描述性物理海洋Descriptive Physical Oceanography

我的海洋动力学知识体系My Framework for Ocean Dynamics

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我把这些知识串成一条线：先描述海水是什么状态，再问它为什么运动、怎样调整，最后用观测检验解释。公式不是孤立的记忆点，而是回答这些问题的工具。I connect the topics by first describing the ocean state, then asking what drives motion and adjustment, and finally checking explanations against observations. Equations serve these questions rather than standing alone.

难点有两个：我们站在自转的地球上看海流，而且海水是连续介质，速度、压力和密度在空间中不断变化。因此既要看受力，也要看水与周围水体之间的交换。Two challenges are that our reference frame rotates with Earth and seawater is a continuum with spatially varying velocity, pressure and density. Both forces and exchanges with surrounding water matter.

题目目录Question Contents

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海洋热量收支与混合层｜9题中英双语解析Ocean Heat Budget and Mixed Layer | Nine Bilingual Explanations

课程复习 · 中文理解 · 英文作答Course revision · Chinese explanations · English answers

使用说明：前两题对应海表热收支，后七题对应混合层、盐度、温跃层。热通量第二题以提供的 Fig. 5.14（Southampton Oceanography Centre climatology, Grist and Josey, 2003）作估读；图像清晰度有限，不能把估读值视为精确全球极值。The first two questions address the surface heat budget; the remaining seven cover the mixed layer, salinity and thermocline. Question 2 uses approximate readings from Fig. 5.14 (Southampton Oceanography Centre climatology; Grist and Josey, 2003). The limited image resolution does not support precise global extrema.

重要的符号约定Sign Convention

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本文按题目提供的 Fig. 5.14：正值表示海洋净获得热量（向下为正），负值表示海洋净失去热量（向上为负）。因此图中的 Qb、Qe、Qh 多为负；部分教科书将“海洋向大气的损失”定义为正值，不能混用。Following Fig. 5.14, positive values represent ocean heat gain (downward positive), while negative values represent ocean heat loss. Qb, Qe and Qh are therefore mostly negative. Some textbooks define upward ocean heat loss as positive; these conventions must not be mixed.

第1题 · 热通量影响因素Question 1 · Heat-flux controls

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Original question｜英文原题

What factors determine the heat budget terms, Qs, Qb, Qe and Qh, respectively? Make clear the importance of each factor of each term.

中文翻译Chinese Translation

分别有哪些因素决定短波辐射 Qs、净长波辐射 Qb、潜热通量 Qe 和感热通量 Qh？说明各因素的重要性。

知识点解析Explanation

Qs｜短波辐射：太阳高度角（纬度、季节、一天中的时间）和云量是主要控制因素；日照时数决定日平均和季节平均入射量；海面反照率决定反射比例。太阳高度角高、少云时，海洋吸收短波辐射通常更多。Qs — Shortwave radiation: Solar elevation (latitude, season and time of day) and cloud cover are the main controls. Day length affects daily and seasonal mean input, and surface albedo determines the reflected fraction. Higher solar elevation and fewer clouds generally increase absorbed shortwave radiation.

Qb｜净长波辐射：由海面向上的红外辐射和大气向下的长波辐射之差决定。SST 影响海面的向上发射（近似与绝对温度的四次方相关）；云量、大气温度和水汽含量影响向下辐射。云和水汽多时通常减弱海洋净长波热损失。Qb — Net longwave radiation: The balance between upward infrared emission from the sea surface and downward atmospheric radiation. SST controls upward emission, approximately proportional to the fourth power of absolute temperature. Clouds, air temperature and water vapour affect downward radiation; more clouds and water vapour usually reduce net ocean longwave heat loss.

Qe｜蒸发潜热：风速和海表饱和比湿与近海面空气比湿之差是直接控制因素；SST 通过提高海表饱和水汽压改变湿度差。较强风、较干空气和较暖海水通常导致更强蒸发及海洋热损失。Qe — Evaporative latent heat: Wind speed and the difference between saturation specific humidity at the sea surface and near-surface air humidity are the direct controls. SST affects this difference through saturation vapour pressure. Stronger winds, drier air and warmer water generally increase evaporation and ocean heat loss.

Qh｜感热：海气温差（SST−近海面气温）与风速为主要因素；大气稳定度也改变湍流交换效率。海面比空气暖时海洋通常损失感热；海面较冷时可得到感热。Qh — Sensible heat: Wind speed and the sea–air temperature difference are the main controls; atmospheric stability affects turbulent exchange. A warmer sea usually loses sensible heat to the air, while a colder sea can gain sensible heat.

第2题 · 通量范围与极值Question 2 · Flux ranges and extrema

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Original question｜英文原题

What are the ranges of the magnitude of the four terms? For each term, please specify the location and value of the maximum and minimum center.

中文翻译Chinese Translation

四种热通量的数值范围是多少？各自最大值和最小值中心在哪里，数值约为多少？

依据｜Fig. 5.14Basis | Fig. 5.14

依据课程提供的全球海洋年平均热通量分布图；单位均为 W/m²。该图中 a/c 等值线间隔约 50，b 为 25，d 为 15 W/m²。以下位置与数值仅为图上近似估读（尤其是 Qb、Qh）。Based on the course figure of global annual-mean ocean heat fluxes. All values are in W/m². Contour intervals are approximately 50 for panels a/c, 25 for b and 15 W/m² for d. Locations and values are approximate visual estimates, particularly for Qb and Qh.

图片来源：用户提供的课堂资料；本页解释与翻译由OpenAI Codex辅助整理，原图未由本助手生成。Image supplied by the user. OpenAI Codex assisted with interpretation and translation; the original image was not generated by this assistant.

Fig. 5.14. 全球海洋年平均热通量分布；图片由课程资料提供。Fig. 5.14. Global annual-mean ocean heat fluxes; image supplied in the course materials.

辨析：题目“maximum / minimum”按带正负号的数学大小定义。比如 Qe 最大值是接近 0 的区域，而“最强蒸发热损失”对应最小值 −200 左右。图中没有明确标注每个极值中心的精确经纬度，所以不宜虚构具体坐标。Maximum and minimum refer to signed numerical values. For Qe, the maximum occurs near zero; the strongest evaporative heat loss corresponds to a minimum of around −200. The figure does not label exact coordinates for every extremum, so precise coordinates should not be invented.

第3题 · 混合层深度Question 3 · Mixed-layer depth

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Original question｜英文原题

How deep is a typical mixed layer if mixed by wind? How deep can it reach if driven by cooling?

