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Wind Shear Due to the California Marine Layer

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Wind Shear Due to the California Marine Layer Fog Driven Wind • November 2016 • Remy Margerum Wind Shear due to the California Marine Layer Remy Margerum∗ University of California, Santa Barbara [email protected] November 2016 Abstract A. The purpose of this paper is to estimate the magnitude of the wind shear at the edge of fog banks. The hypothesis is that the effect will be 0.5-1 m/s in the direction perpendicular to the fog bank. Multiple methods of estimation will be used to ensure consistency of results. First a qualitative view of the effect will be given, based on both personal observation and the weather trends of the California coast. This will be followed by an application of Bernoulli’s principle, that will estimate the effect of the shear to be 0.31-0.62 m/s at altitudes of 5m to 10m. I. Introduction make this assumption since it is only under these prevailing conditions that the marine he California coastline is commonly layer will form. Under other wind directions, thought of as the quintessential coast such as a Santa Ana wind from the east for Tline, with travelers from all over the example, there is not enough moisture in the world coming to witness the unique natural air for fog to form. phenomena that occur daily. Much of what Lastly, since there is a saying in Southern makes the California coast so unique is the me- California that the month of June should be teorological phenomenon of the marine layer. called "June Gloom", this paper will arbitrarily The marine layer is a layer of cold air that use data from the month of June while estimat- forms over the Pacific Ocean, and since cold ing the magnitude of the "Fog Shear" effect. air is denser than warm air, it is trapped at low altitude. Normally, this layer of cold air leads to fog due to the humid air mass being cooled to it’s saturation point. It is a common misconception that the marine layer is the fog bank, when really fog is a byproduct of the marine layer. The whole process is primarily a wind Figure 1: Fog Bank, Santa Barbara driven phenomenon. The predominant wind direction in California is west-northwest. This is due to north pacific high, a semi-permanent II. Fog Formation weather phenomenon west of California. For the purposes of this paper, the wind direction The winds due to the north pacific high play will always be assumed to be consistently from two important roles in the formation of fog this prevailing wind direction. We can safely along the California Coast. First it brings warm ∗Physics Undergraduate at UCSB 1 Fog Driven Wind • November 2016 • Remy Margerum humid air from the middle of the pacific to The following two maps (Figures 3 & 4) il- the coast. This is crucial since without humid lustrate this, the striped red areas are where air, the fog bank can’t form. Second the wind fog will be slower to form, or will not form at drives coastal upwelling along the coast, which all: causes the SST (Sea Surface Temperature) to drop. This SST drop cools the low-level air mass, thereby creating the marine layer. Fog that forms along the California coast is a type of fog known as advection fog. Advec- tion fog forms due to a warm and humid air mass moving over a cold surface. This forms fog as the warm air is cooled to it’s saturation Figure 3: Map of Point Conception (OSM) point. It is important to note that the fog is not formed by evaporation from the water beneath it. Figure 4: Map of San Francisco(OSM) Figure 2: Inversion Layer IV. Estimation of the Humid to Dry Air Interface Since air cools close to the sea surface but remains warm higher in the altitude, a large I. Temperatures vertical temperature difference develops. The interface between the warm air mass and the A good estimate of temperature within a fog cool one is called the inversion layer (Figure 2). bank is the mean air temperature of "Station This inversion of the standard air being cooler 46063" located off the coast of Point Concep- with height, prevents mixing of air within the tion (red buoy in Figure 5) . This buoy during marine layer with the air above. the month of June will typically consistently be in advection fog. The mean historical air temperature for the month of June is T = 13 ◦C III. Geographic Effects (NDBC-NOAA) For the wind shear effect to occur there must be a humid to dry air interface. The primary rea- son for the formation of fog banks over certain parts of the ocean and not others, and hence the formation of fog/dry air boundaries, is due to the coastal