly, and the internal gravity-wave solutions are calculated exactly. In flow over a 2D ridge, the normalized surface drag is given by a closed-form analytical expression, while in flow over an axisymmetric mountain it is given by an expression involving a simple 1D integral. The drag is found to depend on two dimensionless parameters: a dimensionless height formed with z1, and the Richardson number, Ri, in the shear layer. The drag oscillates as z1 increases, with a period of half the hydrostatic vertical wavelength of the gravity waves. The amplitude of this modulation increases as Ri decreases. This behaviour is due to wave reflection at z1. Drag maxima correspond to constructive interference of the upward- and downward-propagating waves in the region z Effects of shear sheltering in a stable atmospheric boundary layer with strong shearTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 596 2004Ann-Sofi Smedman Abstract Data from two marine field experiments in the Baltic Sea with stable stratification have been analysed. The purpose was to test the concept of the ,detached' or ,top-down' eddies and the ,shear-sheltering' mechanism in the presence of a low-level wind speed maximum in the atmosphere. Data used include turbulence and profile measurements on two 30 m towers and concurrent wind profiles throughout the boundary layer obtained from pilot-balloon soundings. Measurements show that large eddies are being suppressed when there is a low-level wind speed maximum present somewhere in the layer 40,300 m above the water surface and when the stratification is slightly stable. The effect is seen both in normalized standard deviations of the velocity components and in corresponding component spectra. In previous work it was argued that the relatively large eddies, which dominate the low wave number spectra in measurements in the surface layer, are detached or top-down eddies generated higher up in the boundary layer, that interact with the surface layer. The low-level wind maximum introduces a distinct layer with strong vorticity which, according to the shear-sheltering hypothesis, prevents these eddies from penetrating downwards. In the limit of the wind maximum occurring at a very low height (less than about 100 m), usual turbulence statistics characteristic of the ,canonical' boundary layer are found. Combining all the statistics, it is demonstrated that the wavelength of maximum spectral energy is locally related to a turbulence length-scale, which shows that for values of the Richardson number of unity or less the effect of the local wind gradient is greater than that of static stability. The reduction of length-scale with the strength of a low-level wind maximum, explains the observed reduction (by a factor of two) of the turbulent flux of sensible heat at the surface. This result indicates that the shear-sheltering mechanism is likely to play an important role in the turbulent exchange process at the surface in sea areas where low-level wind maxima are a frequently occurring phenomenon, such as the Baltic and other large water bodies surrounded by landmasses. Copyright © 2004 Royal Meteorological Society [source] Linear criteria for gravity-wave breaking in resonant stratified flow over a ridgeTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 609 2005M. A. C. Teixeira Abstract Using linear theory, it is shown that, in resonant flow over a 2D mountain ridge, such as exists when a layer of uniform wind is topped by an environmental critical level, the conditions for internal gravity-wave breaking are different from those determined in previous studies for non-resonant flows. For Richardson numbers in the shear layer not exceeding 2.25, two zones of flow overturning exist, respectively below and downstream and above and upstream of the expected locations. Flow overturning occurs for values of the dimensionless height of the ridge smaller than those required for a uniform wind profile. These results may have implications for the physical understanding of high-drag states. Copyright © 2005 Royal Meteorological Society. [source]
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