中文翻译Chinese Translation

风驱动形成的典型混合层有多深？如果由表面冷却驱动，混合层最深可达到多少？

知识点解析Explanation

风驱动：典型风生混合层为数十米，常用参考量级约 10–50 m；强风和风暴条件下可达到约 100 m 或更深。Wind-driven mixing: The typical depth is a few tens of metres, often about 10–50 m. Strong winds and storms can deepen the mixed layer to roughly 100 m or more.

冷却驱动：海面失热使表层海水密度增大，触发对流；冬季混合层常可达到 100–500 m，在深对流区如拉布拉多海、格陵兰海及南大洋局部，极端情况下可超过 1000 m，甚至达到约 2000 m 量级。Cooling-driven mixing: Surface heat loss increases water density and triggers convection. Winter mixed layers can commonly reach 100–500 m. In deep-convection regions such as the Labrador Sea, Greenland Sea and parts of the Southern Ocean, extreme cases can exceed 1,000 m and approach 2,000 m.

注意：深度不是固定常数，取决于原有层结、浮力通量、风与海流等。These depths are not fixed constants; they depend on existing stratification, buoyancy fluxes, winds and currents.

第4题 · 温盐垂直剖面Question 4 · Vertical temperature and salinity profiles

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Original question｜英文原题

What are the typical vertical temperature and salinity profiles in the subtropical and subpolar regions of the North Pacific?

中文翻译Chinese Translation

北太平洋副热带和副极地海区的典型温度与盐度垂直剖面分别有什么特点？

知识点解析Explanation

副热带温度：表层暖；表层混合层下有明显温跃层，温度随深度迅速下降；深层低温且变化缓慢。Subtropical temperature: Warm surface water overlies a distinct thermocline below the mixed layer, where temperature decreases rapidly. Deep water is cold and varies more slowly with depth.

副热带盐度：表层通常较咸，或在表层下出现盐度极大值；其下有较淡的中层水（如北太平洋中层水的盐度极小值），再向深层变化较小。Subtropical salinity: Surface water is often relatively saline, or there is a near-surface salinity maximum. Fresher intermediate water, such as the salinity minimum of North Pacific Intermediate Water, lies below; deeper salinity changes are smaller.

副极地温度：表面冷，温度的垂向变化一般弱于副热带；一些海区存在冷淡表层下方的次表层温度最大值或逆温结构。Subpolar temperature: Surface water is cold and the vertical temperature contrast is generally weaker than in the subtropics. Some regions have a subsurface temperature maximum or inversion below the cold, fresh surface layer.

副极地盐度：由于降水和其他淡水输入，表层较淡；盐度一般随深度增加，形成显著盐跃层，盐度分层可主导密度稳定性。Subpolar salinity: Rainfall and other freshwater inputs produce a fresh surface layer. Salinity generally increases with depth across a pronounced halocline; salinity stratification can dominate density stability.

第5题 · 净蒸发区域Question 5 · Net evaporation regions

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Original question｜英文原题

What are the dominant regions of net evaporation in the ocean?

中文翻译Chinese Translation

全球海洋哪些区域以净蒸发（蒸发量 E 大于降水量 P）为主？

知识点解析Explanation

主要位置：南北半球约 15°–35° 的副热带海域，尤其副热带高压带下少云、降水较少的海区，包括副热带北大西洋、南大西洋、南印度洋及太平洋大范围海域。Main regions: Subtropical oceans at roughly 15°–35° in both hemispheres, especially low-rainfall, relatively cloud-free areas beneath subtropical highs. These include large areas of the North and South Atlantic, southern Indian Ocean and Pacific.

成因：副热带下沉气流抑制降水，信风及较暖水温有利于蒸发；因此 E−P > 0。Mechanism: Subtropical descending air suppresses rainfall, while trade winds and warm water favour evaporation. Consequently, E−P > 0.

对比：赤道辐合带（ITCZ）和很多高纬区域通常净降水更显著，不能把“潜热损失强”与“净蒸发最大”直接等同。Contrast: The ITCZ and many high-latitude regions are dominated by net precipitation. Strong latent heat loss is not necessarily the same as the greatest net evaporation.

第6题 · 混合层热收支Question 6 · Mixed-layer heat budget

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Original question｜英文原题

What are the key components of the Mixed Layer heat budget?

中文翻译Chinese Translation

海洋混合层热收支的主要组成部分有哪些？

知识点解析Explanation

海表净热通量：太阳短波、净长波、潜热和感热四项之和，即 Qnet = Qs + Qb + Qe + Qh（按本题向海洋为正）。Net surface heat flux: The sum of shortwave, net longwave, latent and sensible heat fluxes: Qnet = Qs + Qb + Qe + Qh, with positive values directed into the ocean.

水平平流：海流输送不同温度的水，造成混合层增暖或降温。Horizontal advection: Currents transport water of different temperatures, warming or cooling the mixed layer.

底部交换：混合层底部的卷入（entrainment）、湍流扩散和垂向平流将上下层热量相互交换。Exchange at the base: Entrainment, turbulent diffusion and vertical advection exchange heat between the mixed layer and deeper water.

混合层深度变化：混合层深度 h 变化影响相同热通量造成的温度变化幅度；还有太阳短波穿透到混合层底以下的能量需要扣除。Changing mixed-layer depth: Depth h affects the temperature response to a given heat flux. Shortwave energy penetrating below the mixed-layer base must also be excluded from the heat retained in the layer.

第7题 · 大西洋与太平洋盐度Question 7 · Atlantic and Pacific salinity

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Original question｜英文原题

Is the North Atlantic Ocean saltier or fresher on average than the Pacific? Why?

中文翻译Chinese Translation

北大西洋平均而言比太平洋更咸还是更淡？为什么？

知识点解析Explanation

结论：北大西洋总体上比北太平洋更咸，尤其在副热带及高纬北大西洋很明显。Conclusion: The North Atlantic is generally saltier than the North Pacific, particularly in subtropical and high-latitude North Atlantic regions.

原因一：大西洋流域总体蒸发相对于降水和径流更强，且水汽可通过大气向太平洋及其他流域输送，相当于从大西洋移走淡水。Reason 1: Evaporation is stronger relative to rainfall and runoff in the Atlantic basin. Atmospheric moisture transport to the Pacific and other basins effectively exports freshwater from the Atlantic.

原因二：较咸的表层海水在北大西洋高纬冷却后可变得足够密，利于深水形成，是大西洋经向翻转环流的重要条件；这是与盐度分布相关的环流反馈，而不是唯一成因。Reason 2: Saline surface water can become sufficiently dense when cooled at high northern latitudes, facilitating deep-water formation and the Atlantic overturning circulation. This is a circulation feedback associated with salinity, rather than its sole cause.

