Scale Optimization Scheme In Hurricane Boundary Layer And Eye Formation In The Boundary Layer From An Adjustment Process

A novel theoretical framework for the hurricane boundary layer is developed in this thesis, which is based on the "scale optimization" idea, i.e. consider the large scale first, then the meso-scale, the small scale the last. Through "scale optimization", This article employ the method from the pioneer on the large scale dynamics in meteorology, which is the Geostrophic Momentum Approximation (GMA) boundary scheme (a four forces balance model). Above the GMA, the radial flow is set to one order less than the tangential flow in the meso and small scale to consider the real hurricane dynamics, in such a way realize the "scale optimization"Also this thesis gives the answer to why some other theories not deal the hurricane boundary well, i.e. too much considerations are given to the meso-scle and small-scale problem, while neglect the most important background, the large scale problem. It is argued that a good background is firstly needed, under which the research on the meso and small scale problem does work. This new scheme is compared to some other large scale boundary schemes, the results show they agree with each other well.After the dealing with large scale problem, the new scheme is applied to hurricane-like vortex boundary layer, the problem is considered in axisymmetric and non-axisymmetric frameworks. In the axisymmetric hurricane boundary layer, the simple analytic solution from the pioneer works. When the vortex is in an intensifying state, the radial flow appears a three-layer structure, i.e. an inflow-outflow-inflow structure from the center outward, and from the ground to the top. When the vortex is in a weakening state, the radial flow appears a two-layer structure, i.e. an inflow-outflow structure from the ground to the top. The tangential flow in the intensifying state is a little smaller than the flow in the weakening state, which is caused by the tangential energy is transformed to radial energy to supply more moisture to the intensifying vortex. However, there is no downwards in the center of the axisymmetric hurricane boundary layer. This phenomenon is mainly caused by the fact that the new scheme can not include the forcing from the free atmosphere.In the non-axisymmetric hurricane boundary layer, the simple analytic solution does not work well. The author develops the applicable condition for the analytic solution. However the condition is not applicable everywhere in the hurricane-like vortex, other two alternative numerical methods are given by this thesis. One is the super relaxation iteration method, which uses the analytic solution as the first guess field. The other is the pentadiagonal matrix inverse method, which features high calculated amount and high accuracy. The latter scheme is adopted, and gives some results very similar to numerical simulation and data observation:in the upper boundary layer, the super-gradient flow and the sub-gradient flow coexists, the super-gradient flow is a little larger in the scale, the whole tangential flow appears super-gradient flow after azimuth averaging; in the lower boundary layer, the flow is super-gradient at the maximum wind radius, where also exists the outward radial flow, the flow is sub-gradient outside of the maximum wind radius, where also exists the inward radial flow. Downwards is found in the center of this non-axisymmetric theoretical work. Because the new scheme cannot include the supplement downwards from the free atmosphere, it is guessed that the downwards here are due to some spontaneous adjustment process, and this process is in essence a non-axisymmetric process.A "super-gradient flow" appears in the eye of the low boundary layer, however, the numerical simulations from the other researchers show there is a "sub-gradient flow", it is hard to say which is right. But we think the "super-gradient flow" here are necessary to form a outward slant-wise eye-wall. If result here is right, then maybe there is a "center-determining" problem in the "sub-gradient flow" results, which causes the "sub-gradient flow" outside the eye-wall into the eye.In addition, a Lagrange view is used to explain the "sub-gradient flow" and "super-gradient flow", which is different from the Euler view of others. In the lower boundary layer, suppose there is an air parcel (First Parcel) in the radius far away from the eye-wall, more than 200 kilometers from the center, the background of the parcel is "sub-gradient flow", the net force exert an inward acceleration on the air parcel, assume the initial velocity of the parcel is zero, this forces the parcel move into the center, however, when the parcel moves into a "super-gradient" region which is near the eye-wall, the total forces on the parcel is in the outward direction, then the parcel has a decelerated motion (inward motion), the velocity is near zero when it moves to the eye-wall. Still in the lower boundary layer, suppose there is an air parcel (Second Parcel) in the radius in the center of the eye, and the initial velocity of the parcel is zero. Because the background of the air parcel is "super-gradient flow", which exerts an outward acceleration on the air parcel, this causes the parcel to move towards to the eye-wall. When the Second Parcel in the eye-wall region, the velocity is in the outward direction, while the velocity of First Parcel is near zero, after a merger process of these two parcels the total velocity is outward in the radial direction, according to the conservation law of momentum. The new parcel moves upward in an outward slant-wise way.With the same Lagrange method, the "super-gradient flow" phenomenon in the upper and middle boundary layer is explained.A three-dimensional high-resolution numerical simulation is done to investigate the problem "can the hurricane boundary layer forms the downwards in its center spontaneously?" The results show some interests. The initial condition is an axisymmetric hurricane in a hydrostatic and gradient wind balance state. The imbalance originates from the frictional terms. The results features an eye structure, which forms a downwards in the center of the hurricane boundary layer and two upwards on both sides of the hurricane. At the start of the simulation, the vertical flow features an antisymmetry, which owns an upwards on the left side of the center, and a downwards on the other side. The downwards in the center forms through a process, which is a contraction to the center and a little movement to the center and other side. Then an upwards forms in the original downwards side and intensifies, the original upwards weakens. In the subsequent time, the center downwards intensifies, the smaller upwards intensifies, and the larger upwards weakens, until a near final balanced state forms.Also we investigate the origins of the downwards in the center of the hurricane boundary layer, but we discuss the problem using the time scale concept.The downwards of the center in the hurricane boundary layer can be classified into two classes:one is the supplement flow from the free atmosphere, the other is the downwards formed through a spontaneous non-axisymmetric adjustment process. The downwards from the spontaneous process in the hurricane boundary layer is much stronger than that from the free atmosphere. The above results can explain the phenomena appear in the extant theoretical schemes and the numerical models:there is no downwards in the no free-atmosphere forcing including and axisymmetric schemes; the downwards in the non-axisymmetric schemes comes from a non-axisymmetric spontaneous adjustment process; the downwards form in the extant axisymmetric numerical models are too week than its nature.