CONTINGENT VALUATION OF MARINE PROTECTED AREAS: SOUTHERN CALIFORNIA ROCKY INTERTIDAL ECOSYSTEMS

ABSTRACT. Designation as Marine Protected Areas (MPAs) can protect coastal ecosystems, but apparently has not effectively protected the rocky intertidal zone in urban Southern California. Here, illegal collecting and habitat disturbance harm coastal marine life. We surveyed day visitors to sandy beaches or adjacent rocky habitats in Orange County. Using the close‐ended, double‐bounded contingent valuation method, we estimate the benefit of more effective enforcement and management of MPAs designed to avoid coastal ecosystem decay. We solve the problem of sample selection bias, introduced by the likelihood that the sample disproportionately includes respondents who visit more frequently and who may have a higher willingness to pay (WTP). We estimate the WTP for enacting policies to reduce illegal collecting and on‐site habitat disturbance to average $6 per family‐visit. Our estimate is consistent with other studies that estimate consumer surplus at $15 per person‐trip for nearby, lower quality beaches, and extrapolates from other studies to $3.6 $4.8 million per mile of coastline.     

On the Non-linear Evolution of Gortler Vortices in Non-parallel Boundary Layers

The non-linear development of finite amplitude Görtlervortices in a non-parallel boundary layer on a curved wall isinvestigated using perturbation methods based on the smallnessof e, the non-dimensional wavelength of the vortices. The crucialstage in the growth or decay of the vortices takes place inan interior viscous layer of thickness O(²) and length O().In this region the downstream velocity component of the perturbationcontains a mean flow correction of the same order of magnitudeas the fundamental which is driving it. Moreover, these functionssatisfy a pair of coupled non-linear partial differential equationswhich must be solved subject to some initial conditions imposedat a given downstream location. It is found that, dependingon whether the boundary layer is more or less unstable downstreamof this location, the initial disturbance either grows intoa finite amplitude Görtler vortex or decays to zero. Forthe Blasius boundary layer on a concave wall it is found thatGörtler vortices can only develop if the rate of increaseof curvature of the wall is sufficiently large. In this casethe finite amplitude solution which develops initially in an-neighbourhood of the position where the disturbance is introducedchanges its structure further downstream. This structure isinvestigated at a distance O() (with 0< <1) downstreamof the above -neighbourhood. In this régime the downstreamfundamental velocity component has an elliptical profile overmost of the flow field. However, in two thin boundary layerslocated symmetrically either side of the centre of the viscouslayer the fundamental velocity component decays exponentiallyto zero. The locations of these layers are determined by aneigenvalue problem associated with the one-dimensional diffusionequation. The mean flow correction persists both sides of theboundary layer and ultimately decays exponentially to zero. This large amplitude motion is not sensitive to the imposedinitial conditions and appears to be the ultimate state of anyinitial disturbance. However, in the initial stages of the growthof the vortex, some surprising flows are possible. For example,it is possible to set up a vortex flow similar to that observedby Wortmann (1969) which consists of a sequence of cells inclinedat an angle to the vertical.