第8题 · 季节变化Question 8 · Seasonal variability

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Original question｜英文原题

What regions of the ocean are characterized by large differences from summer to winter? What regions have the least seasonal variability?

中文翻译Chinese Translation

全球海洋哪些海域夏冬差异最大？哪些海域季节变化最小？

知识点解析Explanation

季节变化大：中高纬度海洋，尤其北半球中纬度西边界流区及其延伸区（湾流、黑潮）和北大西洋、北太平洋的部分海域；表层温度、海气热通量和混合层深度的季节对比突出。Large seasonal changes: Mid- and high-latitude oceans, especially Northern Hemisphere western boundary currents and their extensions (Gulf Stream and Kuroshio), and parts of the North Atlantic and North Pacific. SST, air–sea heat flux and mixed-layer depth show strong seasonal contrasts.

季节变化小：赤道附近和低纬热带开阔海域，由于全年太阳高度角与日长的季节差异较小，海表温度的季节循环通常较弱。Small seasonal changes: Equatorial and tropical open oceans, where seasonal changes in solar elevation and day length are smaller; the SST seasonal cycle is generally weaker.

限定：如讨论的是混合层深度，热带仍有风、降水和 ENSO 等变化；如果讨论温度，季风海区和强上升流区也会有明显季节性。Qualifications: Tropical mixed-layer depth still responds to winds, rainfall and ENSO. Monsoon regions and strong upwelling regions can also exhibit substantial seasonal temperature changes.

第9题 · 温跃层维持机制Question 9 · Thermocline maintenance

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Original question｜英文原题

Please describe the two processes that maintain the thermocline.

中文翻译Chinese Translation

请描述维持温跃层的两种主要过程。

知识点解析Explanation

过程一｜表面加热与浮力层结：太阳辐射加热表层，使暖而轻的水覆盖冷而密的下层水；较稳定的密度层结限制垂直混合，形成或强化上部温跃层，季节性温跃层尤其明显。Process 1 — Surface heating and buoyancy stratification: Solar heating places warm, light water above cold, dense water. Stable density stratification restricts vertical mixing and forms or strengthens the upper thermocline, especially the seasonal thermocline.

过程二｜风驱动环流与水体潜沉：副热带环流中的 Ekman 辐合与下沉，以及露出海面的密度面上水团的冬季通气、侧向输送和潜沉（subduction），将表面形成的温度/密度结构带入海洋内部，帮助维持大尺度永久温跃层。Process 2 — Wind-driven circulation and subduction: Ekman convergence and downwelling in subtropical gyres, together with winter ventilation, lateral transport and subduction along outcropping density surfaces, carry surface temperature and density structures into the ocean interior and help maintain the permanent thermocline.

维持平衡：从更长期的观点看，内部上升流、湍流/跨密度面混合及平流共同调节温跃层深度和形态。这里两条分别强调“热力分层”与“风驱动动力过程”。Long-term balance: Interior upwelling, turbulent/diapycnal mixing and advection jointly regulate thermocline depth and shape. The two processes above emphasize thermal stratification and wind-driven dynamics.

速记与答题提醒Revision Notes

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① 按给定图的符号：Qs 多为正，Qb/Qe/Qh 多为负。② 潜热损失的“绝对值最大”与“带符号的最小值”是同一强蒸发位置。③ 净蒸发看 E−P，不等同于 Qe 的极值。④ 风混合通常数十米；冬季深对流可达数百至千米以上。⑤ 混合层热收支不只有海气热通量，还包括海流平流与混合层底部交换。1. With this sign convention, Qs is mainly positive and Qb/Qe/Qh mainly negative. 2. Maximum latent heat-loss magnitude corresponds to the most negative signed flux. 3. Net evaporation depends on E−P, not simply on extrema of Qe. 4. Wind mixing usually reaches tens of metres; winter deep convection can reach hundreds to over a thousand metres. 5. The mixed-layer heat budget also includes current advection and exchange at the layer base.

参考图：Grist, J. P. & Josey, S. A. (2003), Southampton Oceanography Centre air–sea flux climatology（图由课程材料提供，原图题为 Annual average heat fluxes）。极值位置是依据所提供的低分辨率图片估读。Reference figure: Grist, J. P. & Josey, S. A. (2003), Southampton Oceanography Centre air–sea flux climatology. The course-supplied figure is titled Annual average heat fluxes. Extremum locations are estimated from the low-resolution image.

数据分析的四类基本概念与方法Four Basic Concepts and Methods of Data Analysis

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以下结合海洋学例子，说明基础统计、时间序列分析、客观分析和 EOF 分析各自解决的问题。Oceanographic examples illustrate the different questions addressed by statistics, time-series analysis, objective analysis and EOF analysis.

1. Basic concepts · 基础统计概念

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用来描述数据的平均状态、波动大小，以及不同变量之间的关系。These concepts describe average conditions, the magnitude of variability, and relationships between variables.

• 随机误差（random error）：测量结果不规则地偏高或偏低。例如，同一水温反复测量得到略有不同的结果。独立重复测量取平均通常能减小它的影响。Random error: Irregular positive or negative measurement deviations. Repeated measurements of the same water temperature may differ slightly. Averaging independent measurements generally reduces its influence.
• 系统误差（systematic error）：测量存在持续的偏差。例如，温度计总是高出真实值 0.5°C。多测几次取平均也不能消除，需要校准。Systematic error: A persistent measurement bias, such as a thermometer always reading 0.5°C too high. Repeated averaging does not remove it; calibration is required.
• 均值（mean）：数据的平均水平，例如某海域的年平均海温。Mean: The average level of the data, such as annual-mean sea temperature in a region.
• 方差（variance）：数据偏离均值的平方的平均，表示波动大小。总体方差用总体大小作分母；样本方差的常见无偏估计使用 n−1。Variance: The mean squared deviation from the mean, measuring variability. Population variance uses the population size as the denominator; the usual unbiased sample estimate uses n−1.
• 标准差（standard deviation）：方差的平方根，与原数据单位相同，更方便理解波动幅度。Standard deviation: The square root of variance. It has the same units as the original data and is easier to interpret.
• 协方差（covariance）：两个变量是否倾向于一起变化。正值表示通常同增同减，负值表示通常一个增、另一个减。Covariance: Whether two variables tend to vary together. Positive values indicate same-direction variation; negative values indicate opposite-direction variation.
• 相关系数（correlation）：标准化后的协方差，通常指皮尔逊相关系数，范围为 [−1, 1]，衡量线性关系的方向和强弱。相关不代表因果；零相关也不一定意味着没有非线性关系。Correlation: Standardized covariance, usually Pearson correlation, ranging from −1 to 1 and measuring linear association. Correlation does not imply causation, and zero correlation does not rule out nonlinear relationships.

