11 a coastline due to turbulent surface fluxes, turbulent mixing effects are frontolytical once a well-developed sea-breeze front is formed. Table 2.4 summarizes the effects of offshore and onshore geostrophic flow on sea breezes. Most numerical studies with a non-zero background flow have focused on the impact of offshore geostrophic flow. If the offshore geostrophic wind speed is above some critical value, then sea breezes do not form as the synoptic pressure gradient effectively cancels the local pressure gradient. The critical value of the offshore geostrophic wind above which sea breezes are likely to be absent has been found to be m s-1, depending on the strength of the land-water temperature gradient (Biggs and Graves 1962; Arritt 1993; Porson et al. 2007c). For small and medium-sized lakes, the critical value is unknown, but likely ranges between 3-5 m s-1 (Segal et al. 1997). For offshore winds greater than 4-8 m s-1 but less than 6-10 m s-1, the sea-breeze front may stall at the coastline where shear instabilities help to retard its inland penetration (Grisogono et al. 1998). Offshore geostrophic flow also shifts sea breezes so that they are no longer symmetric about the shoreline (Finkele et al. 1995) and may then not be closed circulations (Banta et al. 1993). For offshore geostrophic flows of 1-2 m s-1, l is on the order of 50 km, while l is on the order of km for offshore geostrophic flows of 4-5 m s-1 and onshore penetration occurs later in the afternoon (Arritt 1993; Tijm et al. 1999b; Porson et al. 2007c). Inland penetration speed of the sea-breeze front is likewise Table 2.4: Summary of key results from numerical studies pertaining to geostrophic wind (Vg). Study focus Findings References Offshore (OFF) ambient Geostrophic OFF Vg > 6-11 m s-1 no SB forms (smaller Vg for lakes) OFF Vg > 4-8 m s-1 but < 6-10 m s-1 SBF Estoque 1962; Physick 1976, 1980;
Interactions For high (low) N, circulation less (more) sensitive to area of surface heating and geostrophic wind Initial inversion strength, initial boundary-layer depth, terrain slope, and multiple inversions also factors Feliks 1993; Xian and Pielke 1991; Tijm et al. 1999a; Talbot et al. 2007 Only a few studies have investigated the characteristics of sea breezes when the initial temperature profile deviates substantively from the standard atmosphere (Garratt and Physick 1985; Yan and Anthes 1987; Savijarvi and Alestalo 1988). Increasing stability has been found to decrease h (Troen 1982; Arritt 1989, 1993; Xian and Pielke 1991; Porson et al. 2007a), while a similar dependence has been found between stability and w (Bechtold et al. 1991; Yang 1991; Arritt 1993; Wang et al. 1998). Complex interactions among stability and geostrophic winds, terrain height, and terrain slope are recognized to be important too; for example, Xian and Pielke (1991) found that for high stability, u becomes insensitive to the size of a heated peninsula, while several authors have noted that decreasing stability increases the dependence of sea breezes on the geostrophic flow. According to linear theory (Walsh 1974; Rotunno 1983), u is inversely proportional to stability while l is proportional to stability, i.e., increasing stability leads to slightly weaker winds near the shoreline and increased inland extent. In agreement with linear theory, Yang (1991) found u to decrease slightly with increasing stability. However, there remains disagreement between studies on the dependence of l on stability. Arritt (1989) found that increasing stability leads to slight increases in the offshore extent of sea