Abstract

In this work, a single-hemisphere 4-box model is used to study the low-frequency variability of the Atlantic meridional overturning circulation (AMOC). We introduce an enhanced mixing mechanism in the subpolar ocean to balance the positive salinity advection feedback, so that the AMOC in the 4-box model exhibits a self-sustained multicentennial oscillation. The enhanced mixing mechanism is proposed based on results from a coupled climate model, which show that the eddy-induced mixing or diffusion in the subpolar ocean is always enhanced when the AMOC anomaly is large; namely, the enhancement is due to weak stratification when the AMOC is strong, and is due to mesoscale and submesoscale eddies when the AMOC is weak. Without the enhanced mixing, the 4-box model system can be either stable or unstable, but cannot realize a self-sustained stable oscillation. With the enhanced mixing, the 4-box model can be interpreted approximately as a reduced 3-box model, so that the theoretical solution to the multicentennial oscillation can be obtained. The oscillation period is determined by the eigenvalue of the system, which is fundamentally controlled by the turnover time of the upper ocean. We also illustrate that the multicentennial oscillation can be excited by stochastic freshwater forcing. This study suggests that the Atlantic Ocean has an intrinsic multicentennial mode, which may help us understand this class of variability identified in paleoclimatic proxy data.

Abstract

In the first part of our research on self-sustained multicentennial oscillation of the Atlantic meridional overturning circulation (AMOC), we utilized a hemispheric box model considering only the salinity equations. In this study, we consider both thermal and saline processes in the box model to investigate the AMOC multicentennial oscillation and the role of temperature. The thermal processes have mainly two effects, shortening the oscillation period and stabilizing the system, which are caused by the fast surface temperature restoration and negative feedback between temperature advection and AMOC, respectively. Introducing nonlinearity into the system can lead to self-sustained AMOC oscillation that is controlled by ocean internal dynamics, whose mechanism is generalized as a growing oscillation restrained by nonlinearity. The nonlinearity can arise from subpolar vertical mixing, or a nonlinear relation between the AMOC anomaly and the meridional difference of density anomaly. Linear stability analyses reveal that the eigenmode of the system is sensitive to model parameters, including model geometry, mean strength of the AMOC, and the AMOC’s sensitivity to density perturbation, surface virtual salt flux, and meridional temperature gradient. A larger surface virtual salt flux enhances the positive salinity advection feedback, and a smaller meridional temperature gradient weakens the negative temperature advection feedback. Both processes destabilize the AMOC multicentennial oscillation. Such situations may be expected in the future due to more intense warming and freshwater hosing at the high latitudes of the Northern Hemisphere.

Abstract

In this study the author investigates the 3D evolution of the Ertel potential vorticity (PV) and N₂O in Northern Hemisphere winter from 1 to 10 February of model year 1984 in the GFDL SKYHI model. The diagnosis was done on three isentropic surfaces—800, 450, and 320 K—by using output from the GFDL SKYHI model, which has 1.2° × 1° horizontal resolution, 40 layers in vertical, and 60-s time resolution. The data output was taken twice daily. The high resolution Lagrangian Field Advection Model (FAM), which has no diabatic heating and diffusion, is used to study the evolution of these two fields. The 1° × 1° resolution in FAM gives reasonable results. The following results are found. 1) In the stratosphere there are two kinds of barriers, that is, subtropical barrier and polar barrier for both PV and N₂O. The existence of the subtropical barrier is coincident with the subtropical jet. The subtropical barrier is more permeable than the polar barrier. Even though the tropopause acts like a barrier, there is substantial exchange between the troposphere and the stratosphere at 320 K. 2) The inside edge of the polar vortex is marked by a nearby high-PV ring, and the outside edge is indicated by the maximum gradient of N₂O at 800 K. 3) On all three isentropic surfaces, both PV and N₂O are conserved quite well. 4) Poleward transport from the Tropics to the high latitudes and equaterward transport from the high latitudes to the middle latitudes due to Rossby wave breaking takes place simultaneously and is captured remarkably well in FAM. 5) The polar vortex is kinematically isolated from outside both on the 800- and the 450-K surfaces, with a small amount of outside air entrainment into the edge of the polar vortex on the 450-K surface. The probability distribution function and the finite-time Lyapunov exponents are proven to be useful to characterize the structure and mixing properties of PV and N₂O. 6) The transport and mixing channels between the Tropics and the high latitudes have been identified by the positive high Lyapunov exponents. 7) Three clear separate peaks in the PDFs identify with three distinct regions of N₂O (tropical reservoir, surf zone, and polar vortex), bounded by the subtropical barrier and the polar barrier between them, suggesting that the mixing may occur separately in each region in the stratosphere. The implications of these findings are discussed briefly.

Abstract

In its working state, the bit used in underwater horizontal directional drilling (UHDD) produces a high-frequency vibration that can affect accuracy of navigation. We designed a low-pass filter with linear phase on the basis of spectral characteristics of sensor data. To improve further the accuracy of navigation, we deduce the state error model on the basis of the random walk model of acceleration and angular velocity. We use an indirect Kalman filter algorithm to correct the attitude and position of the bit used with UHDD on the basis of observations coming from our working state analysis. Last, we derive a complete navigation algorithm function, including the acquisition method of steady-state component of acceleration and angular velocity. Experimental results show that the navigation algorithm proposed in this paper can obtain accurate attitude and location information of the bit in a vibration environment.