2. Time series analysis · 时间序列分析

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研究一个变量如何随时间变化，例如某海域连续几十年的月平均海温。可以研究趋势、周期、时间上的关联等。Time-series analysis studies how a variable changes over time, such as decades of monthly SST. It examines trends, cycles and temporal relationships.

课件重点讲的是其中的频谱分析：把复杂变化分解成不同频率的成分，判断哪些周期最明显。频谱分析是时间序列分析的一种方法，二者不能完全等同。Spectral analysis separates complex variability into frequency components to identify dominant periods. It is one method within time-series analysis, not an exact synonym for it.

• 一年周期：季节变化。Annual cycle: Seasonal changes.
• 一天周期：昼夜变化。Daily cycle: Day–night changes.
• 数年尺度变化：与 ENSO 等过程有关，不一定具有严格固定的周期。Multi-year variability: Processes such as ENSO, which need not have a strictly fixed period.

频率 f 表示单位时间内变化多少次，周期 T 表示一次变化需要多久，二者满足 T = 1/f。分析空间变化时，可以用波数描述空间上的起伏频繁程度，对应波长。Frequency f is the number of cycles per unit time; period T is the duration of one cycle, with T = 1/f. Spatial variations can be described by wavenumber and wavelength.

红谱：低频、缓慢变化的功率较大。白谱：功率谱密度在各频率上大致相同。谱的形状可以帮助理解变化背后的物理过程，但不能单凭谱形确定唯一机制。Red spectrum: Greater power at low frequencies and slow variations. White spectrum: Approximately constant power spectral density across frequencies. Spectral shape can inform physical interpretation but does not uniquely identify a mechanism.

3. Multi-dimensional data analysis · 多维数据分析

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多维数据可以同时涉及经度、纬度、深度和时间。课件在这里主要介绍客观分析（objective analysis）：将分布不规则的观测转换成规则网格上的估计值。Multidimensional data may involve longitude, latitude, depth and time. Here, objective analysis estimates values on a regular grid from irregularly distributed observations.

例如，船舶只在部分位置测量了海温，但我们希望得到完整的海温地图，就需要估计没有观测的网格点。估计时会考虑：For example, ships sample temperature at only some locations, but a complete map requires estimates at unobserved grid points. The analysis considers:

• 空间相关尺度：相隔多远的观测仍能提供有用信息。Spatial correlation scale: How far away an observation still provides useful information.
• 观测噪声：测量有多可靠。Observation noise: How reliable each measurement is.
• 观测之间的关系：避免把高度重复的信息算得过重。Relationships among observations: Avoiding excessive weight on highly redundant information.

最终估计常表现为附近观测的加权组合；有背景场时，通常是对观测与背景之差进行加权修正。因此，它不只是简单取最近几个点的平均。An estimate often takes the form of a weighted combination of nearby observations. When a background field is available, weighted observation-minus-background differences provide corrections. This is more than simply averaging the nearest points.

4. Empirical Orthogonal Functions · 经验正交函数分析

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EOF 从大量时空数据中提取主要空间变化模式及其随时间变化的强度。在常见设置下，它对应主成分分析（PCA）。EOF analysis extracts dominant spatial patterns and their time-varying amplitudes from a spatiotemporal dataset. Under common settings it corresponds to principal component analysis (PCA).

例如，分析太平洋多年海温数据，先减去各位置的时间平均海温，得到异常，再将其近似表示为：For a multi-year Pacific temperature dataset, first subtract the temporal mean at each location to obtain anomalies. These can then be approximated as:

T′(x, t) ≈ ∑_k EOF_k(x) · PC_k(t)

• EOF_k(x)：空间模式。描述哪些区域一起变暖，哪些区域一起变冷。EOF_k(x): Spatial pattern, indicating which regions warm or cool together.
• PC_k(t)：时间系数。描述这个模式何时增强、减弱或反向。PC_k(t): Time coefficient, describing when a pattern strengthens, weakens or reverses.
• 第一模态：解释的数据方差最多；之后的模态依次解释剩余方差。The first mode explains the most variance; later modes explain successively smaller portions of the remaining variance.

“经验”表示模式由实际数据提取，而不是预先指定为正弦波等数学函数；“正交”表示不同空间模式在采用的内积下互相正交。实际海洋网格分析常需要考虑面积权重。Empirical means that the patterns are derived from data rather than prescribed mathematical functions. Orthogonal means the spatial modes have zero inner product under the chosen metric. Ocean grid analyses often require area weighting.

EOF 模式可能对应 ENSO 等物理过程，但方差最大的模式不一定就是某个独立的物理机制。EOF/PCA 与因子分析并不严格等同。EOF patterns may be associated with physical processes such as ENSO, but the mode explaining the most variance is not necessarily an independent physical mechanism. EOF/PCA and factor analysis are not strictly identical.

动画：空间模式 × 时间系数Animation: Spatial Patterns × Time Coefficients

47 秒动画使用 8 个位置、120 个时刻的合成海温异常数据，演示两个 EOF 模式如何随时间系数变化而叠加重建。两个模式分别解释 80% 和 20% 的方差；这是为教学构造的例子，并非实际海洋观测。This 47-second animation uses synthetic temperature anomalies at eight locations and 120 times. Two modes explain 80% and 20% of variance and combine with changing time coefficients to reconstruct the data. It is a teaching example, not actual ocean observations.

动画制作：OpenAI Codex生成及修改Python脚本，Manim Community渲染。中英双语屏幕文字由Codex辅助撰写；无配音，内容为理想化教学示意。Animation: Python scripts generated and revised with OpenAI Codex, rendered with Manim Community. Bilingual text was AI-assisted. Idealized teaching illustration, without narration.

下载 EOF 动画（MP4） · 中文画面说明，无配音。Download EOF animation (MP4) · Chinese on-screen explanations; no narration.

四类方法分别回答什么？What Question Does Each Method Answer?

海洋热通量Ocean Heat Fluxes

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1. 热通量是什么？ / What is heat flux?

热通量表示单位时间穿过单位面积的热能，单位为 W/m²，即 J/(s·m²)。它描述热量传递的速率，不是温度，也不是总热量。通量乘以面积和持续时间才得到传递的能量。Heat flux is the rate of heat transfer per unit area, measured in W/m² or J/(s·m²). It is neither temperature nor total heat. Multiplying a uniform, constant flux by area and duration gives the transferred energy.

本站统一约定：向海洋为正。Q > 0 表示海洋获得热量，Q < 0 表示海洋失去热量。不同数据集可能采用不同方向，下载数据后要先检查定义和单位。Throughout this site, positive flux is into the ocean: Q > 0 is ocean heat gain and Q < 0 is heat loss. Dataset conventions vary; check direction and units before combining terms.

