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W12 · Physics · Heat capacity, circulation

sea breezes

On a sunny afternoon at the beach the wind blows in off the water, and after dark it often turns around. Both come from one fact: water needs about five times more heat than rock or dry soil to warm by the same amount, and the sea spreads that heat through meters of water. The land warms fast, the air above it expands, and a small pressure difference pulls cool sea air inland.

LAB 1

why land heats faster

Two columns get the same sunshine for a day. On land, the day's heat reaches only the top or so of soil. At sea, waves and wind stir the warmed water through a mixed layer meters deep. Each column is a single slab that gains sunlight and loses heat faster when it is warmer than its daily mean. Drag the time or play the day.

noon
land surfacesea surfacetime now
2:00 pm
33 ft 700 W/m²

How to read this: the top shows the sea and land side by side under the same sun. The bottom graph tracks each one's surface temperature through the day. Notice how much more the amber land curve swings than the blue sea curve.

  • colored top layer: its temperature, cool → hot
  • faint band on the graph: daytime

Try this: press Play day, then drag Ocean mixed layer to its smallest value and watch the blue sea curve start to swing.

—
Land surface now
—
Sea surface now
—
Land minus sea
—
Heat needed, sea vs land
—
Land daily range
—
Sea daily range

Energy balance (toy model)

C·dT/dt = S(t) − S̄ − λ·(T − T₀)
C = ρ·c·depth
land: 1600 kg/m³ · 800 J/(kg·K) · 0.15 m
sea: 1000 kg/m³ · 4186 J/(kg·K) · hmix

S(t) is absorbed sunlight, a half-sine from 6 am to 6 pm. S̄ is its daily average, so both columns end the day where they started. λ = 40 W/(m²·K) lumps together infrared, conduction and evaporation losses. Both share the same daily mean T₀ = , so only the size of the swing differs.

Now

Why the sea barely moves

Per kilogram, water takes 4186 J to warm by 1 K and dry soil about 800 J. The bigger factor is depth. Sunlight reaches meters into clear water and mixing spreads the heat further, while heat creeps into soil by slow conduction. With a mixed layer or more deep, that gives the sea hundreds of times more heat capacity per square meter of surface.

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LAB 2

the circulation

This lab takes the land and sea temperatures from Lab 1. Warm air over land fills a thicker layer than the same mass of cool air over the sea, so at a given height aloft the pressure over land is higher. Air drifts seaward up there, the land column loses mass, and its surface pressure drops. Near the ground the cool sea air flows in toward that low. Real sea breezes often reach –; the land breeze at night is usually weaker. Slide through the day.

cross-section
air parcelsisobars (tilt ×25)surface wind over the day
3:00 pm
30°N

How to read this: a slice through the coast with sea on the left and land on the right. Green dots are air. The amber arrows show the breeze at the ground and the air returning higher up. The small box in the corner looks down from above and traces the ground breeze's direction over the whole day.

  • low arrow: breeze at ground level
  • high arrow: air returning aloft
  • L / H lower / higher pressure (small dim letters: the reverse pattern aloft)
  • lines of equal pressure (isobars), tilt drawn 25× steeper
  • corner box: the wind right now

Try this: press Play day and watch the arrows flip around sunset. Then set Latitude to 0° and the corner loop collapses to a straight line.

—
Surface wind
—
Blowing from
—
Surface pressure, land minus sea
—
Return flow aloft

Hydrostatics to wind (toy model)

thickness ∝ T ⇒ Δpsurface ≈ ½·p₀·(g·H/Rd)·ΔTair/T²
du/dt = Δp/(ρ·L) + f·v − u/τ
dv/dt = −f·u − v/τ, f = 2Ω·sin φ

The air warms by β = 0.3 of the surface difference from Lab 1, through a layer H = deep by day and at night when the cooling stays near the ground. The pressure difference acts across L = , and friction drains the wind with a τ = 2 h time scale. p₀ = 1000 hPa, Rd = 287 J/(kg·K), g = 9.81 m/s², ρ = 1.2 kg/m³.

The picture spreads the return flow over a layer twice as deep as the inflow, so it moves at one third the speed and carries the same air back.

Now

Why it turns

The breeze lasts many hours, long enough for Earth's rotation to matter. In the Northern Hemisphere the Coriolis effect keeps nudging the moving air to its right, so the wind direction swings clockwise through the day. The gold loop is that turn seen from above. At the equator f = 0 and the breeze only blows straight in and out. Near 30° latitude the inertial period is a full day, which helps the turning stay in step with the sun.

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LAB 3

the sea-breeze front

The incoming sea air is cooler and denser, so it slides inland as a shallow wedge with a sharp leading edge, like water poured along a floor. Warm land air is shoved up over the edge. When that lift carries it past the condensation level, a line of cumulus marks the front. On a calm day the front can travel tens of miles inland by late afternoon.

one coast
4:00 pm
2 mph 14°F

How to read this: sea on the left, land to the right. The blue wedge is cool sea air sliding inland. Where its nose pushes in, warm land air is shoved up (amber arrows), and clouds form if that air rises past the dotted line.

  • cool sea air
  • gold triangle: the front's position
  • rising warm air
  • height where clouds form
  • zigzag: lightning

Try this: pick Peninsula and press Play day. The two fronts meet in the middle and set off a storm. Dew point gap is how dry the air is: smaller means more cloud.

—
Front distance inland
—
Front speed
—
Cloud base (condensation level)
—
Sky at the front

A density current (toy model)

c = Fr·√(g′·h) ∓ Uwind, g′ = g·ΔTair/T
Fr = 0.6, h = 300 m
cloud base ≈ 125 m per K of (T − Td)

The front moves like a gravity current, with ΔTair again 0.3 of Lab 1's surface difference. Fr = 0.6 sits below the ideal value to stand in for friction and mixing. A wind blowing from the land slows the west-coast front. The lift at the front is taken as , so clouds form when the cloud base is below that.

Now

Two coasts, one collision

Florida gets sea breezes from both the Gulf and the Atlantic. On many summer days the two fronts push inland, meet over the middle of the peninsula, and the doubled lift sets off thunderstorms. That is a big reason central Florida is one of the most thunderstorm-prone places in the US. Switch to Peninsula to watch them meet; the prevailing wind decides which front gets farther. The thunderstorm in the picture is qualitative.

Related: W05 · Thunderstorms and W02 · Highs & lows.

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