Abstract

A concept of the δ-approxiniation for the earth's surface has been introduced. Using the Rossby wave packet approximation and the WKB method, the evolution of a single geostrophic synoptic disturbance system has been further studied on the δ-surface of the earth. The global behavior of the structural changes of the wave packet due to the zonal, the meridional and the asymmetric basic currents and the variety of the topography on the δ-surface of the earth have been discussed and compared with those an the earth's,β-plane by using the WKB phase plane, i.e., the wave packet's local wavenumber phase plane. The results show that the governing system on the earth's δ-surface may be dynamically different from that on the earth's β-plane. Moreover, the wave packet structural vacillation has been found on both the β-plane and the δ-surface. Wave packet structural vacillation is characterized by the time-periodic changes of the wave packet's structure. Both the tilt and the spatial scales of the packet will evolve periodic changes simultaneously. The wave packet structural vacillations are also characterized by the closed WKB trajectories on the WKB phase plane. The results show that in the presence of the asymmetric basic currents, the WKB trajectories on the WKB phase plane appear simply to be elliptical, e.g., in the case of a southwesterly jet, or hyperbolic, e.g., in the case of a southeasterly jet. The results suggest that it is possible for the packet structural vacillations to exist in the presence of some asymmetric basic currents, e.g., a southwesterly jet. The behaviors related to topography in various distributions have also been discussed. It has been demonstrated that the quadratic east-west oriented topography modifies only the δ-effect, and that with some topographies, e.g., convex topographies, the wave packet structural vacillation can also exist. In some cases, however, the behaviors of the evolution of a packet will be qualitatively different on the earth's δ-surface from those on the earth's β-plane. For example, in the meridional basic current or on the north-south oriented topographies. only on the δ-surface of the earth do there exist such wave packet structural vacillations. On the other hand, in some cases, the wave packet solutions have been obtained on both the β-plane and the δ-surface. The wave packet vacillation suggests a possible mechanism of vacillations observed in the atmosphere.

Abstract

Using the Rossby wave packet approximation and the WKB method, the evolution of a single geostrophic synoptic disturbance has been studied. The structural changes of the wave packet due to the variation of β with latitude, the asymmetric basic currents and the variety of topography are thoroughly discussed. However, there are different effects on the wave packet in the various asymmetric basic currents, depending on the different positions of the wave packet relative to the basic current and the variety of topography. The δ-effect always lengthens the Rossby wave packet's longitudinal scale and causes the westward-tilting trough line to lean toward the Y-axis, i.e., to the north. When the Rossby wave packet is located to the left (right) side of a southwesterly jet its longitudinal scale (latitudinal scale) will lengthen and its latitudinal scale (longitudinal scale) will shrink, while the westward-tilting trough line will become more westward (toward the Y-axis). Linearly sloping topographies will not affect the structure of the Rossby wave packet, but nonlinear topographies do affect the structure of the packet. The results suggest that the mountains, especially the Rocky Mountains, may decrease (increase) the X-propagating disturbance system when it is westward- (eastward) tilted. The effects of topography on distributions of east-west oriented, north-south oriented, convex and concave models have been discussed in detail. Two examples of the entire evolution of the Rossby wave packet are also presented.

Abstract

Based on previous theory, which was made by using the Rossby wave-packet approximation and the WKB method, the evolution of a single geostrophic synoptic disturbance system has been further investigated. In the presence of both the basic current and topography, bifurcation properties of the evolution of the wave packet due to symmetric topography and asymmetric topography have been studied analytically as the topography parameter changes, using bifurcation diagrams and the WKB phase space, i.e., the local wavenumber phase span.

The results show that both topography and the basic current play very important roles in the bifurcation properties of the dynamics of geophysical flows. The results also show that the topological structure of the evolution of a Rossby wave packet in various basic currents and topographies can vary accordingly. Both subcritical and supercritical bifurcations have been found analytically. Moreover, reverse supercritical and sub-critical bifurcations also have been found. The effect of a zonal basic current on the bifurcation is different from that of a meridional basic current. For example, on concave topography the bifurcation will be supercritical (subcritical) when the packet is located on the left-hand side (right-hand side) of a westerly jet. However, in a meridional basic current, the evolution on the concave topography exhibits a reverse supercritical (subcritical) bifurcation on the left- (right) hand side of the current. On symmetric topography there exist only two kinds of equilibria, i.e., the largest scale state and the two pure latitudinal-scale states or the pure longitudinal-scale states. On asymmetric topography mixed-scale equilibrium states exist. The existence of the mixed-scale state suggests that there is a different kind of evolution for a Rossby wave packet. The results suggest that the evolution of a Rossby wave packet on one side of a basic current could be different from that on the other side, which is expected in real geophysical flows. At the center of a basic current, the dynamical system of the Rossby wave packet is structurally unstable.