示意图制作：OpenAI Codex辅助编写Python绘图代码，使用Matplotlib渲染；为教学模型或示意，不是真实观测。OpenAI Codex assisted with Python/Matplotlib code. This is a teaching model or illustration, not an observation.

2. 四项表面热通量 / Four surface heat-flux terms

短波辐射 Qs：主要来自太阳。净短波是到达海面的向下短波减去反射部分，受太阳高度角、日长、云和海面反照率影响；一部分能穿透到混合层以下。Shortwave radiation Qs: Mainly solar energy. Net shortwave equals incoming radiation minus reflection. Solar elevation, day length, clouds and surface albedo matter. Some radiation penetrates below the mixed layer.

净长波辐射 Qb：是大气向下长波与海面向上红外发射之差，常使海洋失热。海温越高，向上发射通常越强；温暖、湿润、多云的大气往往增强向下辐射。Net longwave radiation Qb: Downward atmospheric longwave minus upward ocean infrared emission; it often cools the ocean. Warmer seas emit more, while warm, moist and cloudy atmospheres tend to increase downward radiation.

潜热通量 Qe：水蒸发时吸收能量，通常使海洋失热。关键因素是风速和海面饱和比湿与空气比湿之差；海温会通过饱和比湿影响蒸发。在凝结条件下，方向可能反转。Latent heat flux Qe: Evaporation consumes energy and usually cools the sea. Wind and the sea-surface saturation-to-air humidity difference are key controls; SST influences saturation humidity. Condensation can reverse the direction.

感热通量 Qh：由海气温差引起的湍流热交换。海水比空气暖时，通常向空气放热；空气更暖时可向海水供热。风速与大气稳定度影响交换效率。Sensible heat flux Qh: Turbulent heat exchange associated with the sea–air temperature difference. A warmer sea typically heats the air; warmer air can heat the sea. Wind and atmospheric stability affect exchange efficiency.

3. 符号、公式与热量平衡 / Signs, equations and balance

Qnet = Qs + Qb + Qe + Qh

这里四项都已转换为向下为正。如果某资料将长波、潜热和感热的向上损失记为正值 L、E、H，则应写成 Qnet = Qs − L − E − H，不能把两种约定混在同一公式里。All four terms above use downward-positive signs. If a source instead reports upward-positive longwave, latent and sensible losses L, E and H, use Qnet = Qs − L − E − H. Do not mix conventions.

示意图制作：OpenAI Codex辅助编写Python绘图代码，使用Matplotlib渲染；为教学模型或示意，不是真实观测。OpenAI Codex assisted with Python/Matplotlib code. This is a teaching model or illustration, not an observation.

4. 为什么同样加热，海温反应不同？ / Why does temperature respond differently?

在混合层厚度 h 固定、层内温度均匀，且忽略平流、底部交换和短波穿透的理想条件下：For a fixed-depth, uniformly mixed layer, neglecting advection, exchange at the base and penetrating shortwave radiation:

ΔT = Qnet · Δt / (ρ · cp · h)

ρ 是海水密度，cp 是比热容，h 是混合层厚度。相同热量分配给越薄的水层，温度变化就越大。下图假设持续 +100 W/m²，ρ = 1025 kg/m³、cp = 3990 J/(kg·K)：30 天后，10 米水层升温约 6.34°C，50 米水层约 1.27°C。Here ρ is seawater density, cp is specific heat capacity and h is layer depth. The same heat input warms a thinner layer more. With a constant +100 W/m², ρ = 1025 kg/m³ and cp = 3990 J/(kg·K), the 30-day increases are about 6.34°C for 10 m and 1.27°C for 50 m.

示意图制作：OpenAI Codex辅助编写Python绘图代码，使用Matplotlib渲染；为教学模型或示意，不是真实观测。OpenAI Codex assisted with Python/Matplotlib code. This is a teaching model or illustration, not an observation.

5. 完整混合层热收支 / The full mixed-layer heat budget

净表面通量为正不保证海温立即上升：冷水平流、卷入深层冷水或底部混合都可能抵消加热。计算混合层吸收的热量时，还应从表面净热通量中扣除穿透混合层底部的短波。混合层加深也会改变温度和储热量的关系。Positive surface flux does not guarantee immediate warming: cold-water advection, entrainment and mixing at the base can offset heating. Shortwave radiation passing through the layer base must be subtracted when calculating heat retained by the mixed layer. Deepening also changes the relationship between temperature and heat storage.

6. 观测与数据使用 / Observations and data use

辐射可用辐射计观测；潜热、感热常利用风速、海温、气温和湿度通过海气通量算法估计。常规 Argo 主要测量温盐压力剖面，不能仅靠它直接得到全部表面热通量。使用浮标、卫星或再分析资料时，要核对质量标记、时间平均、空间分辨率及“通量”还是“累计能量”；J/m² 需要除以对应的秒数才能转换为该时段平均 W/m²。Radiometers measure radiation; latent and sensible fluxes are often estimated with bulk algorithms using wind, SST, air temperature and humidity. Standard Argo profiles alone do not directly provide all surface fluxes. Check quality flags, temporal averaging, resolution and whether a variable is flux or accumulated energy. Divide J/m² by the matching accumulation duration in seconds to obtain mean W/m².

参考资料 / References

• NASA PO.DAAC — Ocean Heat Budget
• Cronin & McPhaden — Upper ocean heat balance (NOAA PMEL)
• NOAA PMEL — Ocean Station Papa flux metadata

本节三图由 Python / Matplotlib 生成。示例参数与假设已在正文及图注中列出。All three figures were generated with Python / Matplotlib. Example parameters and assumptions are stated above and in the captions.

海流动力学：从漂流瓶到地转平衡Ocean Current Dynamics: From an Ideal Drifter to Geostrophic Balance

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本节整理科氏力、离心力、理想漂流模型、地转流及近惯性观测。动图是理想模型；后面的地图使用真实观测处理产品，两者用途不同。This section covers Coriolis and centrifugal effects, ideal drifters, geostrophic balance and near-inertial observations. The animation is an idealized model; the maps use processed observations.

1. 科氏力 / Coriolis force

在随地球旋转的参考系中，运动水团受到科氏加速度 aC = −2Ω × u。海洋大尺度水平运动常使用其水平近似 aC = −f k × u，其中 f = 2Ω sinφ，φ 为纬度，k 为竖直单位向量。科氏力与相对流速垂直，北半球使运动向右偏，南半球向左偏；它本身不对水团做功。In the Earth-rotating frame, a moving parcel experiences Coriolis acceleration aC = −2Ω × u. The usual horizontal approximation is aC = −f k × u, with f = 2Ω sinφ. It deflects motion to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. Being perpendicular to velocity, it does no work on the parcel.

