OS16I-01
Non-axisymmetric effects of stratified spin-up flows in axisymmetric geometries
The present work is focused on stability of an impulsively forced baroclinic zonal current in axisymmetric geometries (an axisymmetric cylinder, annular channel and cone). The zonal current is initiated via incremental spin-up of a linearly stratified fluid, when the initial rotation rate of the system is changed during some time interval. Secular as well as instantaneous variation in rotation speeds were investigated for a wide range of Rossby numbers. It is demonstrated that the formation of cyclonic and anticyclonic vortices may occur under certain conditions at late times (several tens of rotation period). The vortices facilitate transport of angular momentum from the solid boundaries to the bulk of the fluid and substantially reduce the spin-up time compared to the spin-up viscous time scale of a homogeneous fluid. Most of the previous studies of stratified spin-up have been restricted to the analysis of axisymmetric perturbations or early times of the flow development (several rotation periods), while the non-axisymmetric phase was left unconsidered until recently. Although a complete theoretical description of a nonlinear stratified spin-up problem is still lacking, numerous laboratory and numerical studies have demonstrated that the transient Ekman layer forming during early times of spin-up plays a crucial role in determining the subsequent flow evolution. The long-time flow evolution is governed by the Rossby (Ro) and Burger (Bu) numbers. Observations demonstrated that isopycnals experience large vertical displacements near the lateral boundaries during spin-up. The density gradient reduces to near zero in the corner regions, where the fluid is stirred, and increases above/below them near the outer/inner sidewalls respectively. The relative height of the corner regions was found to be determined only by the relative values of Ro and Bu. A flow stability regime diagram is presented as a function of the Rossby and Burger numbers. Introduction of roughness elements at the inner sidewall did not alter significantly the process and time scales of stratified spin-up, large eddy formation, and subsequent relaxation to the initial state obtained with smooth sidewalls. The extended Eady model of baroclinic instability, in which the sheared wall layers are taken into account, is advanced to explain this mechanism of eddy formation. This model accounts for most of the observed features of the instability and provides a realistic estimate for the time of onset of eddy formation. The presence of a sloping wall (for conic geometry) modifies significantly the flow behavior, i.e. it stabilizes the spin-up flows, while the spin-down flows still remain unstable at late times.
OS16I-02
Model Studies of the Faroe Bank Outflow
Results are presented from a lab/analytical study of the dense deep-water flow through the Faroe Bank Channel. The temporal and spatial development of a turbulent, dense discharge has been studied as it flows down a sloping diverging channel in a rotating fluid. Measurements show that the flow maintains geostrophic balance and adjusts by Ekman dynamics. The flow structure consists of a dominant axial component with a significant transverse secondary flow. Density measurements provide evidence of mixing with the overlying fluid. An analytical model based on Ekman dynamics is developed and the predictions of the dimensions of the flow are shown to accord well with the laboratory data. The results are interpreted in terms of recent field measurements.
OS16I-03
Necking and Strangling Plumes
It is well known that the rate of diffusion of salt in sea ice directly affects the structure of the fluid flow beneath. Depending on the diffusivity either heavy `puffs' of fluid can be released intermittently downwards, or a relatively steady plume of heavy fluid can be established. This paper introduces theoretical work aimed at understanding the transition from a puff regime to a plume regime, or vice-versa, motivated by the work of Hunt et al. (2003). Starting with the simple jet and plume models of Morton, Taylor & Turner (1956), time dependent models have been developed which show the effect of temporal variation of the buoyancy flux at the boundary where plumes or puffs are formed. It is shown that reducing the buoyancy flux at the source of a plume causes a transitional `necking' region to form in the plume. Above and below this necking region, the classical plume shape of Morton, Taylor & Turner (1956) is found. The necking region has lower buoyancy closer to the origin and higher buoyancy further away. This is well modelled by Batchelor's (1954) similarity solutions in unstable stratifications. The surprising result that the necking, i.e. the minimum plume radius to steady plume radius ratio, is independent of buoyancy flux is demonstrated. Batchelor, G. K. 1954 Heat convection and buoyancy effects in fluids. Q. J. R. Met. Soc. 80, 339--358. Hunt, J. C. R., Vrieling, A. J., Nieuwstadt, F. T. M. & Fernando, H. J. S. 2003 The influence of the thermal diffusivity of the lower boundary on eddy motion in convection. J. Fluid Mech. 491, 183--205. Morton, B. R., Taylor, G. I. & Turner, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. Roy. Soc. Lon. A. 234, 1--32.
OS16I-04
Disturbance growth in a baroclinic wave-mean oscillation
The study of the transient development and asymptotic evolution of linear disturbances to nonlinear model trajectories are two complementary approaches to understanding the linear predictability of geophysical fluid flows. The transient development of linear disturbances is described by singular vectors, while normal modes characterize asymptotic stability. For time-periodic flows, the normal modes are given in terms of time-dependent Floquet vectors. The structures and dynamics of complete sets of these time-dependent linear normal modes and singular vectors are discussed for a time-periodic nonlinear baroclinic wave-mean oscillation in a high-dimensional model of the baroclinic instability. The physical structures of the singular and Floquet vectors are explored, as well as the physical and mathematical connections between the two. The results offer new insights into the mechanisms of disturbance growth and decay that control the predictability of atmospheric and oceanic motions.