The “homoclinic orbits” and the ”heteroclinic orbits” also have been discussed, which are separatrices of the wave-packet vacillations in the WKB phase space. The structural vacillations in the Rossby wave packet and their implications in geophysical flows associated with the bifurcation properties of the evolution of a Rossby wave packet are investigated. The results suggest that the transitions between two kinds of wave-packet structural vacillations only can occur on one side of the basic current as the topography parameter is varied.

Abstract

Based on a simplified mathematical model (Yang), using the Rossby wave packet approximation and the WKB method, the bifurcation properties of the evolution of a single geostrophic synoptic disturbance system were further studied. This analytical investigation was in the presence of an asymmetric basic current and utilized general topography as the topography parameter changes, using bifurcation diagrams and the WKB phase space.

The results showed that both the basic current and topography play very important roles in the bifurcation properties of geophysical flows. The results suggest that with the same type of topography, topological structure on one side of an asymmetric basic current will be different from that on the other side. On one side of an asymmetric basic current there exists only the primary bifurcation with three equilibrium states. However, on the other side of the asymmetric basic current, there are two distinct bifurcations. As the topography parameter reaches the first critical value, the primary bifurcation with five equilibrium states occurs. The equilibrium states are the 1argest spatial-scale state, two pure longitudinal-scale status and two pure latitudinal-scale status. As the topography parameter is increased further to the second critical value, a secondary bifurcation with the mixed-scale equilibrium states occurs. The evolution of a Rossby wave packet could exhibit the supercritical and subcritical primary bifurcations and the reverse supercritical and subcritical primary bifurcations accordingly, as the topography parameter varies. The secondary bifurcation, however, is the transcritical bifurcation. The WKB trajectories in the phase space are discussed for the different topography parameters. Both homoclinic orbits and heteroclinic orbits exist, as the separatrices of the wave packet structural vacillations. It has been shown that for the stable mixed-scale domain of the WKB phase space. For the unstable mixed-scale states the trajectories of the evolution constitute a family hyperbolic curves in the WKB phase space.

The structural vacilliations in the Rossby wave packet and their implications in geophysical flows are investigated. The results suggest that on side of an asymmetric basic current, the transitions can occur among three kinds of wave structural vacillations, while on the other side of the asymmetric basic current, the transitions can occur among three kinds of wave packet structural vacillations, while on the other side of the asymmetric basic current the transitions can only occur between two kinds of wave packet structural vacillations, as the topography parameter is varied.

Abstract

The oceanic Ekman transport and pumping are among the most important parameters in studying the ocean general circulation and its variability. Upwelling due to the Ekman transport divergence has been identified as a leading mechanism for the seasonal to interannual variability of the upper-ocean heat content in many parts of the World Ocean, especially along coasts and the equator. Meanwhile, the Ekman pumping is the primary mechanism that drives basin-scale circulations in subtropical and subpolar oceans. In those ice-free oceans, the Ekman transport and pumping rate are calculated using the surface wind stress. In the ice-covered Arctic Ocean, the surface momentum flux comes from both air–water and ice–water stresses. The data required to compute these stresses are now available from satellite and buoy observations. But no basin-scale calculation of the Ekman transport in the Arctic Ocean has been done to date. In this study, a suite of satellite and buoy observations of ice motion, ice concentration, surface wind, etc., will be used to calculate the daily Ekman transport over the whole Arctic Ocean from 1978 to 2003 on a 25-km resolution. The seasonal variability and its relationship to the surface forcing fields will be examined. Meanwhile, the contribution of the Ekman transport to the seasonal fluxes of heat and salt to the Arctic Ocean mixed layer will be discussed. It was found that the greatest seasonal variations of Ekman transports of heat and salt occur in the southern Beaufort Sea in the fall and early winter when a strong anticyclonic wind and ice motion are present. The Ekman pumping velocity in the interior Beaufort Sea reaches as high as 10 cm day⁻¹ in November while coastal upwelling is even stronger. The contributions of the Ekman transport to the heat and salt flux in the mixed layer are also considerable in the region.

Abstract

Organized rainstorms and their associated overturning circulations can self-emerge over an ocean surface with uniform temperature in cloud-resolving simulations. This phenomenon is referred to as convective self-aggregation. Convective self-aggregation is argued to be an important building block for tropical weather systems and may help regulate tropical atmospheric humidity and thereby tropical climate stability. Here the author presents a boundary layer theory for the horizontal scale λ of 2D (x, z) convective self-aggregation by considering both the momentum and energy constraints for steady circulations. This theory suggests that λ scales with the product of the boundary layer height h and the square root of the amplitude of density variation between aggregated moist and dry regions in the boundary layer, and that this density variation mainly arises from the moisture variation due to the virtual effect of water vapor. This theory predicts the following: 1) the order of magnitude of λ is ~2000 km, 2) the aspect ratio of the boundary layer λ/h increases with surface warming, and 3) λ decreases when the virtual effect of water vapor is disabled. These predictions are confirmed using a suite of cloud-resolving simulations spanning a wide range of climates.