“向右偏”是相对于水团当前运动方向而言，不是固定向东或向西。f 在赤道为零、向两极绝对值增大；常规地转公式不能在赤道直接除以 f。Right or left is relative to the parcel’s direction of travel, not a fixed compass direction. The magnitude of f increases poleward and is zero at the equator, where the conventional geostrophic formulas cannot be used by division by f.

2. 离心力与向心加速度 / Centrifugal force and centripetal acceleration

地球自转参考系的离心加速度为 −Ω × (Ω × r)，方向远离自转轴，即使水团相对地球静止也存在。它与引力合成有效重力，海洋方程中的 g 通常已包含这一背景影响，不能再重复加一次。Earth-frame centrifugal acceleration, −Ω × (Ω × r), points away from the rotation axis and exists even for a parcel at rest relative to Earth. Together with gravitational attraction it forms effective gravity; the usual oceanographic g already incorporates this background effect.

弯曲流线的向心加速度大小为 U²/R，指向曲率中心。若在随流弯曲的参考系描述，也会引入向外的离心惯性项，但不能与地球自转的离心项混淆。曲率效应不可忽略时，应考虑梯度流平衡，而不能只用最简单的地转平衡。Centripetal acceleration of a curved trajectory has magnitude U²/R and points toward the curvature centre. An outward centrifugal term may be introduced in a frame following that curved motion; it is distinct from Earth’s background centrifugal acceleration. Significant curvature requires gradient-wind/current balance rather than the simplest geostrophic balance.

3. 漂流瓶假设：理想水团与真实浮标 / Ideal drifter assumptions

这里将“漂流瓶假设”用作教学中的理想示踪粒子模型，并非一个统一的标准定律：瓶子足够小、完全随周围水流运动，忽略自身惯性、直接风拖曳、波浪漂移和与水体的滑移。于是 dx/dt = u，dy/dt = v，轨迹用来表示局地水团运动。Here “drifting-bottle assumption” means an ideal passive-tracer model, not a universally named law: a small tracer follows the surrounding water exactly, neglecting its own inertia, direct wind drag, wave drift and slip relative to water. Thus dx/dt = u and dy/dt = v describe its path.

真实漂流瓶露出水面的部分会受风，轨迹也可能包含波浪斯托克斯漂移；带水帆浮标能减少风滑移，但仍需质量控制。因此“漂流瓶路径”等于“地转流路径”通常不成立。真实轨迹可叠加地转流、风生流、潮流和近惯性运动。Real bottles can be directly wind-driven and affected by wave-induced Stokes drift. Drogued drifters reduce wind slip but still require quality control. A drifter track is not automatically a geostrophic streamline: geostrophic, wind-driven, tidal and near-inertial components may all contribute.

4. 无压强梯度时：惯性振荡 / With no pressure gradient: inertial oscillations

在水平无压强梯度、无摩擦、无持续风应力，且 f 为常数的理想情形，运动方程为 du/dt = fv、dv/dt = −fu。水团保持恒定速率，速度方向不断旋转：北半球顺时针、南半球逆时针。周期 T = 2π/|f|，半径 R = U/|f|；45°纬度的周期约为 16.9 小时。With no horizontal pressure gradient, friction or continuing wind stress, and constant f, du/dt = fv and dv/dt = −fu. Speed stays constant while velocity rotates clockwise in the Northern Hemisphere and anticlockwise in the Southern Hemisphere. The period is T = 2π/|f| and radius R = U/|f|; at 45° latitude the period is about 16.9 hours.

这是惯性运动，不是地转平衡。真实海洋的近惯性运动可与背景流叠加并以内部波形式传播，轨迹未必是闭合圆。This is inertial motion, not geostrophic balance. In the real ocean, near-inertial motions combine with background currents and can propagate as internal waves; trajectories need not form closed circles.

5. 有压强梯度时：地转平衡 / With a pressure gradient: geostrophic balance

大尺度、缓慢变化、远离赤道且摩擦较弱的流动，水平压强梯度力可近似与科氏力抵消。此时流速沿等压线方向，而不是直接从高压流向低压。小罗斯贝数 Ro = U/(|f|L) ≪ 1 是常用适用条件之一；边界层、强曲率涡旋和快速变化过程可能偏离地转近似。For large-scale, slowly varying flow away from the equator with weak friction, the horizontal pressure-gradient and Coriolis forces can approximately balance. Flow is along isobars rather than directly from high to low pressure. A small Rossby number, Ro = U/(|f|L) ≪ 1, supports the approximation; boundary layers, strongly curved eddies and rapid transients can depart from it.

f k × ug = −∇h p / ρ

在 x 向东、y 向北，海面高度为 η 的简化情形下：With x eastward, y northward and sea-surface height η, the simplified surface expressions are:

ug = −(g/f) ∂η/∂y  ；  vg = (g/f) ∂η/∂x

北半球沿流向看，高海面在右侧；南半球则在左侧。这些是海面坡度对应的表面地转流关系；海洋内部密度水平差异也能产生随深度变化的压强梯度与地转流。Looking downstream, high sea level lies on the right in the Northern Hemisphere and on the left in the Southern Hemisphere. These formulas relate surface slope to surface geostrophic flow; internal horizontal density differences also generate depth-dependent pressure gradients and geostrophic currents.

6. 地转流动图 / Animated geostrophic balance

示意图制作：OpenAI Codex辅助编写Python绘图代码，使用Matplotlib渲染；为教学模型或示意，不是真实观测。OpenAI Codex assisted with Python/Matplotlib code. This is a teaching model or illustration, not an observation.

下载动图 / Download GIF · 查看静态图 / View still image

7. 真实观测地图 / Maps from real observations

以下是近惯性运动图，不能作为地转流能量图。只重绘作者公开的处理产品，没有独立重跑原始浮标轨迹的全部分析，也没有使用模拟数据填补观测缺测。These maps describe near-inertial motion, not geostrophic-current energy. They replot public author-processed products; the full raw-trajectory analyses were not independently rerun, and missing observations were not filled with synthetic data.

图表制作：OpenAI Codex辅助编写Python代码，使用Matplotlib与Cartopy重绘公开观测处理产品；数据来源见原图说明，不是AI合成观测。OpenAI Codex assisted with Python plotting code using Matplotlib and Cartopy. Public observational products were replotted, not synthesized.

图表制作：OpenAI Codex辅助编写Python代码，使用Matplotlib与Cartopy重绘公开观测处理产品；数据来源见原图说明，不是AI合成观测。OpenAI Codex assisted with Python plotting code using Matplotlib and Cartopy. Public observational products were replotted, not synthesized.

