Mixing in Haro Strait
Abstract : The long-term goal is to better understand mixing processes in estuaries. Of particular interest are the processes at work in the Haro Strait region between Washington State and British Columbia, which are modulated by a spring/neap cycle in tidal velocities. The field phase of the Haro Strait experiment took place in the summer of 1996 and involved a collaborative effort between MIT, WHOI and IOS. Our objectives are to understand the dynamics associated with intense coastal mixing processes in which separation of tidal flows past topography leads to formation of fronts accompanied by instability and mixing. During this year, we have begun to analyze this data in two different areas. First, we wanted to better quantify the large-scale dynamics. This means estimating horizontal layer transports, rates and amounts of mixing that take place. Second, we want to use these results to understand the importance of smaller-scale mixing that occurs at convergence fronts within this region.
Diagnosing vertical mixing in a two-layer exchange flow
Most classification schemes and analyses of estuarine and exchange flows use only salinity as a tracer. Temperatures are generally ignored. However, a proper understanding of the effects of surface heating can explain observed seaward changes in the slope of temperature-salinity correlations. A theory is proposed relating changes in temperature and salinity with transport and mixing parameters in a two-layer exchange flow. Results show that along-channel changes in the slope of T-S correlations are virtually independent of vertical mixing but are directly related to horizontal layer transport. Changes in the layer salinities can be related to various ratios of horizontal and vertical transports. Combining these two features of the theory permits a diagnostic determination of Lagrangian transport and mixing from standard hydrographic observations of layer temperature and salinity and an estimate of the surface heat input. The theory is applied to observations made through the spring/neap tidal cycle of mixing in Haro Strait, British Columbia.
NUMBER OF TRIANGULATIONS OF A MÖBIUS STRIP
Consider a Möbius strip with n chosen points on its edge. A triangulation is a maximal collection of arcs among these points and cuts the strip into triangles. In this paper, we proved the number of all triangulations that one can obtain from a Möbius strip with n chosen points on its edge is given by 4n−1 + (2n−2 n−1 ) , then we made the connection with the number of clusters in the quasi-cluster algebra arising from the Möbius strip.