Meteorological measurements within Hurricane Art reveal the x direction pressure gradient acceleration apgx to be 0.0021 ms-2 and a y-direction pressure gradient acceleration apgy of 0.0026 ms-2. If the hurricane is located at 28 degrees latitude, compute the geostrophic wind velocity in ms-1

Question

Meteorological measurements within Hurricane Art reveal the x direction pressure gradient acceleration apgx to be 0.0021 ms-2 and a y-direction pressure gradient acceleration apgy of 0.0026 ms-2.  If the hurricane is located at 28 degrees latitude, compute the geostrophic wind velocity in ms-1

BlackTom AI · Accepted Answer

The problem asks for the geostrophic wind velocity given pressure-gradient accelerations in x and y directions at a latitude of 28°.

First, recall the geostrophic wind relations in the horizontal plane:
- u_g = -(1/f) * (∂p/∂y)/ρ, which in the given form corresponds to u_g = -(1/f) * a_p_y
- v_g = +(1/f) * (∂p/∂x)/ρ, which corresponds to v_g = +(1/f) * a_p_x
where a_p_x and a_p_y are the pressure-gradient accelerations provided (since apx = (1/ρ) ∂p/∂x and apy = (1/ρ) ∂p/∂y).

Second, compute the Coriolis parameter f at 28° latitude:
- Ω (Earth’s rotation rate) ≈ 7.2921 × 10^-5 s^-1
- f = 2 Ω sin(φ)
- sin(28°) ≈ 0.4695
- f ≈ 2 × 7.2921e-5 × 0.4695 ≈ 6.85 × 10^-5 s^-1

Third, plug in the given pressure-gradient accelerations:
- ap_x = 0.0021 m s^-2
- ap_y = 0.0026 m s^-2

Calculate the geostrophic wind components:
- u_g = -(1/f) × ap_y ≈ -(0.0026) / (6.85e-5) ≈ -37.96 m s^-1
- v_g = +(1/f) × ap_x ≈ (0.0021) / (6.85e-5) ≈ 30.66 m s^-1

Finally, determine the geostrophic wind speed (magnitude):
- |v_g| = sqrt(u_g^2 + v_g^2) ≈ sqrt((-37.96)^2 + (30.66)^2)
- ≈ sqrt(1440 + 940) ≈ sqrt(2380) ≈ 48.8 m s^-1

Thus, the geostrophic wind velocity magnitude is about 48.8 m s^-1, with components roughly u_g ≈ -38 m s^-1 and v_g ≈ 31 m s^-1.

EAS1600 AtmosphericPressure_StabilityHW_2025

Meteorological measurements within Hurricane Art reveal the x direction pressure gradient acceleration apgx to be 0.0021 ms-2 and a y-direction pressure gradient acceleration apgy of 0.0026 ms-2. If the hurricane is located at 28 degrees latitude, compute the geostrophic wind velocity in ms-1

查看解析

登录即可查看完整答案

类似问题

Examine the following surface isobars (purple) and wind vectors (red). In which figure is the red surface wind vector correctly drawn?

Meteorological measurements within Hurricane Art reveal the x direction pressure gradient acceleration apgx to be 0.0021 ms-2 and a y-direction pressure gradient acceleration apgy of 0.0026 ms-2. If the hurricane is located at 28 degrees latitude, compute the geostrophic wind velocity in ms-1

In a consumer society, many adults channel creativity into buying things

Economic stress and unpredictable times have resulted in a booming industry for self-help products

People born without creativity never can develop it

A product has a selling price of $20, a contribution margin ratio of 40% and fixed cost of $120,000. To make a profit of $30,000. The number of units that must be sold is: Type the number without $ and a comma. Eg: 20000

Which of the following statement regarding cost is correct:

Under the assumptions used in cost-volume-profit analysis, as the activity increases:

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单