与最初参考图的区别：参考图是全球混合层面积能量 J/m²；这里分别是区域单位质量动能与全球流速，不能直接比较颜色值。若假设混合层内近惯性流垂向均匀，可用 Earea = ρh KE 转成面积能量，但还需匹配密度、混合层厚度及取样条件；这里未任意指定 h。The reference slide shows global mixed-layer energy per area (J/m²); these products show regional energy per mass and global speed. Their color values are not directly comparable. Under a vertically uniform mixed-layer assumption, Earea = ρh KE, but matching density, layer depth and sampling are required. No arbitrary h was imposed here.

8. 与热通量的关系 / Connection to heat fluxes

表面加热、冷却改变海水密度和混合层深度，进而影响层结、水平压强梯度及地转流的垂向切变；风应力可以激发近惯性运动，相关剪切和混合又会影响海温。风应力不是热通量，科氏力也不是热源。单位为 J/m² 的能量与 W/m² 的热通量并不是同一物理量。Surface heating and cooling alter density, mixed-layer depth and stratification, affecting horizontal pressure gradients and vertical geostrophic shear. Wind stress can excite near-inertial motion; associated shear and mixing can in turn affect temperature. Wind stress is not heat flux, and Coriolis force is not a heat source. Energy in J/m² differs from heat flux in W/m².

9. 湾流剖面图：怎样判断流向？9. Gulf Stream section: how do we determine the flow direction?

图片来源：用户提供的课堂资料；本页解释与翻译由OpenAI Codex辅助整理，原图未由本助手生成。Image supplied by the user. OpenAI Codex assisted with interpretation and translation; the original image was not generated by this assistant.

先看剖面方向：图(a)横轴从左侧约38°N到右侧40°N，因此左侧偏南、右侧偏北；A在B的南侧。图是跨越湾流的垂直剖面，流速主要垂直于剖面，不能把右侧速度曲线误读为水沿剖面向右流。First establish the section orientation: panel (a) runs from roughly 38°N on the left to 40°N on the right, so A is south of B. This is a cross-stream vertical section. The current is primarily normal to the section; the rightward velocity curve does not mean water flows rightward along the section.

图(a)、(b)：上层A侧同一深度的海水较轻，比容异常较大；B侧较密，比容异常较小。等密度线向北（向右）抬升，显示明显的水平密度差。图中26—27.88这样的标值应理解为位密度异常，不能当成海水实际密度只有约27 kg/m³。Panels (a) and (b): in the upper ocean, A has lighter water and a larger specific-volume anomaly than B at the same depth. Isopycnals rise northward (to the right), indicating a horizontal density contrast. Labels such as 26–27.88 represent potential-density anomaly, not an actual seawater density of about 27 kg/m³.

图(c)：在相同参考压力下向上积分比容异常，A上层的动力高度高于B。因此上层动力高度由南向北减小，对应向北的水平压强梯度力。动力高度是由水文剖面积分得到的量，并不直接等于卫星测得的海面高度。Panel (c): integrating specific-volume anomaly upward from a common reference pressure gives greater upper-ocean dynamic height at A than at B. Dynamic height decreases northward, implying a northward pressure-gradient force in the upper ocean. Dynamic height is derived from hydrographic integration and is not simply satellite-measured sea-surface height.

流向结论：北半球f>0，取x向东、y向北，u_g=−(1/f)∂D/∂y，其中D为动力位势异常。由∂D/∂y<0得到u_g>0：在近似南北剖面下，流动向东。其右侧（南侧A）动力高度高，左侧（北侧B）低；向东流对应向南的科氏力，恰与向北的压强梯度力平衡。实际湾流在此区域常向东北流；精确方位需结合站位经纬度和剖面朝向，单凭这张图不能唯一确定东北偏角。Direction: in the Northern Hemisphere f>0. With x eastward and y northward, u_g=−(1/f)∂D/∂y, where D is dynamic geopotential anomaly. Since ∂D/∂y<0, u_g>0: an approximately north–south section implies eastward flow. Higher dynamic height lies on its right (south, A); the southward Coriolis force balances the northward pressure-gradient force. The actual Gulf Stream often flows northeastward here, but an exact bearing requires station coordinates and section orientation.

图(d)：曲线显示上层流速最大，表层约90 cm/s，向深处明显减弱。这是从图上估读的数量级。水文资料首先给出相对于参考层的地转流；若未提供参考层的绝对流速，不能把整条曲线无条件称为绝对流速，也不能仅凭深层接近零断言深海完全静止。Panel (d): speed is strongest near the surface, approximately 90 cm/s by visual reading, and weakens with depth. Hydrography initially provides geostrophic velocity relative to a reference level. Without its absolute velocity, the profile cannot unconditionally be treated as absolute flow, and a near-zero deep value does not prove that the deep ocean is motionless.

参考阅读 / Further reading: Descriptive Physical Oceanography — Geostrophic circulation

资料与来源 / References and data sources

• NOAA — The Coriolis Effect
• NOAA — Glossary: geostrophic flow
• Laxenaire et al. — SEANOE gridded spectra and KE product
• Zheng — Near-inertial currents replication archive
• Elipot et al. (2010) — Reference study

环流概念补充Circulation Concepts

AI辅助整理：OpenAI Codex｜本节的解释、中文改写、英文翻译或网页编排含AI生成内容；引用资料及用户原始材料不因此变为AI生成。AI assistance: OpenAI Codex. Explanations, rewriting, English translation or layout include AI-generated work; cited and supplied source materials retain their own provenance.

重力波波速与频散：两页课件解读Gravity-wave Speed and Dispersion

AI辅助整理：OpenAI Codex｜本节的解释、中文改写、英文翻译或网页编排含AI生成内容；引用资料及用户原始材料不因此变为AI生成。AI assistance: OpenAI Codex. Explanations, rewriting, English translation or layout include AI-generated work; cited and supplied source materials retain their own provenance.

这里讨论线性表面重力波，忽略表面张力、旋转与背景流。相速度C是波峰移动速度；群速度Cg描述波包与能量传播，两者不能混用。These are linear surface gravity waves without surface tension, rotation or mean flow. Phase speed C tracks crests; group speed Cg describes wave packets and energy propagation.

符号：k=2π/L，ω=2π/T；L为波长，T为周期，h为水深。完整关系为ω²=gk tanh(kh)，C=ω/k=√[(g/k)tanh(kh)]。Definitions: k=2π/L, ω=2π/T; L is wavelength, T period and h depth. Dispersion: ω²=gk tanh(kh); C=ω/k=√[(g/k)tanh(kh)].