geography. Warm winds from the north pacific high are oftentimes blocked by landmasses and points along the coast. This al- lows fog to form over the areas where the wind flows uninhibited, while not forming where the wind is blocked. Figure 5: Buoy Locations (NDBC-NOAA) 2 Fog Driven Wind • November 2016 • Remy Margerum An estimate of temperature outside the fog The equation for air density in fog is thus: bank is more difficult. I propose that "NTBC1 ◦ Buoy", Tmean = 15 C in June (NDBC-NOAA), 7.5T P 610.78 ∗ 10 T+237.3 located near the Santa Barbara Harbor (green r = abs − buoy in Figure 5), gives a good estimate. While Rair(T + 273.15) Rair(T + 273.15) 7.5T (6) this buoy may experience some fog, I believe 610.78 ∗ 10 T+237.3 that this cooling is offset due to it’s proximity + RvaporT to land. While this is a very ad hoc reasoning, it ◦ does agree with the DT = 1 − 2 C observed by This is now dependent solely on T and Pabs. the R/V Acania sea fog expedition (Pilié et al.). As discussed previously: Since it is DT that we are worried about any- ◦ ◦ ◦ ways we will accept the ansantz that T = 15 C Toutside = 15 C , Tf og = 13 C (7) is a good estimate for the temperature outside Using these temperatures, the appropriate the fog bank. specific gas constants, and Pabs = 1atm = 101325Pa: II. Air Density R = 287.058 J/(kg ∗ K) (8) The most important values, to understand the air fog shear phenomenon, are the densities of the Rvapor = 461.495 J/(kg ∗ K) (9) air within the fog bank and outside it. It is this density gradient that drives the flow of air. To r f og = 1.26311 and rdry = 1.22498 (10) calculate these densities we turn to the ideal gas law. III. Suspended Water Droplet Correction to Fog Density P = rR T (1) speci f ic It should be said that fog is not completely a Thus the density of humid air can be expressed gas, and therefore the density of fog should as: take into account the effect of the liquid water P Pvapor r = air + (2) suspended within it. The liquid water con- RairT RvaporT tent (LWC) can be determined by performing The next step is to convert this equation into a latent heat calculation a form dependent on absolute pressure rather Q Q than partial pressures. L = , m = (11) m L Pvapor = fPsaturation (3) Q = m f og ∗ Cp ∗ DT (12) By using the Tetens’ Formula (Tetens) , an ap- proximation of the Clausius-Clapeyron relation We set m f og = 1.26311Kg so that we get an −3 for water vapor, we can estimate Pvapor. Note estimate of the mwater/m , i.e the LWC. For −1 −1 that in this equation, temperature is in degrees water vapor at STP: Cp, ≈ 2Jg K . We also Celsius. It is also a good time to note that fog assume DT = −2 ◦C) as discussed previously. is typically at 100% so the relative humidity L = −2444Jg−1 (Marsh) term f will be equal to 1. (1.26311kg) ∗ (2Jg−1K−1) ∗ (−2 ◦C) 7.5T = mwater −1 Pvapor = f ∗ 610.78 ∗ 10 T+237.3 (4) −2444Jg (13) The partial pressure of air is simply the abso- lute pressure minus the partial pressure of the mwater = 0.0020kg (14) water vapor So the calculated LWC is equal to −3 Pair = Pabs − Pvapor (5) 2000 mg/m . 3 Fog Driven Wind • November 2016 • Remy Margerum However, mixing effects below the inver- tion. Therefore we must show that the flow sion layer cause the observed LWC to be even from the fog bank to the outside is a relatively lower, so we must turn to field data. Accord- incompressible flow. This may seem counter- ing to observations from the R/V Acania, mea- intuitive since the process is driven by a dif- sured LWC was between 100 and 350 mg/m−3. ference in densities, therefore disproving that (Pilié et al) This corresponds to at most a the air is incompressible. Luckily, the effects of 0.00035 Kg/m−3 increase in fog density. Over- compressible can be ignored at low Mach num- all, there is at most a negligible increase from bers (Shaughnessy et al, p. 512). The expected r f og = 1.26311 to r f og0 = 1.26346. velocity of the effect is Mach 0.003, well within Mach 0.3, the incompressible flow regime. V. Bernoulli’s Principle Lastly, we must make the idealization that the process is isobaric. Since the effect is lo- I. Conditions to the use of Bernoulli’s calized and subject to the same non-local phe- Principle nomenon of the pacific high, I believe that this is a reasonable assumption Since Bernoulli’s equation is fundamentally a In conclusion, we make the assumptions statement of energy conservation, it must be that energy is conserved in the system, flow is shown to a reasonable extent, that energy is incompressible, and the process is frictionless conserved in the marine layer system.
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