OS16I-05
An approach to improving Large, McWilliams and Doney KPP mixing scheme
The surface wave induced vertical mixing mechanism is incorporated to modify the K profile parameterization (KPP) scheme. The effect of this approach is examined in a global oceanic general circulation model. In contrast to original KPP scheme, the modified KPP scheme can improve the simulation of upper layer temperature and upper mixed layer depth on the mid-latitudes and high latitudes. To evaluate the simulated upper layer temperature (0-50m) and upper mixed layer depth, the seasonal cycle of temperature and upper mixed layer depth obtained from the model simulations are compared with Levitus climatology. Analysis of the global errors maps shows that the surface wave induced mixing reduces the global root-mean-square difference of upper layer temperature from 1.19$\deg$C to 0.78$\deg$C and increases the mean global correlation coefficient from 0.78 to 0.88. For the upper mixed layer depth, the surface wave induced mixing reduces the global root-mean-square difference from 73.8m to 49.8m and increases the mean global correlation coefficient from 0.74 to 0.80. Comparing with different seasons, wave induced mixing improves the summer upper mixed layer depth in both hemispheres more obviously than other seasons. Since the parameterization of wave induced mixing is deduced from the oceanic dynamics mechanism and can better solve the problem of the weakness of the summer thermocline and the shallowness of the summer upper mixed layer on mid-latitudes and high latitudes, it can be applied to other ocean models in predicting the upper layer temperature and upper mixed layer depth.
OS16I-06
Linear instability of an anticyclonic vortex in a two-layer rotating fluid
The linear stability of a uinform potential vorticity baroclinic vortex is investigated using a two-layer inviscid model. The stability properties are described by two parameters: the nondimensional potential vorticity of the vortex $Q^*$ and the ratio Δ$ between vortex depth and total depth. Numerical results are compared with experiments carried out on a rotating table. Agreement is good except when the vortex extends through the water column.
OS16I-07
Horizontal Convection in Water Heated by Infra-red Radiation and Cooled by Evaporation. Part I: Experimental Results and Scaling Analysis.
A new technique of heating water with infra-red light has been utilized in a horizontal convection (i.e. the type of convection that arises in a fluid that is heated and cooled at the same pressure level) experiment. Fresh water was heated from above by an infra-red lamp placed at one end of a tank, and then cooled as the water moved away from the heat source. The heat from the lamp was absorbed in a thin layer next to the surface, and then advected and diffused away from the lamp region. The surface cooling was greatly dominated by evaporation, which accounted for over 80 percent of the total energy loss. The velocity- and temperature fields were recorded with PIV technology, thermometers and an IR camera. In similarity with previous horizontal convection experiments, the measurements showed a closed, steady circulation with a thin, fast, gradually cooling surface current away from the lamp. Below the surface current the water was stably stratified with a comparatively thick and slow return current. The thickness and speed of the surface- as well as the return current increased with distance from the lamp. Three new results were obtained during this experiment; (i) The velocity in the surface layer is independent of the interior velocity and temperature fields (ii) The surface temperature is independent of the interior velocity and temperature fields, and (iii) a new scaling law in which the length scale and temperature difference are obtained as a function of the radiative forcing rather than being imposed by the experiment geometry. The new scaling law indicates that the circulation strength is very sensitive to the distribution of the heat loss, i.e. how effective the temperature relaxation is. In the ocean the buoyancy flux (and thereby the effectiveness of the temperature relaxation) is highly dependent on wind speed, and the present results indicate that the sea surface temperature as well as the ocean overturning circulation strength may be sensitive to wind speed even if the wind does not directly force the circulation by momentum transfer through the surface.
OS16I-08
Horizontal Convection in Water Heated by Infra-red Radiation and Cooled by Evaporation. Part II: Boundary Layer Theory.
A new technique of heating water with infra-red light has been utilized in a horizontal convection (i.e. the type of convection that arises in a fluid that is heated and cooled at the same pressure level) experiment. Fresh water was heated from above by an infra-red lamp placed at one end of a tank, and then cooled as the water moved away from the heat source. In similarity with previous horizontal convection experiments, the measurements showed a closed, steady circulation with a thin, fast, gradually cooling surface current away from the lamp. Below the surface current the water was stably stratified with a comparatively thick and slow return current. The thickness and speed of the surface- as well as the return current increased with distance from the lamp. Three new results were obtained during the experiment; (i) The velocity in the surface layer is independent of the interior velocity and temperature fields (ii) The surface temperature is independent of the interior velocity and temperature fields, and (iii) a new scaling law in which the length scale and temperature difference are obtained as a function of the radiative forcing rather than being imposed by the experiment geometry. A simplified boundary-layer theory utilizing these results and the thinness of the warm surface layer is presented. This is work in progress.
OS16I-09
Slow Nonhydrostatic Flow and Balanced Energetics
Gravity wave radiation by balanced flow evolution is currently the subject of considerable debate, with laboratory, numerical and theoretical examinations arguing the effect is anywhere from vanishingly weak to routine. Here a theoretical and numerical examination of balanced evolution characterized by O(1) aspect ratios is carried out, as such a parameter setting is typical of many laboratory settings. Accordingly, it is argued that the wave properties of the system are quite distinct from a system characterized by small aspect ratio. In particular, the fluid exhibits superinertial and subinertial linear wave modes characterized by vertical shear in layers of constant density. The restoring force on the flow comes from a combination of Coriolis acceleration and pressure gradients, so the oscillations are not strictly inertial. The flows are `slow', yet nonhydrostatic effects are leading order. The predicted long time behavior of the system departs markedly from that of the hydrostatic one in that exchanges between balanced and unbalanced flows appear at leading order and importantly involve the nonhydrostatic effects. Numerical experimentation supports the basic results of the analytic development and yields evolution broadly consistent with the laboratory.