深水条件通常取h>L/2：tanh(kh)≈1，所以C≈√(g/k)=√(gL/2π)。波速近似不依赖水深，波长越长速度越快，因此频散。For deep water, commonly h>L/2, tanh(kh)≈1. Thus C≈√(g/k)=√(gL/2π): longer waves travel faster, with little depth dependence.

浅水条件通常取h<L/20：tanh(kh)≈kh，所以C≈√(gh)。同一水深下，波速近似不依赖波长，因此在该理想极限中无频散。深浅是相对波长而言，几千米深的大洋也可能满足海啸的浅水条件。For shallow water, commonly h<L/20, tanh(kh)≈kh and C≈√(gh). At fixed depth the ideal limit is nondispersive. Depth is relative to wavelength; even a deep ocean may be shallow for a tsunami.

风暴生成不同周期的波。离开主要风区后，不同成分按传播速度逐渐分离，远处的涌浪往往较规则。讨论到达顺序应使用群速度：Cg=dω/dk；深水重力波Cg=C/2=gT/(4π)，长周期波群通常先到。Storms generate many periods. After leaving the forcing region, components separate by speed, producing more regular distant swell. Arrival times use group speed: Cg=dω/dk; for deep-water gravity waves Cg=C/2=gT/(4π), so longer-period groups generally arrive first.

有限水深下Cg=(C/2)[1+2kh/sinh(2kh)]；浅水极限Cg≈C。第一张课件的“长波”指相对水深很长，第二张说“长波更快”是在深水重力波之间比较，不能推广到所有波。At finite depth Cg=(C/2)[1+2kh/sinh(2kh)], approaching C in shallow water. “Long wave” in the first slide is relative to depth; the second compares wavelengths in deep-water gravity waves, not every wave type.

海洋波动：七道思考题Ocean Waves: Seven Review Questions

AI辅助整理：OpenAI Codex｜本节的解释、中文改写、英文翻译或网页编排含AI生成内容；引用资料及用户原始材料不因此变为AI生成。AI assistance: OpenAI Codex. Explanations, rewriting, English translation or layout include AI-generated work; cited and supplied source materials retain their own provenance.

1. 何时可以忽略科氏力？1. When can rotation be neglected?

当ω≫|f|，即周期T远小于当地惯性周期2π/|f|时，单个周期内旋转影响较小。普通秒级风浪通常满足；不能仅由水深判断。Rotation is small over a cycle when ω≫|f|, or T≪2π/|f|. Ordinary wind waves usually satisfy this; depth alone is not the criterion.

2. 哪些波有频散？2. Which waves are dispersive?

频散看相速度是否随波数变化。表面重力波ω²=gK tanh(Kh)，一般频散，浅水极限无频散；旋转浅水惯性重力波ω²=f²+c²K²，一般频散，高频极限近似无频散；经典无背景流罗斯贝波ω=−βk/(k²+l²+Rd⁻²)，一般频散，理想长波极限可近似无频散。K=√(k²+l²)，c为对应模态波速；这些公式属于不同模型。Dispersion means phase speed varies with wavenumber. Surface gravity waves obey ω²=gK tanh(Kh), with a nondispersive shallow limit. Rotating shallow-water inertia–gravity waves obey ω²=f²+c²K² and are generally dispersive. Classical Rossby waves obey ω=−βk/(k²+l²+Rd⁻²), with a nondispersive ideal long-wave limit. K=√(k²+l²); these formulas apply to different models.

3. 赤道波导怎样形成？3. Why is the equator a waveguide?

赤道附近f≈βy，跨赤道变号，旋转背景的空间变化使某些模态局限在赤道附近。主要包括向东的开尔文波、经典相位向西的罗斯贝波、混合罗斯贝—重力波（Yanai波），以及向东或向西的惯性重力波分支。Near the equator f≈βy changes sign, trapping certain modes near the equator. Modes include eastward Kelvin waves, westward-phase Rossby waves, mixed Rossby–gravity (Yanai) waves, and eastward and westward inertia–gravity branches.

4. 陆架长波有哪些？4. What are shelf and coastal long waves?

常讨论沿岸开尔文波、地形罗斯贝／大陆架波，以及分层沿岸俘获波。它们分别或共同受海岸、地形、层结和旋转约束。理想常规地形与无背景流下，低频俘获波通常沿浅水在右（北半球）、左（南半球）的方向传播；不同模态的频散与能量方向需具体判断。Common types are coastal Kelvin waves, topographic Rossby or shelf waves, and stratified coastal-trapped waves. Coastlines, topography, stratification and rotation constrain them. Under standard ideal conditions, shallow water is typically on the right in the Northern Hemisphere and left in the Southern; modal dispersion and energy propagation need separate analysis.

5. 海湾静振与重力波有何异同？5. How does a seiche relate to gravity waves?

表面静振通常就是受边界约束的重力驻波：有较固定的波节和波腹，而行进波的波峰前进。理想均匀深度水盆的基频周期：两端封闭T₁≈2L/√(gh)；一端封闭、一端理想开口T₁≈4L/√(gh)。实际几何与开口会改变周期。A surface seiche is usually a bounded standing gravity wave, with fixed nodes and antinodes. For ideal uniform-depth basins, T₁≈2L/√(gh) for two closed ends and T₁≈4L/√(gh) for one closed and one ideal open end. Real geometry changes the periods.

6. 内波发生的基本条件？6. What allows internal waves?

需要稳定密度层结提供浮力恢复作用，并有扰动激发。Boussinesq近似下取z向上，N²=−(g/ρ₀)dρ̄/dz>0；真实海水需正确处理压缩性。局地稳定分层旋转流体中的自由内惯性重力波通常满足|f|<ω<N。Stable stratification provides buoyancy restoring forces and disturbances excite waves. With z upward in the Boussinesq approximation, N²=−(g/ρ₀)dρ̄/dz>0; seawater compressibility requires care. Freely propagating internal inertia–gravity waves typically satisfy |f|<ω<N.

7. 海啸如何产生，跨洋传播受旋转影响吗？7. How are tsunamis generated, and does rotation matter?

海底升降、滑坡或火山等造成快速、大范围水体位移，重力使扰动传播。长波海啸常满足C≈√(gh)。许多成分ω≫|f|，旋转对单周期影响较弱，但跨洋精确计算仍可需要保留科氏项；应结合周期、纬度、传播时间和精度判断，不能仅凭距离下结论。Rapid large-scale water displacement from seabed motion, landslides or volcanic activity generates gravity waves. Long tsunamis often have C≈√(gh). Many components have ω≫|f|, yet accurate transoceanic calculations may retain Coriolis terms. Importance depends on period, latitude, travel time and required accuracy.